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1
Possible indirect evidence for axion-like particles from far away AGN
Alessandro De AngelisINFN INAF and Udine University
bull Photon propagationbull Observation of distant AGNbull Axion-Like Particles amp the DaRMa
scenariobull Conclusions
The work on axions has been done in collaboration with M Roncadelli O Mansutti and M Persic
2
Intergalactic absorption of VHE photons
Cross section maximized for infraredoptical photons
(Extragalactic Background Light)
(Heitler 1960)
3
What is the attenuation
bull
bull = cos
bull n (z) is the spectral
energy density of background
photons lt=EBL
)(emobs )()( zEeEzE
MAGIC Science 2008
4
(An approximation)
bull Neglecting evolutionary effects for simplicity
1
Coppi amp Aharonian ApJ 1997
)(emobs )()(
1
)()(
E
D
eEDE
E
DDE
5
Consequencesbull Since becomes lt RHubble for E gt 100 GeV
ndash The observed flux should be exponentially suppressed at large distances so that very far-away sources should become invisible as energy increases
ndash The observed flux should be exponentially suppressed at VHE so that the SED should be steeper than the emitted one
6
The VHE Universe far awayhellip
35 SourceshellipPKS 0447-439 z=020 HESS 20091ES 1011+496 z=021 MAGIC 20071ES 0414+009 z=029 HESS amp Fermi 2009S5 0716+71 z=031plusmn008 MAGIC 20091ES 0502+675 z=034 VERITAS 20093C 66A z=044 VERITAS 2009 3C 279 z=054 MAGIC 2008
7
The distant quasar 3C 279
bull Flat spectrum radio quasar at z=054bull Very bright and strongly variable
ndash Brightest EGRET AGNndash Gamma-ray flares in 1991 and 1996 Fast time variation (~ 6hr in 1996 flare)
bull MAGIC observationsndash 10 h between Jan-April 2006
ndash clear detection on 23rd Feb at 62σ
First FSRQ in TeV -rays
Major jump in redshift
8
The distant quasar 3C 279 is back
bull New observations after optical outburst in Jan 2007
New flare detected
Most distant object ever detected at VHE - two flares (Feb 2006 and Jan 2007)
Emission harder than expected -gt constrains the EBL universe more transparent to -rays than expected
9
Implications on Extragalactic Background Light
e-e+
EBL
VHE
blazarIACT
10
bull At ~05 TeV flux attenuated by 2 orders of magnitudebull The measurement of spectral features permits to constrain EBL models
ndash Power law Γ = 41 plusmn 07 measured up to 05 TeV Spectrum sensitive to 02 to 2 μm
ndash Assume minimum reasonable index Γem = 15
bull Upper limit close to lower limit from galaxy countbull Explanations go
ndash from standard ones
bull very hard emission mechanisms with intrinsic slope lt 15 (Stecker 2008)
bull Very low EBL
ndash to possible evidence for new physics
bull Oscillation to a particle traveling unimpeded
rarr X rarr
Could it be seen
11
Oscillation to an Axion-Like Particle
ndash Oscillation during the propagation DA Roncadelli amp Mansutti [DARMa] PLB2008 PRD2008
ndash Conversion at the emitter (Hooper et al PRD2008)
ndash Mixed mechanisms (Sanchez-Condersquo et al PRD 2009)
ndash hellip
BEaM
Ptrans
1
12
Phenomenology of the oscillations
bull Photon-ALP oscillations are similar to neutrino oscillations but external B is needed
bull Bounds on the parameters M and m ndash CAST amp astrophysical arguments
M gt 114 1010 GeV for m lt 002 eV
ndash Energetics of SN 1987a
M gt 1011 GeV for m lt 10-10 GeV model dependent
13
(DA FARE) Which EBL First analysis of 3C279 EBL model by Kneiske et al 2004
To be updated including Franceschini et al 2008
14
DARMa Intergalactic magnetic fields
Their morphology is poorly known It is supposed that they have a domain-like structure with
bull strength ~ 05 nG bull coherence length ~ 10 Mpc bull random orientation in each domain
NB - Picture consistent with first AUGER data
strength 03 ndash 09 nG for coherence length 1 ndash 10 Mpc
(DA Persic amp Roncadelli MPLA 2008)
15
Hooper amp Serpico (DA FARE)
16
Sanchez-Condersquo et al (DA FARE)
17
Experimental input from more sources at high z MAGIC S5 0716+714
bull After trigger MAGIC observed 26h April 28 Swift reports flux about 50 larger
than that observed in 2007
Apr 29 ATel 1500 MAGIC reports 68 discovery Apr 23-25 F(gt400 GeV) asymp25 Crab
bull 3rd low-peaked VHE blazar after BL Lac amp W comae
bull Host galaxy detected Z=031+-008 =gt 3rd farthest VHE emitter for which the spectral index has been measured
S5 0716+714Trigger in April
2008
Clear signal 68σNew
discoveryarXiv09072386
18
Deformation of the SED
PKS 0447-439 z=020 HESS 20091ES 1011+496 z=021 MAGIC 20071ES 0414+009 z=029 HESS amp Fermi 2009S5 0716+71 z=031plusmn008 MAGIC 20091ES 0502+675 z=034 VERITAS 20093C 66A z=044 VERITAS 2009 3C 279 z=054 MAGIC 2008
hellipand more new sources are coming into the game (VERITAS HESS MAGIC)
19
Other possible explanationsrelated to new physics
bull Kifune 2001 Violation of the Lorentz invariance
bull We should keep in mind thatndash Extraordinary claims require extraordinary evidence
bull New Scientist SciAm blognews hellip and then
ndash Claims must be followed upbull What else do we expect
bull Fundamental implications of unexpected findings
bull Are we seeing a part of the same big picture
2
222 1 ss E
EO
E
EEpc
20
Conclusions
bull The existence of a very light ALP predicted by many extensions of the SM naturally explains the observed transparency of the VHE gamma-ray sky
bull As a bonus it explains why only the most distant AGN seem to demand an unconventional emission spectrum
bull The DaRMa prediction in particular concerns the spectral change of observed AGN flux at VHE and becomes observable if the TeV band is carefully probed
bull It can be tested with IACTs with Fermi and with EAS
21
rdquoA textbook example of the merging of
particle physics and astronomy into the
modern field of astroparticle
physicsrdquo
22
BACKUP
23
PROPAGATION OVER ONE DOMAIN
We work in the short-wavelength approximation so
the beam with energy E is formally a 3-level non
relativistic quantum system described by the wave
equation
with
24
and mixing matrix
which in the presence of absorption becomes
with
25
Hence the conversion probability reads
in terms of the propagation matrix We find
that a nonvanishing conversion probability over the
WHOLE range requires
with
26
In the present situation we have
and so the mixing matrix reduces to
Following Csaki et al ICAP 05 (2003) 005 we
get the explicit form of the propagation matrix
27
PROPAGATION OVER MANY DOMAINS
When all domains are considered at once one has to
allow for the randomness of the direction of B in the
n-th domain Let be the direction of B in the n-th
domain with respect to a FIXED fiducial direction for
all domains and denote by the evolution
matrix in the n-th domain
Then the overall beam propagation is described by
28
We evaluate by numerically
computing and iterating the result
times by randomly choosing each time
We repeat this procedure 5000 times and next
average all these realizations of the propagation
process over all random angles So the PHYSICAL
propagation matrix of the beam is
29
Assuming that the initial state of the beam is
unpolarized and fully made of photons the initial
beam state is
So we finally get
30
Ideal case z = 1 ndash EBL of Franceschini et al
2
Intergalactic absorption of VHE photons
Cross section maximized for infraredoptical photons
(Extragalactic Background Light)
(Heitler 1960)
3
What is the attenuation
bull
bull = cos
bull n (z) is the spectral
energy density of background
photons lt=EBL
)(emobs )()( zEeEzE
MAGIC Science 2008
4
(An approximation)
bull Neglecting evolutionary effects for simplicity
1
Coppi amp Aharonian ApJ 1997
)(emobs )()(
1
)()(
E
D
eEDE
E
DDE
5
Consequencesbull Since becomes lt RHubble for E gt 100 GeV
ndash The observed flux should be exponentially suppressed at large distances so that very far-away sources should become invisible as energy increases
ndash The observed flux should be exponentially suppressed at VHE so that the SED should be steeper than the emitted one
6
The VHE Universe far awayhellip
35 SourceshellipPKS 0447-439 z=020 HESS 20091ES 1011+496 z=021 MAGIC 20071ES 0414+009 z=029 HESS amp Fermi 2009S5 0716+71 z=031plusmn008 MAGIC 20091ES 0502+675 z=034 VERITAS 20093C 66A z=044 VERITAS 2009 3C 279 z=054 MAGIC 2008
7
The distant quasar 3C 279
bull Flat spectrum radio quasar at z=054bull Very bright and strongly variable
ndash Brightest EGRET AGNndash Gamma-ray flares in 1991 and 1996 Fast time variation (~ 6hr in 1996 flare)
bull MAGIC observationsndash 10 h between Jan-April 2006
ndash clear detection on 23rd Feb at 62σ
First FSRQ in TeV -rays
Major jump in redshift
8
The distant quasar 3C 279 is back
bull New observations after optical outburst in Jan 2007
New flare detected
Most distant object ever detected at VHE - two flares (Feb 2006 and Jan 2007)
Emission harder than expected -gt constrains the EBL universe more transparent to -rays than expected
9
Implications on Extragalactic Background Light
e-e+
EBL
VHE
blazarIACT
10
bull At ~05 TeV flux attenuated by 2 orders of magnitudebull The measurement of spectral features permits to constrain EBL models
ndash Power law Γ = 41 plusmn 07 measured up to 05 TeV Spectrum sensitive to 02 to 2 μm
ndash Assume minimum reasonable index Γem = 15
bull Upper limit close to lower limit from galaxy countbull Explanations go
ndash from standard ones
bull very hard emission mechanisms with intrinsic slope lt 15 (Stecker 2008)
bull Very low EBL
ndash to possible evidence for new physics
bull Oscillation to a particle traveling unimpeded
rarr X rarr
Could it be seen
11
Oscillation to an Axion-Like Particle
ndash Oscillation during the propagation DA Roncadelli amp Mansutti [DARMa] PLB2008 PRD2008
ndash Conversion at the emitter (Hooper et al PRD2008)
ndash Mixed mechanisms (Sanchez-Condersquo et al PRD 2009)
ndash hellip
BEaM
Ptrans
1
12
Phenomenology of the oscillations
bull Photon-ALP oscillations are similar to neutrino oscillations but external B is needed
bull Bounds on the parameters M and m ndash CAST amp astrophysical arguments
M gt 114 1010 GeV for m lt 002 eV
ndash Energetics of SN 1987a
M gt 1011 GeV for m lt 10-10 GeV model dependent
13
(DA FARE) Which EBL First analysis of 3C279 EBL model by Kneiske et al 2004
To be updated including Franceschini et al 2008
14
DARMa Intergalactic magnetic fields
Their morphology is poorly known It is supposed that they have a domain-like structure with
bull strength ~ 05 nG bull coherence length ~ 10 Mpc bull random orientation in each domain
NB - Picture consistent with first AUGER data
strength 03 ndash 09 nG for coherence length 1 ndash 10 Mpc
(DA Persic amp Roncadelli MPLA 2008)
15
Hooper amp Serpico (DA FARE)
16
Sanchez-Condersquo et al (DA FARE)
17
Experimental input from more sources at high z MAGIC S5 0716+714
bull After trigger MAGIC observed 26h April 28 Swift reports flux about 50 larger
than that observed in 2007
Apr 29 ATel 1500 MAGIC reports 68 discovery Apr 23-25 F(gt400 GeV) asymp25 Crab
bull 3rd low-peaked VHE blazar after BL Lac amp W comae
bull Host galaxy detected Z=031+-008 =gt 3rd farthest VHE emitter for which the spectral index has been measured
S5 0716+714Trigger in April
2008
Clear signal 68σNew
discoveryarXiv09072386
18
Deformation of the SED
PKS 0447-439 z=020 HESS 20091ES 1011+496 z=021 MAGIC 20071ES 0414+009 z=029 HESS amp Fermi 2009S5 0716+71 z=031plusmn008 MAGIC 20091ES 0502+675 z=034 VERITAS 20093C 66A z=044 VERITAS 2009 3C 279 z=054 MAGIC 2008
hellipand more new sources are coming into the game (VERITAS HESS MAGIC)
19
Other possible explanationsrelated to new physics
bull Kifune 2001 Violation of the Lorentz invariance
bull We should keep in mind thatndash Extraordinary claims require extraordinary evidence
bull New Scientist SciAm blognews hellip and then
ndash Claims must be followed upbull What else do we expect
bull Fundamental implications of unexpected findings
bull Are we seeing a part of the same big picture
2
222 1 ss E
EO
E
EEpc
20
Conclusions
bull The existence of a very light ALP predicted by many extensions of the SM naturally explains the observed transparency of the VHE gamma-ray sky
bull As a bonus it explains why only the most distant AGN seem to demand an unconventional emission spectrum
bull The DaRMa prediction in particular concerns the spectral change of observed AGN flux at VHE and becomes observable if the TeV band is carefully probed
bull It can be tested with IACTs with Fermi and with EAS
21
rdquoA textbook example of the merging of
particle physics and astronomy into the
modern field of astroparticle
physicsrdquo
22
BACKUP
23
PROPAGATION OVER ONE DOMAIN
We work in the short-wavelength approximation so
the beam with energy E is formally a 3-level non
relativistic quantum system described by the wave
equation
with
24
and mixing matrix
which in the presence of absorption becomes
with
25
Hence the conversion probability reads
in terms of the propagation matrix We find
that a nonvanishing conversion probability over the
WHOLE range requires
with
26
In the present situation we have
and so the mixing matrix reduces to
Following Csaki et al ICAP 05 (2003) 005 we
get the explicit form of the propagation matrix
27
PROPAGATION OVER MANY DOMAINS
When all domains are considered at once one has to
allow for the randomness of the direction of B in the
n-th domain Let be the direction of B in the n-th
domain with respect to a FIXED fiducial direction for
all domains and denote by the evolution
matrix in the n-th domain
Then the overall beam propagation is described by
28
We evaluate by numerically
computing and iterating the result
times by randomly choosing each time
We repeat this procedure 5000 times and next
average all these realizations of the propagation
process over all random angles So the PHYSICAL
propagation matrix of the beam is
29
Assuming that the initial state of the beam is
unpolarized and fully made of photons the initial
beam state is
So we finally get
30
Ideal case z = 1 ndash EBL of Franceschini et al
3
What is the attenuation
bull
bull = cos
bull n (z) is the spectral
energy density of background
photons lt=EBL
)(emobs )()( zEeEzE
MAGIC Science 2008
4
(An approximation)
bull Neglecting evolutionary effects for simplicity
1
Coppi amp Aharonian ApJ 1997
)(emobs )()(
1
)()(
E
D
eEDE
E
DDE
5
Consequencesbull Since becomes lt RHubble for E gt 100 GeV
ndash The observed flux should be exponentially suppressed at large distances so that very far-away sources should become invisible as energy increases
ndash The observed flux should be exponentially suppressed at VHE so that the SED should be steeper than the emitted one
6
The VHE Universe far awayhellip
35 SourceshellipPKS 0447-439 z=020 HESS 20091ES 1011+496 z=021 MAGIC 20071ES 0414+009 z=029 HESS amp Fermi 2009S5 0716+71 z=031plusmn008 MAGIC 20091ES 0502+675 z=034 VERITAS 20093C 66A z=044 VERITAS 2009 3C 279 z=054 MAGIC 2008
7
The distant quasar 3C 279
bull Flat spectrum radio quasar at z=054bull Very bright and strongly variable
ndash Brightest EGRET AGNndash Gamma-ray flares in 1991 and 1996 Fast time variation (~ 6hr in 1996 flare)
bull MAGIC observationsndash 10 h between Jan-April 2006
ndash clear detection on 23rd Feb at 62σ
First FSRQ in TeV -rays
Major jump in redshift
8
The distant quasar 3C 279 is back
bull New observations after optical outburst in Jan 2007
New flare detected
Most distant object ever detected at VHE - two flares (Feb 2006 and Jan 2007)
Emission harder than expected -gt constrains the EBL universe more transparent to -rays than expected
9
Implications on Extragalactic Background Light
e-e+
EBL
VHE
blazarIACT
10
bull At ~05 TeV flux attenuated by 2 orders of magnitudebull The measurement of spectral features permits to constrain EBL models
ndash Power law Γ = 41 plusmn 07 measured up to 05 TeV Spectrum sensitive to 02 to 2 μm
ndash Assume minimum reasonable index Γem = 15
bull Upper limit close to lower limit from galaxy countbull Explanations go
ndash from standard ones
bull very hard emission mechanisms with intrinsic slope lt 15 (Stecker 2008)
bull Very low EBL
ndash to possible evidence for new physics
bull Oscillation to a particle traveling unimpeded
rarr X rarr
Could it be seen
11
Oscillation to an Axion-Like Particle
ndash Oscillation during the propagation DA Roncadelli amp Mansutti [DARMa] PLB2008 PRD2008
ndash Conversion at the emitter (Hooper et al PRD2008)
ndash Mixed mechanisms (Sanchez-Condersquo et al PRD 2009)
ndash hellip
BEaM
Ptrans
1
12
Phenomenology of the oscillations
bull Photon-ALP oscillations are similar to neutrino oscillations but external B is needed
bull Bounds on the parameters M and m ndash CAST amp astrophysical arguments
M gt 114 1010 GeV for m lt 002 eV
ndash Energetics of SN 1987a
M gt 1011 GeV for m lt 10-10 GeV model dependent
13
(DA FARE) Which EBL First analysis of 3C279 EBL model by Kneiske et al 2004
To be updated including Franceschini et al 2008
14
DARMa Intergalactic magnetic fields
Their morphology is poorly known It is supposed that they have a domain-like structure with
bull strength ~ 05 nG bull coherence length ~ 10 Mpc bull random orientation in each domain
NB - Picture consistent with first AUGER data
strength 03 ndash 09 nG for coherence length 1 ndash 10 Mpc
(DA Persic amp Roncadelli MPLA 2008)
15
Hooper amp Serpico (DA FARE)
16
Sanchez-Condersquo et al (DA FARE)
17
Experimental input from more sources at high z MAGIC S5 0716+714
bull After trigger MAGIC observed 26h April 28 Swift reports flux about 50 larger
than that observed in 2007
Apr 29 ATel 1500 MAGIC reports 68 discovery Apr 23-25 F(gt400 GeV) asymp25 Crab
bull 3rd low-peaked VHE blazar after BL Lac amp W comae
bull Host galaxy detected Z=031+-008 =gt 3rd farthest VHE emitter for which the spectral index has been measured
S5 0716+714Trigger in April
2008
Clear signal 68σNew
discoveryarXiv09072386
18
Deformation of the SED
PKS 0447-439 z=020 HESS 20091ES 1011+496 z=021 MAGIC 20071ES 0414+009 z=029 HESS amp Fermi 2009S5 0716+71 z=031plusmn008 MAGIC 20091ES 0502+675 z=034 VERITAS 20093C 66A z=044 VERITAS 2009 3C 279 z=054 MAGIC 2008
hellipand more new sources are coming into the game (VERITAS HESS MAGIC)
19
Other possible explanationsrelated to new physics
bull Kifune 2001 Violation of the Lorentz invariance
bull We should keep in mind thatndash Extraordinary claims require extraordinary evidence
bull New Scientist SciAm blognews hellip and then
ndash Claims must be followed upbull What else do we expect
bull Fundamental implications of unexpected findings
bull Are we seeing a part of the same big picture
2
222 1 ss E
EO
E
EEpc
20
Conclusions
bull The existence of a very light ALP predicted by many extensions of the SM naturally explains the observed transparency of the VHE gamma-ray sky
bull As a bonus it explains why only the most distant AGN seem to demand an unconventional emission spectrum
bull The DaRMa prediction in particular concerns the spectral change of observed AGN flux at VHE and becomes observable if the TeV band is carefully probed
bull It can be tested with IACTs with Fermi and with EAS
21
rdquoA textbook example of the merging of
particle physics and astronomy into the
modern field of astroparticle
physicsrdquo
22
BACKUP
23
PROPAGATION OVER ONE DOMAIN
We work in the short-wavelength approximation so
the beam with energy E is formally a 3-level non
relativistic quantum system described by the wave
equation
with
24
and mixing matrix
which in the presence of absorption becomes
with
25
Hence the conversion probability reads
in terms of the propagation matrix We find
that a nonvanishing conversion probability over the
WHOLE range requires
with
26
In the present situation we have
and so the mixing matrix reduces to
Following Csaki et al ICAP 05 (2003) 005 we
get the explicit form of the propagation matrix
27
PROPAGATION OVER MANY DOMAINS
When all domains are considered at once one has to
allow for the randomness of the direction of B in the
n-th domain Let be the direction of B in the n-th
domain with respect to a FIXED fiducial direction for
all domains and denote by the evolution
matrix in the n-th domain
Then the overall beam propagation is described by
28
We evaluate by numerically
computing and iterating the result
times by randomly choosing each time
We repeat this procedure 5000 times and next
average all these realizations of the propagation
process over all random angles So the PHYSICAL
propagation matrix of the beam is
29
Assuming that the initial state of the beam is
unpolarized and fully made of photons the initial
beam state is
So we finally get
30
Ideal case z = 1 ndash EBL of Franceschini et al
4
(An approximation)
bull Neglecting evolutionary effects for simplicity
1
Coppi amp Aharonian ApJ 1997
)(emobs )()(
1
)()(
E
D
eEDE
E
DDE
5
Consequencesbull Since becomes lt RHubble for E gt 100 GeV
ndash The observed flux should be exponentially suppressed at large distances so that very far-away sources should become invisible as energy increases
ndash The observed flux should be exponentially suppressed at VHE so that the SED should be steeper than the emitted one
6
The VHE Universe far awayhellip
35 SourceshellipPKS 0447-439 z=020 HESS 20091ES 1011+496 z=021 MAGIC 20071ES 0414+009 z=029 HESS amp Fermi 2009S5 0716+71 z=031plusmn008 MAGIC 20091ES 0502+675 z=034 VERITAS 20093C 66A z=044 VERITAS 2009 3C 279 z=054 MAGIC 2008
7
The distant quasar 3C 279
bull Flat spectrum radio quasar at z=054bull Very bright and strongly variable
ndash Brightest EGRET AGNndash Gamma-ray flares in 1991 and 1996 Fast time variation (~ 6hr in 1996 flare)
bull MAGIC observationsndash 10 h between Jan-April 2006
ndash clear detection on 23rd Feb at 62σ
First FSRQ in TeV -rays
Major jump in redshift
8
The distant quasar 3C 279 is back
bull New observations after optical outburst in Jan 2007
New flare detected
Most distant object ever detected at VHE - two flares (Feb 2006 and Jan 2007)
Emission harder than expected -gt constrains the EBL universe more transparent to -rays than expected
9
Implications on Extragalactic Background Light
e-e+
EBL
VHE
blazarIACT
10
bull At ~05 TeV flux attenuated by 2 orders of magnitudebull The measurement of spectral features permits to constrain EBL models
ndash Power law Γ = 41 plusmn 07 measured up to 05 TeV Spectrum sensitive to 02 to 2 μm
ndash Assume minimum reasonable index Γem = 15
bull Upper limit close to lower limit from galaxy countbull Explanations go
ndash from standard ones
bull very hard emission mechanisms with intrinsic slope lt 15 (Stecker 2008)
bull Very low EBL
ndash to possible evidence for new physics
bull Oscillation to a particle traveling unimpeded
rarr X rarr
Could it be seen
11
Oscillation to an Axion-Like Particle
ndash Oscillation during the propagation DA Roncadelli amp Mansutti [DARMa] PLB2008 PRD2008
ndash Conversion at the emitter (Hooper et al PRD2008)
ndash Mixed mechanisms (Sanchez-Condersquo et al PRD 2009)
ndash hellip
BEaM
Ptrans
1
12
Phenomenology of the oscillations
bull Photon-ALP oscillations are similar to neutrino oscillations but external B is needed
bull Bounds on the parameters M and m ndash CAST amp astrophysical arguments
M gt 114 1010 GeV for m lt 002 eV
ndash Energetics of SN 1987a
M gt 1011 GeV for m lt 10-10 GeV model dependent
13
(DA FARE) Which EBL First analysis of 3C279 EBL model by Kneiske et al 2004
To be updated including Franceschini et al 2008
14
DARMa Intergalactic magnetic fields
Their morphology is poorly known It is supposed that they have a domain-like structure with
bull strength ~ 05 nG bull coherence length ~ 10 Mpc bull random orientation in each domain
NB - Picture consistent with first AUGER data
strength 03 ndash 09 nG for coherence length 1 ndash 10 Mpc
(DA Persic amp Roncadelli MPLA 2008)
15
Hooper amp Serpico (DA FARE)
16
Sanchez-Condersquo et al (DA FARE)
17
Experimental input from more sources at high z MAGIC S5 0716+714
bull After trigger MAGIC observed 26h April 28 Swift reports flux about 50 larger
than that observed in 2007
Apr 29 ATel 1500 MAGIC reports 68 discovery Apr 23-25 F(gt400 GeV) asymp25 Crab
bull 3rd low-peaked VHE blazar after BL Lac amp W comae
bull Host galaxy detected Z=031+-008 =gt 3rd farthest VHE emitter for which the spectral index has been measured
S5 0716+714Trigger in April
2008
Clear signal 68σNew
discoveryarXiv09072386
18
Deformation of the SED
PKS 0447-439 z=020 HESS 20091ES 1011+496 z=021 MAGIC 20071ES 0414+009 z=029 HESS amp Fermi 2009S5 0716+71 z=031plusmn008 MAGIC 20091ES 0502+675 z=034 VERITAS 20093C 66A z=044 VERITAS 2009 3C 279 z=054 MAGIC 2008
hellipand more new sources are coming into the game (VERITAS HESS MAGIC)
19
Other possible explanationsrelated to new physics
bull Kifune 2001 Violation of the Lorentz invariance
bull We should keep in mind thatndash Extraordinary claims require extraordinary evidence
bull New Scientist SciAm blognews hellip and then
ndash Claims must be followed upbull What else do we expect
bull Fundamental implications of unexpected findings
bull Are we seeing a part of the same big picture
2
222 1 ss E
EO
E
EEpc
20
Conclusions
bull The existence of a very light ALP predicted by many extensions of the SM naturally explains the observed transparency of the VHE gamma-ray sky
bull As a bonus it explains why only the most distant AGN seem to demand an unconventional emission spectrum
bull The DaRMa prediction in particular concerns the spectral change of observed AGN flux at VHE and becomes observable if the TeV band is carefully probed
bull It can be tested with IACTs with Fermi and with EAS
21
rdquoA textbook example of the merging of
particle physics and astronomy into the
modern field of astroparticle
physicsrdquo
22
BACKUP
23
PROPAGATION OVER ONE DOMAIN
We work in the short-wavelength approximation so
the beam with energy E is formally a 3-level non
relativistic quantum system described by the wave
equation
with
24
and mixing matrix
which in the presence of absorption becomes
with
25
Hence the conversion probability reads
in terms of the propagation matrix We find
that a nonvanishing conversion probability over the
WHOLE range requires
with
26
In the present situation we have
and so the mixing matrix reduces to
Following Csaki et al ICAP 05 (2003) 005 we
get the explicit form of the propagation matrix
27
PROPAGATION OVER MANY DOMAINS
When all domains are considered at once one has to
allow for the randomness of the direction of B in the
n-th domain Let be the direction of B in the n-th
domain with respect to a FIXED fiducial direction for
all domains and denote by the evolution
matrix in the n-th domain
Then the overall beam propagation is described by
28
We evaluate by numerically
computing and iterating the result
times by randomly choosing each time
We repeat this procedure 5000 times and next
average all these realizations of the propagation
process over all random angles So the PHYSICAL
propagation matrix of the beam is
29
Assuming that the initial state of the beam is
unpolarized and fully made of photons the initial
beam state is
So we finally get
30
Ideal case z = 1 ndash EBL of Franceschini et al
5
Consequencesbull Since becomes lt RHubble for E gt 100 GeV
ndash The observed flux should be exponentially suppressed at large distances so that very far-away sources should become invisible as energy increases
ndash The observed flux should be exponentially suppressed at VHE so that the SED should be steeper than the emitted one
6
The VHE Universe far awayhellip
35 SourceshellipPKS 0447-439 z=020 HESS 20091ES 1011+496 z=021 MAGIC 20071ES 0414+009 z=029 HESS amp Fermi 2009S5 0716+71 z=031plusmn008 MAGIC 20091ES 0502+675 z=034 VERITAS 20093C 66A z=044 VERITAS 2009 3C 279 z=054 MAGIC 2008
7
The distant quasar 3C 279
bull Flat spectrum radio quasar at z=054bull Very bright and strongly variable
ndash Brightest EGRET AGNndash Gamma-ray flares in 1991 and 1996 Fast time variation (~ 6hr in 1996 flare)
bull MAGIC observationsndash 10 h between Jan-April 2006
ndash clear detection on 23rd Feb at 62σ
First FSRQ in TeV -rays
Major jump in redshift
8
The distant quasar 3C 279 is back
bull New observations after optical outburst in Jan 2007
New flare detected
Most distant object ever detected at VHE - two flares (Feb 2006 and Jan 2007)
Emission harder than expected -gt constrains the EBL universe more transparent to -rays than expected
9
Implications on Extragalactic Background Light
e-e+
EBL
VHE
blazarIACT
10
bull At ~05 TeV flux attenuated by 2 orders of magnitudebull The measurement of spectral features permits to constrain EBL models
ndash Power law Γ = 41 plusmn 07 measured up to 05 TeV Spectrum sensitive to 02 to 2 μm
ndash Assume minimum reasonable index Γem = 15
bull Upper limit close to lower limit from galaxy countbull Explanations go
ndash from standard ones
bull very hard emission mechanisms with intrinsic slope lt 15 (Stecker 2008)
bull Very low EBL
ndash to possible evidence for new physics
bull Oscillation to a particle traveling unimpeded
rarr X rarr
Could it be seen
11
Oscillation to an Axion-Like Particle
ndash Oscillation during the propagation DA Roncadelli amp Mansutti [DARMa] PLB2008 PRD2008
ndash Conversion at the emitter (Hooper et al PRD2008)
ndash Mixed mechanisms (Sanchez-Condersquo et al PRD 2009)
ndash hellip
BEaM
Ptrans
1
12
Phenomenology of the oscillations
bull Photon-ALP oscillations are similar to neutrino oscillations but external B is needed
bull Bounds on the parameters M and m ndash CAST amp astrophysical arguments
M gt 114 1010 GeV for m lt 002 eV
ndash Energetics of SN 1987a
M gt 1011 GeV for m lt 10-10 GeV model dependent
13
(DA FARE) Which EBL First analysis of 3C279 EBL model by Kneiske et al 2004
To be updated including Franceschini et al 2008
14
DARMa Intergalactic magnetic fields
Their morphology is poorly known It is supposed that they have a domain-like structure with
bull strength ~ 05 nG bull coherence length ~ 10 Mpc bull random orientation in each domain
NB - Picture consistent with first AUGER data
strength 03 ndash 09 nG for coherence length 1 ndash 10 Mpc
(DA Persic amp Roncadelli MPLA 2008)
15
Hooper amp Serpico (DA FARE)
16
Sanchez-Condersquo et al (DA FARE)
17
Experimental input from more sources at high z MAGIC S5 0716+714
bull After trigger MAGIC observed 26h April 28 Swift reports flux about 50 larger
than that observed in 2007
Apr 29 ATel 1500 MAGIC reports 68 discovery Apr 23-25 F(gt400 GeV) asymp25 Crab
bull 3rd low-peaked VHE blazar after BL Lac amp W comae
bull Host galaxy detected Z=031+-008 =gt 3rd farthest VHE emitter for which the spectral index has been measured
S5 0716+714Trigger in April
2008
Clear signal 68σNew
discoveryarXiv09072386
18
Deformation of the SED
PKS 0447-439 z=020 HESS 20091ES 1011+496 z=021 MAGIC 20071ES 0414+009 z=029 HESS amp Fermi 2009S5 0716+71 z=031plusmn008 MAGIC 20091ES 0502+675 z=034 VERITAS 20093C 66A z=044 VERITAS 2009 3C 279 z=054 MAGIC 2008
hellipand more new sources are coming into the game (VERITAS HESS MAGIC)
19
Other possible explanationsrelated to new physics
bull Kifune 2001 Violation of the Lorentz invariance
bull We should keep in mind thatndash Extraordinary claims require extraordinary evidence
bull New Scientist SciAm blognews hellip and then
ndash Claims must be followed upbull What else do we expect
bull Fundamental implications of unexpected findings
bull Are we seeing a part of the same big picture
2
222 1 ss E
EO
E
EEpc
20
Conclusions
bull The existence of a very light ALP predicted by many extensions of the SM naturally explains the observed transparency of the VHE gamma-ray sky
bull As a bonus it explains why only the most distant AGN seem to demand an unconventional emission spectrum
bull The DaRMa prediction in particular concerns the spectral change of observed AGN flux at VHE and becomes observable if the TeV band is carefully probed
bull It can be tested with IACTs with Fermi and with EAS
21
rdquoA textbook example of the merging of
particle physics and astronomy into the
modern field of astroparticle
physicsrdquo
22
BACKUP
23
PROPAGATION OVER ONE DOMAIN
We work in the short-wavelength approximation so
the beam with energy E is formally a 3-level non
relativistic quantum system described by the wave
equation
with
24
and mixing matrix
which in the presence of absorption becomes
with
25
Hence the conversion probability reads
in terms of the propagation matrix We find
that a nonvanishing conversion probability over the
WHOLE range requires
with
26
In the present situation we have
and so the mixing matrix reduces to
Following Csaki et al ICAP 05 (2003) 005 we
get the explicit form of the propagation matrix
27
PROPAGATION OVER MANY DOMAINS
When all domains are considered at once one has to
allow for the randomness of the direction of B in the
n-th domain Let be the direction of B in the n-th
domain with respect to a FIXED fiducial direction for
all domains and denote by the evolution
matrix in the n-th domain
Then the overall beam propagation is described by
28
We evaluate by numerically
computing and iterating the result
times by randomly choosing each time
We repeat this procedure 5000 times and next
average all these realizations of the propagation
process over all random angles So the PHYSICAL
propagation matrix of the beam is
29
Assuming that the initial state of the beam is
unpolarized and fully made of photons the initial
beam state is
So we finally get
30
Ideal case z = 1 ndash EBL of Franceschini et al
6
The VHE Universe far awayhellip
35 SourceshellipPKS 0447-439 z=020 HESS 20091ES 1011+496 z=021 MAGIC 20071ES 0414+009 z=029 HESS amp Fermi 2009S5 0716+71 z=031plusmn008 MAGIC 20091ES 0502+675 z=034 VERITAS 20093C 66A z=044 VERITAS 2009 3C 279 z=054 MAGIC 2008
7
The distant quasar 3C 279
bull Flat spectrum radio quasar at z=054bull Very bright and strongly variable
ndash Brightest EGRET AGNndash Gamma-ray flares in 1991 and 1996 Fast time variation (~ 6hr in 1996 flare)
bull MAGIC observationsndash 10 h between Jan-April 2006
ndash clear detection on 23rd Feb at 62σ
First FSRQ in TeV -rays
Major jump in redshift
8
The distant quasar 3C 279 is back
bull New observations after optical outburst in Jan 2007
New flare detected
Most distant object ever detected at VHE - two flares (Feb 2006 and Jan 2007)
Emission harder than expected -gt constrains the EBL universe more transparent to -rays than expected
9
Implications on Extragalactic Background Light
e-e+
EBL
VHE
blazarIACT
10
bull At ~05 TeV flux attenuated by 2 orders of magnitudebull The measurement of spectral features permits to constrain EBL models
ndash Power law Γ = 41 plusmn 07 measured up to 05 TeV Spectrum sensitive to 02 to 2 μm
ndash Assume minimum reasonable index Γem = 15
bull Upper limit close to lower limit from galaxy countbull Explanations go
ndash from standard ones
bull very hard emission mechanisms with intrinsic slope lt 15 (Stecker 2008)
bull Very low EBL
ndash to possible evidence for new physics
bull Oscillation to a particle traveling unimpeded
rarr X rarr
Could it be seen
11
Oscillation to an Axion-Like Particle
ndash Oscillation during the propagation DA Roncadelli amp Mansutti [DARMa] PLB2008 PRD2008
ndash Conversion at the emitter (Hooper et al PRD2008)
ndash Mixed mechanisms (Sanchez-Condersquo et al PRD 2009)
ndash hellip
BEaM
Ptrans
1
12
Phenomenology of the oscillations
bull Photon-ALP oscillations are similar to neutrino oscillations but external B is needed
bull Bounds on the parameters M and m ndash CAST amp astrophysical arguments
M gt 114 1010 GeV for m lt 002 eV
ndash Energetics of SN 1987a
M gt 1011 GeV for m lt 10-10 GeV model dependent
13
(DA FARE) Which EBL First analysis of 3C279 EBL model by Kneiske et al 2004
To be updated including Franceschini et al 2008
14
DARMa Intergalactic magnetic fields
Their morphology is poorly known It is supposed that they have a domain-like structure with
bull strength ~ 05 nG bull coherence length ~ 10 Mpc bull random orientation in each domain
NB - Picture consistent with first AUGER data
strength 03 ndash 09 nG for coherence length 1 ndash 10 Mpc
(DA Persic amp Roncadelli MPLA 2008)
15
Hooper amp Serpico (DA FARE)
16
Sanchez-Condersquo et al (DA FARE)
17
Experimental input from more sources at high z MAGIC S5 0716+714
bull After trigger MAGIC observed 26h April 28 Swift reports flux about 50 larger
than that observed in 2007
Apr 29 ATel 1500 MAGIC reports 68 discovery Apr 23-25 F(gt400 GeV) asymp25 Crab
bull 3rd low-peaked VHE blazar after BL Lac amp W comae
bull Host galaxy detected Z=031+-008 =gt 3rd farthest VHE emitter for which the spectral index has been measured
S5 0716+714Trigger in April
2008
Clear signal 68σNew
discoveryarXiv09072386
18
Deformation of the SED
PKS 0447-439 z=020 HESS 20091ES 1011+496 z=021 MAGIC 20071ES 0414+009 z=029 HESS amp Fermi 2009S5 0716+71 z=031plusmn008 MAGIC 20091ES 0502+675 z=034 VERITAS 20093C 66A z=044 VERITAS 2009 3C 279 z=054 MAGIC 2008
hellipand more new sources are coming into the game (VERITAS HESS MAGIC)
19
Other possible explanationsrelated to new physics
bull Kifune 2001 Violation of the Lorentz invariance
bull We should keep in mind thatndash Extraordinary claims require extraordinary evidence
bull New Scientist SciAm blognews hellip and then
ndash Claims must be followed upbull What else do we expect
bull Fundamental implications of unexpected findings
bull Are we seeing a part of the same big picture
2
222 1 ss E
EO
E
EEpc
20
Conclusions
bull The existence of a very light ALP predicted by many extensions of the SM naturally explains the observed transparency of the VHE gamma-ray sky
bull As a bonus it explains why only the most distant AGN seem to demand an unconventional emission spectrum
bull The DaRMa prediction in particular concerns the spectral change of observed AGN flux at VHE and becomes observable if the TeV band is carefully probed
bull It can be tested with IACTs with Fermi and with EAS
21
rdquoA textbook example of the merging of
particle physics and astronomy into the
modern field of astroparticle
physicsrdquo
22
BACKUP
23
PROPAGATION OVER ONE DOMAIN
We work in the short-wavelength approximation so
the beam with energy E is formally a 3-level non
relativistic quantum system described by the wave
equation
with
24
and mixing matrix
which in the presence of absorption becomes
with
25
Hence the conversion probability reads
in terms of the propagation matrix We find
that a nonvanishing conversion probability over the
WHOLE range requires
with
26
In the present situation we have
and so the mixing matrix reduces to
Following Csaki et al ICAP 05 (2003) 005 we
get the explicit form of the propagation matrix
27
PROPAGATION OVER MANY DOMAINS
When all domains are considered at once one has to
allow for the randomness of the direction of B in the
n-th domain Let be the direction of B in the n-th
domain with respect to a FIXED fiducial direction for
all domains and denote by the evolution
matrix in the n-th domain
Then the overall beam propagation is described by
28
We evaluate by numerically
computing and iterating the result
times by randomly choosing each time
We repeat this procedure 5000 times and next
average all these realizations of the propagation
process over all random angles So the PHYSICAL
propagation matrix of the beam is
29
Assuming that the initial state of the beam is
unpolarized and fully made of photons the initial
beam state is
So we finally get
30
Ideal case z = 1 ndash EBL of Franceschini et al
7
The distant quasar 3C 279
bull Flat spectrum radio quasar at z=054bull Very bright and strongly variable
ndash Brightest EGRET AGNndash Gamma-ray flares in 1991 and 1996 Fast time variation (~ 6hr in 1996 flare)
bull MAGIC observationsndash 10 h between Jan-April 2006
ndash clear detection on 23rd Feb at 62σ
First FSRQ in TeV -rays
Major jump in redshift
8
The distant quasar 3C 279 is back
bull New observations after optical outburst in Jan 2007
New flare detected
Most distant object ever detected at VHE - two flares (Feb 2006 and Jan 2007)
Emission harder than expected -gt constrains the EBL universe more transparent to -rays than expected
9
Implications on Extragalactic Background Light
e-e+
EBL
VHE
blazarIACT
10
bull At ~05 TeV flux attenuated by 2 orders of magnitudebull The measurement of spectral features permits to constrain EBL models
ndash Power law Γ = 41 plusmn 07 measured up to 05 TeV Spectrum sensitive to 02 to 2 μm
ndash Assume minimum reasonable index Γem = 15
bull Upper limit close to lower limit from galaxy countbull Explanations go
ndash from standard ones
bull very hard emission mechanisms with intrinsic slope lt 15 (Stecker 2008)
bull Very low EBL
ndash to possible evidence for new physics
bull Oscillation to a particle traveling unimpeded
rarr X rarr
Could it be seen
11
Oscillation to an Axion-Like Particle
ndash Oscillation during the propagation DA Roncadelli amp Mansutti [DARMa] PLB2008 PRD2008
ndash Conversion at the emitter (Hooper et al PRD2008)
ndash Mixed mechanisms (Sanchez-Condersquo et al PRD 2009)
ndash hellip
BEaM
Ptrans
1
12
Phenomenology of the oscillations
bull Photon-ALP oscillations are similar to neutrino oscillations but external B is needed
bull Bounds on the parameters M and m ndash CAST amp astrophysical arguments
M gt 114 1010 GeV for m lt 002 eV
ndash Energetics of SN 1987a
M gt 1011 GeV for m lt 10-10 GeV model dependent
13
(DA FARE) Which EBL First analysis of 3C279 EBL model by Kneiske et al 2004
To be updated including Franceschini et al 2008
14
DARMa Intergalactic magnetic fields
Their morphology is poorly known It is supposed that they have a domain-like structure with
bull strength ~ 05 nG bull coherence length ~ 10 Mpc bull random orientation in each domain
NB - Picture consistent with first AUGER data
strength 03 ndash 09 nG for coherence length 1 ndash 10 Mpc
(DA Persic amp Roncadelli MPLA 2008)
15
Hooper amp Serpico (DA FARE)
16
Sanchez-Condersquo et al (DA FARE)
17
Experimental input from more sources at high z MAGIC S5 0716+714
bull After trigger MAGIC observed 26h April 28 Swift reports flux about 50 larger
than that observed in 2007
Apr 29 ATel 1500 MAGIC reports 68 discovery Apr 23-25 F(gt400 GeV) asymp25 Crab
bull 3rd low-peaked VHE blazar after BL Lac amp W comae
bull Host galaxy detected Z=031+-008 =gt 3rd farthest VHE emitter for which the spectral index has been measured
S5 0716+714Trigger in April
2008
Clear signal 68σNew
discoveryarXiv09072386
18
Deformation of the SED
PKS 0447-439 z=020 HESS 20091ES 1011+496 z=021 MAGIC 20071ES 0414+009 z=029 HESS amp Fermi 2009S5 0716+71 z=031plusmn008 MAGIC 20091ES 0502+675 z=034 VERITAS 20093C 66A z=044 VERITAS 2009 3C 279 z=054 MAGIC 2008
hellipand more new sources are coming into the game (VERITAS HESS MAGIC)
19
Other possible explanationsrelated to new physics
bull Kifune 2001 Violation of the Lorentz invariance
bull We should keep in mind thatndash Extraordinary claims require extraordinary evidence
bull New Scientist SciAm blognews hellip and then
ndash Claims must be followed upbull What else do we expect
bull Fundamental implications of unexpected findings
bull Are we seeing a part of the same big picture
2
222 1 ss E
EO
E
EEpc
20
Conclusions
bull The existence of a very light ALP predicted by many extensions of the SM naturally explains the observed transparency of the VHE gamma-ray sky
bull As a bonus it explains why only the most distant AGN seem to demand an unconventional emission spectrum
bull The DaRMa prediction in particular concerns the spectral change of observed AGN flux at VHE and becomes observable if the TeV band is carefully probed
bull It can be tested with IACTs with Fermi and with EAS
21
rdquoA textbook example of the merging of
particle physics and astronomy into the
modern field of astroparticle
physicsrdquo
22
BACKUP
23
PROPAGATION OVER ONE DOMAIN
We work in the short-wavelength approximation so
the beam with energy E is formally a 3-level non
relativistic quantum system described by the wave
equation
with
24
and mixing matrix
which in the presence of absorption becomes
with
25
Hence the conversion probability reads
in terms of the propagation matrix We find
that a nonvanishing conversion probability over the
WHOLE range requires
with
26
In the present situation we have
and so the mixing matrix reduces to
Following Csaki et al ICAP 05 (2003) 005 we
get the explicit form of the propagation matrix
27
PROPAGATION OVER MANY DOMAINS
When all domains are considered at once one has to
allow for the randomness of the direction of B in the
n-th domain Let be the direction of B in the n-th
domain with respect to a FIXED fiducial direction for
all domains and denote by the evolution
matrix in the n-th domain
Then the overall beam propagation is described by
28
We evaluate by numerically
computing and iterating the result
times by randomly choosing each time
We repeat this procedure 5000 times and next
average all these realizations of the propagation
process over all random angles So the PHYSICAL
propagation matrix of the beam is
29
Assuming that the initial state of the beam is
unpolarized and fully made of photons the initial
beam state is
So we finally get
30
Ideal case z = 1 ndash EBL of Franceschini et al
8
The distant quasar 3C 279 is back
bull New observations after optical outburst in Jan 2007
New flare detected
Most distant object ever detected at VHE - two flares (Feb 2006 and Jan 2007)
Emission harder than expected -gt constrains the EBL universe more transparent to -rays than expected
9
Implications on Extragalactic Background Light
e-e+
EBL
VHE
blazarIACT
10
bull At ~05 TeV flux attenuated by 2 orders of magnitudebull The measurement of spectral features permits to constrain EBL models
ndash Power law Γ = 41 plusmn 07 measured up to 05 TeV Spectrum sensitive to 02 to 2 μm
ndash Assume minimum reasonable index Γem = 15
bull Upper limit close to lower limit from galaxy countbull Explanations go
ndash from standard ones
bull very hard emission mechanisms with intrinsic slope lt 15 (Stecker 2008)
bull Very low EBL
ndash to possible evidence for new physics
bull Oscillation to a particle traveling unimpeded
rarr X rarr
Could it be seen
11
Oscillation to an Axion-Like Particle
ndash Oscillation during the propagation DA Roncadelli amp Mansutti [DARMa] PLB2008 PRD2008
ndash Conversion at the emitter (Hooper et al PRD2008)
ndash Mixed mechanisms (Sanchez-Condersquo et al PRD 2009)
ndash hellip
BEaM
Ptrans
1
12
Phenomenology of the oscillations
bull Photon-ALP oscillations are similar to neutrino oscillations but external B is needed
bull Bounds on the parameters M and m ndash CAST amp astrophysical arguments
M gt 114 1010 GeV for m lt 002 eV
ndash Energetics of SN 1987a
M gt 1011 GeV for m lt 10-10 GeV model dependent
13
(DA FARE) Which EBL First analysis of 3C279 EBL model by Kneiske et al 2004
To be updated including Franceschini et al 2008
14
DARMa Intergalactic magnetic fields
Their morphology is poorly known It is supposed that they have a domain-like structure with
bull strength ~ 05 nG bull coherence length ~ 10 Mpc bull random orientation in each domain
NB - Picture consistent with first AUGER data
strength 03 ndash 09 nG for coherence length 1 ndash 10 Mpc
(DA Persic amp Roncadelli MPLA 2008)
15
Hooper amp Serpico (DA FARE)
16
Sanchez-Condersquo et al (DA FARE)
17
Experimental input from more sources at high z MAGIC S5 0716+714
bull After trigger MAGIC observed 26h April 28 Swift reports flux about 50 larger
than that observed in 2007
Apr 29 ATel 1500 MAGIC reports 68 discovery Apr 23-25 F(gt400 GeV) asymp25 Crab
bull 3rd low-peaked VHE blazar after BL Lac amp W comae
bull Host galaxy detected Z=031+-008 =gt 3rd farthest VHE emitter for which the spectral index has been measured
S5 0716+714Trigger in April
2008
Clear signal 68σNew
discoveryarXiv09072386
18
Deformation of the SED
PKS 0447-439 z=020 HESS 20091ES 1011+496 z=021 MAGIC 20071ES 0414+009 z=029 HESS amp Fermi 2009S5 0716+71 z=031plusmn008 MAGIC 20091ES 0502+675 z=034 VERITAS 20093C 66A z=044 VERITAS 2009 3C 279 z=054 MAGIC 2008
hellipand more new sources are coming into the game (VERITAS HESS MAGIC)
19
Other possible explanationsrelated to new physics
bull Kifune 2001 Violation of the Lorentz invariance
bull We should keep in mind thatndash Extraordinary claims require extraordinary evidence
bull New Scientist SciAm blognews hellip and then
ndash Claims must be followed upbull What else do we expect
bull Fundamental implications of unexpected findings
bull Are we seeing a part of the same big picture
2
222 1 ss E
EO
E
EEpc
20
Conclusions
bull The existence of a very light ALP predicted by many extensions of the SM naturally explains the observed transparency of the VHE gamma-ray sky
bull As a bonus it explains why only the most distant AGN seem to demand an unconventional emission spectrum
bull The DaRMa prediction in particular concerns the spectral change of observed AGN flux at VHE and becomes observable if the TeV band is carefully probed
bull It can be tested with IACTs with Fermi and with EAS
21
rdquoA textbook example of the merging of
particle physics and astronomy into the
modern field of astroparticle
physicsrdquo
22
BACKUP
23
PROPAGATION OVER ONE DOMAIN
We work in the short-wavelength approximation so
the beam with energy E is formally a 3-level non
relativistic quantum system described by the wave
equation
with
24
and mixing matrix
which in the presence of absorption becomes
with
25
Hence the conversion probability reads
in terms of the propagation matrix We find
that a nonvanishing conversion probability over the
WHOLE range requires
with
26
In the present situation we have
and so the mixing matrix reduces to
Following Csaki et al ICAP 05 (2003) 005 we
get the explicit form of the propagation matrix
27
PROPAGATION OVER MANY DOMAINS
When all domains are considered at once one has to
allow for the randomness of the direction of B in the
n-th domain Let be the direction of B in the n-th
domain with respect to a FIXED fiducial direction for
all domains and denote by the evolution
matrix in the n-th domain
Then the overall beam propagation is described by
28
We evaluate by numerically
computing and iterating the result
times by randomly choosing each time
We repeat this procedure 5000 times and next
average all these realizations of the propagation
process over all random angles So the PHYSICAL
propagation matrix of the beam is
29
Assuming that the initial state of the beam is
unpolarized and fully made of photons the initial
beam state is
So we finally get
30
Ideal case z = 1 ndash EBL of Franceschini et al
9
Implications on Extragalactic Background Light
e-e+
EBL
VHE
blazarIACT
10
bull At ~05 TeV flux attenuated by 2 orders of magnitudebull The measurement of spectral features permits to constrain EBL models
ndash Power law Γ = 41 plusmn 07 measured up to 05 TeV Spectrum sensitive to 02 to 2 μm
ndash Assume minimum reasonable index Γem = 15
bull Upper limit close to lower limit from galaxy countbull Explanations go
ndash from standard ones
bull very hard emission mechanisms with intrinsic slope lt 15 (Stecker 2008)
bull Very low EBL
ndash to possible evidence for new physics
bull Oscillation to a particle traveling unimpeded
rarr X rarr
Could it be seen
11
Oscillation to an Axion-Like Particle
ndash Oscillation during the propagation DA Roncadelli amp Mansutti [DARMa] PLB2008 PRD2008
ndash Conversion at the emitter (Hooper et al PRD2008)
ndash Mixed mechanisms (Sanchez-Condersquo et al PRD 2009)
ndash hellip
BEaM
Ptrans
1
12
Phenomenology of the oscillations
bull Photon-ALP oscillations are similar to neutrino oscillations but external B is needed
bull Bounds on the parameters M and m ndash CAST amp astrophysical arguments
M gt 114 1010 GeV for m lt 002 eV
ndash Energetics of SN 1987a
M gt 1011 GeV for m lt 10-10 GeV model dependent
13
(DA FARE) Which EBL First analysis of 3C279 EBL model by Kneiske et al 2004
To be updated including Franceschini et al 2008
14
DARMa Intergalactic magnetic fields
Their morphology is poorly known It is supposed that they have a domain-like structure with
bull strength ~ 05 nG bull coherence length ~ 10 Mpc bull random orientation in each domain
NB - Picture consistent with first AUGER data
strength 03 ndash 09 nG for coherence length 1 ndash 10 Mpc
(DA Persic amp Roncadelli MPLA 2008)
15
Hooper amp Serpico (DA FARE)
16
Sanchez-Condersquo et al (DA FARE)
17
Experimental input from more sources at high z MAGIC S5 0716+714
bull After trigger MAGIC observed 26h April 28 Swift reports flux about 50 larger
than that observed in 2007
Apr 29 ATel 1500 MAGIC reports 68 discovery Apr 23-25 F(gt400 GeV) asymp25 Crab
bull 3rd low-peaked VHE blazar after BL Lac amp W comae
bull Host galaxy detected Z=031+-008 =gt 3rd farthest VHE emitter for which the spectral index has been measured
S5 0716+714Trigger in April
2008
Clear signal 68σNew
discoveryarXiv09072386
18
Deformation of the SED
PKS 0447-439 z=020 HESS 20091ES 1011+496 z=021 MAGIC 20071ES 0414+009 z=029 HESS amp Fermi 2009S5 0716+71 z=031plusmn008 MAGIC 20091ES 0502+675 z=034 VERITAS 20093C 66A z=044 VERITAS 2009 3C 279 z=054 MAGIC 2008
hellipand more new sources are coming into the game (VERITAS HESS MAGIC)
19
Other possible explanationsrelated to new physics
bull Kifune 2001 Violation of the Lorentz invariance
bull We should keep in mind thatndash Extraordinary claims require extraordinary evidence
bull New Scientist SciAm blognews hellip and then
ndash Claims must be followed upbull What else do we expect
bull Fundamental implications of unexpected findings
bull Are we seeing a part of the same big picture
2
222 1 ss E
EO
E
EEpc
20
Conclusions
bull The existence of a very light ALP predicted by many extensions of the SM naturally explains the observed transparency of the VHE gamma-ray sky
bull As a bonus it explains why only the most distant AGN seem to demand an unconventional emission spectrum
bull The DaRMa prediction in particular concerns the spectral change of observed AGN flux at VHE and becomes observable if the TeV band is carefully probed
bull It can be tested with IACTs with Fermi and with EAS
21
rdquoA textbook example of the merging of
particle physics and astronomy into the
modern field of astroparticle
physicsrdquo
22
BACKUP
23
PROPAGATION OVER ONE DOMAIN
We work in the short-wavelength approximation so
the beam with energy E is formally a 3-level non
relativistic quantum system described by the wave
equation
with
24
and mixing matrix
which in the presence of absorption becomes
with
25
Hence the conversion probability reads
in terms of the propagation matrix We find
that a nonvanishing conversion probability over the
WHOLE range requires
with
26
In the present situation we have
and so the mixing matrix reduces to
Following Csaki et al ICAP 05 (2003) 005 we
get the explicit form of the propagation matrix
27
PROPAGATION OVER MANY DOMAINS
When all domains are considered at once one has to
allow for the randomness of the direction of B in the
n-th domain Let be the direction of B in the n-th
domain with respect to a FIXED fiducial direction for
all domains and denote by the evolution
matrix in the n-th domain
Then the overall beam propagation is described by
28
We evaluate by numerically
computing and iterating the result
times by randomly choosing each time
We repeat this procedure 5000 times and next
average all these realizations of the propagation
process over all random angles So the PHYSICAL
propagation matrix of the beam is
29
Assuming that the initial state of the beam is
unpolarized and fully made of photons the initial
beam state is
So we finally get
30
Ideal case z = 1 ndash EBL of Franceschini et al
10
bull At ~05 TeV flux attenuated by 2 orders of magnitudebull The measurement of spectral features permits to constrain EBL models
ndash Power law Γ = 41 plusmn 07 measured up to 05 TeV Spectrum sensitive to 02 to 2 μm
ndash Assume minimum reasonable index Γem = 15
bull Upper limit close to lower limit from galaxy countbull Explanations go
ndash from standard ones
bull very hard emission mechanisms with intrinsic slope lt 15 (Stecker 2008)
bull Very low EBL
ndash to possible evidence for new physics
bull Oscillation to a particle traveling unimpeded
rarr X rarr
Could it be seen
11
Oscillation to an Axion-Like Particle
ndash Oscillation during the propagation DA Roncadelli amp Mansutti [DARMa] PLB2008 PRD2008
ndash Conversion at the emitter (Hooper et al PRD2008)
ndash Mixed mechanisms (Sanchez-Condersquo et al PRD 2009)
ndash hellip
BEaM
Ptrans
1
12
Phenomenology of the oscillations
bull Photon-ALP oscillations are similar to neutrino oscillations but external B is needed
bull Bounds on the parameters M and m ndash CAST amp astrophysical arguments
M gt 114 1010 GeV for m lt 002 eV
ndash Energetics of SN 1987a
M gt 1011 GeV for m lt 10-10 GeV model dependent
13
(DA FARE) Which EBL First analysis of 3C279 EBL model by Kneiske et al 2004
To be updated including Franceschini et al 2008
14
DARMa Intergalactic magnetic fields
Their morphology is poorly known It is supposed that they have a domain-like structure with
bull strength ~ 05 nG bull coherence length ~ 10 Mpc bull random orientation in each domain
NB - Picture consistent with first AUGER data
strength 03 ndash 09 nG for coherence length 1 ndash 10 Mpc
(DA Persic amp Roncadelli MPLA 2008)
15
Hooper amp Serpico (DA FARE)
16
Sanchez-Condersquo et al (DA FARE)
17
Experimental input from more sources at high z MAGIC S5 0716+714
bull After trigger MAGIC observed 26h April 28 Swift reports flux about 50 larger
than that observed in 2007
Apr 29 ATel 1500 MAGIC reports 68 discovery Apr 23-25 F(gt400 GeV) asymp25 Crab
bull 3rd low-peaked VHE blazar after BL Lac amp W comae
bull Host galaxy detected Z=031+-008 =gt 3rd farthest VHE emitter for which the spectral index has been measured
S5 0716+714Trigger in April
2008
Clear signal 68σNew
discoveryarXiv09072386
18
Deformation of the SED
PKS 0447-439 z=020 HESS 20091ES 1011+496 z=021 MAGIC 20071ES 0414+009 z=029 HESS amp Fermi 2009S5 0716+71 z=031plusmn008 MAGIC 20091ES 0502+675 z=034 VERITAS 20093C 66A z=044 VERITAS 2009 3C 279 z=054 MAGIC 2008
hellipand more new sources are coming into the game (VERITAS HESS MAGIC)
19
Other possible explanationsrelated to new physics
bull Kifune 2001 Violation of the Lorentz invariance
bull We should keep in mind thatndash Extraordinary claims require extraordinary evidence
bull New Scientist SciAm blognews hellip and then
ndash Claims must be followed upbull What else do we expect
bull Fundamental implications of unexpected findings
bull Are we seeing a part of the same big picture
2
222 1 ss E
EO
E
EEpc
20
Conclusions
bull The existence of a very light ALP predicted by many extensions of the SM naturally explains the observed transparency of the VHE gamma-ray sky
bull As a bonus it explains why only the most distant AGN seem to demand an unconventional emission spectrum
bull The DaRMa prediction in particular concerns the spectral change of observed AGN flux at VHE and becomes observable if the TeV band is carefully probed
bull It can be tested with IACTs with Fermi and with EAS
21
rdquoA textbook example of the merging of
particle physics and astronomy into the
modern field of astroparticle
physicsrdquo
22
BACKUP
23
PROPAGATION OVER ONE DOMAIN
We work in the short-wavelength approximation so
the beam with energy E is formally a 3-level non
relativistic quantum system described by the wave
equation
with
24
and mixing matrix
which in the presence of absorption becomes
with
25
Hence the conversion probability reads
in terms of the propagation matrix We find
that a nonvanishing conversion probability over the
WHOLE range requires
with
26
In the present situation we have
and so the mixing matrix reduces to
Following Csaki et al ICAP 05 (2003) 005 we
get the explicit form of the propagation matrix
27
PROPAGATION OVER MANY DOMAINS
When all domains are considered at once one has to
allow for the randomness of the direction of B in the
n-th domain Let be the direction of B in the n-th
domain with respect to a FIXED fiducial direction for
all domains and denote by the evolution
matrix in the n-th domain
Then the overall beam propagation is described by
28
We evaluate by numerically
computing and iterating the result
times by randomly choosing each time
We repeat this procedure 5000 times and next
average all these realizations of the propagation
process over all random angles So the PHYSICAL
propagation matrix of the beam is
29
Assuming that the initial state of the beam is
unpolarized and fully made of photons the initial
beam state is
So we finally get
30
Ideal case z = 1 ndash EBL of Franceschini et al
11
Oscillation to an Axion-Like Particle
ndash Oscillation during the propagation DA Roncadelli amp Mansutti [DARMa] PLB2008 PRD2008
ndash Conversion at the emitter (Hooper et al PRD2008)
ndash Mixed mechanisms (Sanchez-Condersquo et al PRD 2009)
ndash hellip
BEaM
Ptrans
1
12
Phenomenology of the oscillations
bull Photon-ALP oscillations are similar to neutrino oscillations but external B is needed
bull Bounds on the parameters M and m ndash CAST amp astrophysical arguments
M gt 114 1010 GeV for m lt 002 eV
ndash Energetics of SN 1987a
M gt 1011 GeV for m lt 10-10 GeV model dependent
13
(DA FARE) Which EBL First analysis of 3C279 EBL model by Kneiske et al 2004
To be updated including Franceschini et al 2008
14
DARMa Intergalactic magnetic fields
Their morphology is poorly known It is supposed that they have a domain-like structure with
bull strength ~ 05 nG bull coherence length ~ 10 Mpc bull random orientation in each domain
NB - Picture consistent with first AUGER data
strength 03 ndash 09 nG for coherence length 1 ndash 10 Mpc
(DA Persic amp Roncadelli MPLA 2008)
15
Hooper amp Serpico (DA FARE)
16
Sanchez-Condersquo et al (DA FARE)
17
Experimental input from more sources at high z MAGIC S5 0716+714
bull After trigger MAGIC observed 26h April 28 Swift reports flux about 50 larger
than that observed in 2007
Apr 29 ATel 1500 MAGIC reports 68 discovery Apr 23-25 F(gt400 GeV) asymp25 Crab
bull 3rd low-peaked VHE blazar after BL Lac amp W comae
bull Host galaxy detected Z=031+-008 =gt 3rd farthest VHE emitter for which the spectral index has been measured
S5 0716+714Trigger in April
2008
Clear signal 68σNew
discoveryarXiv09072386
18
Deformation of the SED
PKS 0447-439 z=020 HESS 20091ES 1011+496 z=021 MAGIC 20071ES 0414+009 z=029 HESS amp Fermi 2009S5 0716+71 z=031plusmn008 MAGIC 20091ES 0502+675 z=034 VERITAS 20093C 66A z=044 VERITAS 2009 3C 279 z=054 MAGIC 2008
hellipand more new sources are coming into the game (VERITAS HESS MAGIC)
19
Other possible explanationsrelated to new physics
bull Kifune 2001 Violation of the Lorentz invariance
bull We should keep in mind thatndash Extraordinary claims require extraordinary evidence
bull New Scientist SciAm blognews hellip and then
ndash Claims must be followed upbull What else do we expect
bull Fundamental implications of unexpected findings
bull Are we seeing a part of the same big picture
2
222 1 ss E
EO
E
EEpc
20
Conclusions
bull The existence of a very light ALP predicted by many extensions of the SM naturally explains the observed transparency of the VHE gamma-ray sky
bull As a bonus it explains why only the most distant AGN seem to demand an unconventional emission spectrum
bull The DaRMa prediction in particular concerns the spectral change of observed AGN flux at VHE and becomes observable if the TeV band is carefully probed
bull It can be tested with IACTs with Fermi and with EAS
21
rdquoA textbook example of the merging of
particle physics and astronomy into the
modern field of astroparticle
physicsrdquo
22
BACKUP
23
PROPAGATION OVER ONE DOMAIN
We work in the short-wavelength approximation so
the beam with energy E is formally a 3-level non
relativistic quantum system described by the wave
equation
with
24
and mixing matrix
which in the presence of absorption becomes
with
25
Hence the conversion probability reads
in terms of the propagation matrix We find
that a nonvanishing conversion probability over the
WHOLE range requires
with
26
In the present situation we have
and so the mixing matrix reduces to
Following Csaki et al ICAP 05 (2003) 005 we
get the explicit form of the propagation matrix
27
PROPAGATION OVER MANY DOMAINS
When all domains are considered at once one has to
allow for the randomness of the direction of B in the
n-th domain Let be the direction of B in the n-th
domain with respect to a FIXED fiducial direction for
all domains and denote by the evolution
matrix in the n-th domain
Then the overall beam propagation is described by
28
We evaluate by numerically
computing and iterating the result
times by randomly choosing each time
We repeat this procedure 5000 times and next
average all these realizations of the propagation
process over all random angles So the PHYSICAL
propagation matrix of the beam is
29
Assuming that the initial state of the beam is
unpolarized and fully made of photons the initial
beam state is
So we finally get
30
Ideal case z = 1 ndash EBL of Franceschini et al
12
Phenomenology of the oscillations
bull Photon-ALP oscillations are similar to neutrino oscillations but external B is needed
bull Bounds on the parameters M and m ndash CAST amp astrophysical arguments
M gt 114 1010 GeV for m lt 002 eV
ndash Energetics of SN 1987a
M gt 1011 GeV for m lt 10-10 GeV model dependent
13
(DA FARE) Which EBL First analysis of 3C279 EBL model by Kneiske et al 2004
To be updated including Franceschini et al 2008
14
DARMa Intergalactic magnetic fields
Their morphology is poorly known It is supposed that they have a domain-like structure with
bull strength ~ 05 nG bull coherence length ~ 10 Mpc bull random orientation in each domain
NB - Picture consistent with first AUGER data
strength 03 ndash 09 nG for coherence length 1 ndash 10 Mpc
(DA Persic amp Roncadelli MPLA 2008)
15
Hooper amp Serpico (DA FARE)
16
Sanchez-Condersquo et al (DA FARE)
17
Experimental input from more sources at high z MAGIC S5 0716+714
bull After trigger MAGIC observed 26h April 28 Swift reports flux about 50 larger
than that observed in 2007
Apr 29 ATel 1500 MAGIC reports 68 discovery Apr 23-25 F(gt400 GeV) asymp25 Crab
bull 3rd low-peaked VHE blazar after BL Lac amp W comae
bull Host galaxy detected Z=031+-008 =gt 3rd farthest VHE emitter for which the spectral index has been measured
S5 0716+714Trigger in April
2008
Clear signal 68σNew
discoveryarXiv09072386
18
Deformation of the SED
PKS 0447-439 z=020 HESS 20091ES 1011+496 z=021 MAGIC 20071ES 0414+009 z=029 HESS amp Fermi 2009S5 0716+71 z=031plusmn008 MAGIC 20091ES 0502+675 z=034 VERITAS 20093C 66A z=044 VERITAS 2009 3C 279 z=054 MAGIC 2008
hellipand more new sources are coming into the game (VERITAS HESS MAGIC)
19
Other possible explanationsrelated to new physics
bull Kifune 2001 Violation of the Lorentz invariance
bull We should keep in mind thatndash Extraordinary claims require extraordinary evidence
bull New Scientist SciAm blognews hellip and then
ndash Claims must be followed upbull What else do we expect
bull Fundamental implications of unexpected findings
bull Are we seeing a part of the same big picture
2
222 1 ss E
EO
E
EEpc
20
Conclusions
bull The existence of a very light ALP predicted by many extensions of the SM naturally explains the observed transparency of the VHE gamma-ray sky
bull As a bonus it explains why only the most distant AGN seem to demand an unconventional emission spectrum
bull The DaRMa prediction in particular concerns the spectral change of observed AGN flux at VHE and becomes observable if the TeV band is carefully probed
bull It can be tested with IACTs with Fermi and with EAS
21
rdquoA textbook example of the merging of
particle physics and astronomy into the
modern field of astroparticle
physicsrdquo
22
BACKUP
23
PROPAGATION OVER ONE DOMAIN
We work in the short-wavelength approximation so
the beam with energy E is formally a 3-level non
relativistic quantum system described by the wave
equation
with
24
and mixing matrix
which in the presence of absorption becomes
with
25
Hence the conversion probability reads
in terms of the propagation matrix We find
that a nonvanishing conversion probability over the
WHOLE range requires
with
26
In the present situation we have
and so the mixing matrix reduces to
Following Csaki et al ICAP 05 (2003) 005 we
get the explicit form of the propagation matrix
27
PROPAGATION OVER MANY DOMAINS
When all domains are considered at once one has to
allow for the randomness of the direction of B in the
n-th domain Let be the direction of B in the n-th
domain with respect to a FIXED fiducial direction for
all domains and denote by the evolution
matrix in the n-th domain
Then the overall beam propagation is described by
28
We evaluate by numerically
computing and iterating the result
times by randomly choosing each time
We repeat this procedure 5000 times and next
average all these realizations of the propagation
process over all random angles So the PHYSICAL
propagation matrix of the beam is
29
Assuming that the initial state of the beam is
unpolarized and fully made of photons the initial
beam state is
So we finally get
30
Ideal case z = 1 ndash EBL of Franceschini et al
13
(DA FARE) Which EBL First analysis of 3C279 EBL model by Kneiske et al 2004
To be updated including Franceschini et al 2008
14
DARMa Intergalactic magnetic fields
Their morphology is poorly known It is supposed that they have a domain-like structure with
bull strength ~ 05 nG bull coherence length ~ 10 Mpc bull random orientation in each domain
NB - Picture consistent with first AUGER data
strength 03 ndash 09 nG for coherence length 1 ndash 10 Mpc
(DA Persic amp Roncadelli MPLA 2008)
15
Hooper amp Serpico (DA FARE)
16
Sanchez-Condersquo et al (DA FARE)
17
Experimental input from more sources at high z MAGIC S5 0716+714
bull After trigger MAGIC observed 26h April 28 Swift reports flux about 50 larger
than that observed in 2007
Apr 29 ATel 1500 MAGIC reports 68 discovery Apr 23-25 F(gt400 GeV) asymp25 Crab
bull 3rd low-peaked VHE blazar after BL Lac amp W comae
bull Host galaxy detected Z=031+-008 =gt 3rd farthest VHE emitter for which the spectral index has been measured
S5 0716+714Trigger in April
2008
Clear signal 68σNew
discoveryarXiv09072386
18
Deformation of the SED
PKS 0447-439 z=020 HESS 20091ES 1011+496 z=021 MAGIC 20071ES 0414+009 z=029 HESS amp Fermi 2009S5 0716+71 z=031plusmn008 MAGIC 20091ES 0502+675 z=034 VERITAS 20093C 66A z=044 VERITAS 2009 3C 279 z=054 MAGIC 2008
hellipand more new sources are coming into the game (VERITAS HESS MAGIC)
19
Other possible explanationsrelated to new physics
bull Kifune 2001 Violation of the Lorentz invariance
bull We should keep in mind thatndash Extraordinary claims require extraordinary evidence
bull New Scientist SciAm blognews hellip and then
ndash Claims must be followed upbull What else do we expect
bull Fundamental implications of unexpected findings
bull Are we seeing a part of the same big picture
2
222 1 ss E
EO
E
EEpc
20
Conclusions
bull The existence of a very light ALP predicted by many extensions of the SM naturally explains the observed transparency of the VHE gamma-ray sky
bull As a bonus it explains why only the most distant AGN seem to demand an unconventional emission spectrum
bull The DaRMa prediction in particular concerns the spectral change of observed AGN flux at VHE and becomes observable if the TeV band is carefully probed
bull It can be tested with IACTs with Fermi and with EAS
21
rdquoA textbook example of the merging of
particle physics and astronomy into the
modern field of astroparticle
physicsrdquo
22
BACKUP
23
PROPAGATION OVER ONE DOMAIN
We work in the short-wavelength approximation so
the beam with energy E is formally a 3-level non
relativistic quantum system described by the wave
equation
with
24
and mixing matrix
which in the presence of absorption becomes
with
25
Hence the conversion probability reads
in terms of the propagation matrix We find
that a nonvanishing conversion probability over the
WHOLE range requires
with
26
In the present situation we have
and so the mixing matrix reduces to
Following Csaki et al ICAP 05 (2003) 005 we
get the explicit form of the propagation matrix
27
PROPAGATION OVER MANY DOMAINS
When all domains are considered at once one has to
allow for the randomness of the direction of B in the
n-th domain Let be the direction of B in the n-th
domain with respect to a FIXED fiducial direction for
all domains and denote by the evolution
matrix in the n-th domain
Then the overall beam propagation is described by
28
We evaluate by numerically
computing and iterating the result
times by randomly choosing each time
We repeat this procedure 5000 times and next
average all these realizations of the propagation
process over all random angles So the PHYSICAL
propagation matrix of the beam is
29
Assuming that the initial state of the beam is
unpolarized and fully made of photons the initial
beam state is
So we finally get
30
Ideal case z = 1 ndash EBL of Franceschini et al
14
DARMa Intergalactic magnetic fields
Their morphology is poorly known It is supposed that they have a domain-like structure with
bull strength ~ 05 nG bull coherence length ~ 10 Mpc bull random orientation in each domain
NB - Picture consistent with first AUGER data
strength 03 ndash 09 nG for coherence length 1 ndash 10 Mpc
(DA Persic amp Roncadelli MPLA 2008)
15
Hooper amp Serpico (DA FARE)
16
Sanchez-Condersquo et al (DA FARE)
17
Experimental input from more sources at high z MAGIC S5 0716+714
bull After trigger MAGIC observed 26h April 28 Swift reports flux about 50 larger
than that observed in 2007
Apr 29 ATel 1500 MAGIC reports 68 discovery Apr 23-25 F(gt400 GeV) asymp25 Crab
bull 3rd low-peaked VHE blazar after BL Lac amp W comae
bull Host galaxy detected Z=031+-008 =gt 3rd farthest VHE emitter for which the spectral index has been measured
S5 0716+714Trigger in April
2008
Clear signal 68σNew
discoveryarXiv09072386
18
Deformation of the SED
PKS 0447-439 z=020 HESS 20091ES 1011+496 z=021 MAGIC 20071ES 0414+009 z=029 HESS amp Fermi 2009S5 0716+71 z=031plusmn008 MAGIC 20091ES 0502+675 z=034 VERITAS 20093C 66A z=044 VERITAS 2009 3C 279 z=054 MAGIC 2008
hellipand more new sources are coming into the game (VERITAS HESS MAGIC)
19
Other possible explanationsrelated to new physics
bull Kifune 2001 Violation of the Lorentz invariance
bull We should keep in mind thatndash Extraordinary claims require extraordinary evidence
bull New Scientist SciAm blognews hellip and then
ndash Claims must be followed upbull What else do we expect
bull Fundamental implications of unexpected findings
bull Are we seeing a part of the same big picture
2
222 1 ss E
EO
E
EEpc
20
Conclusions
bull The existence of a very light ALP predicted by many extensions of the SM naturally explains the observed transparency of the VHE gamma-ray sky
bull As a bonus it explains why only the most distant AGN seem to demand an unconventional emission spectrum
bull The DaRMa prediction in particular concerns the spectral change of observed AGN flux at VHE and becomes observable if the TeV band is carefully probed
bull It can be tested with IACTs with Fermi and with EAS
21
rdquoA textbook example of the merging of
particle physics and astronomy into the
modern field of astroparticle
physicsrdquo
22
BACKUP
23
PROPAGATION OVER ONE DOMAIN
We work in the short-wavelength approximation so
the beam with energy E is formally a 3-level non
relativistic quantum system described by the wave
equation
with
24
and mixing matrix
which in the presence of absorption becomes
with
25
Hence the conversion probability reads
in terms of the propagation matrix We find
that a nonvanishing conversion probability over the
WHOLE range requires
with
26
In the present situation we have
and so the mixing matrix reduces to
Following Csaki et al ICAP 05 (2003) 005 we
get the explicit form of the propagation matrix
27
PROPAGATION OVER MANY DOMAINS
When all domains are considered at once one has to
allow for the randomness of the direction of B in the
n-th domain Let be the direction of B in the n-th
domain with respect to a FIXED fiducial direction for
all domains and denote by the evolution
matrix in the n-th domain
Then the overall beam propagation is described by
28
We evaluate by numerically
computing and iterating the result
times by randomly choosing each time
We repeat this procedure 5000 times and next
average all these realizations of the propagation
process over all random angles So the PHYSICAL
propagation matrix of the beam is
29
Assuming that the initial state of the beam is
unpolarized and fully made of photons the initial
beam state is
So we finally get
30
Ideal case z = 1 ndash EBL of Franceschini et al
15
Hooper amp Serpico (DA FARE)
16
Sanchez-Condersquo et al (DA FARE)
17
Experimental input from more sources at high z MAGIC S5 0716+714
bull After trigger MAGIC observed 26h April 28 Swift reports flux about 50 larger
than that observed in 2007
Apr 29 ATel 1500 MAGIC reports 68 discovery Apr 23-25 F(gt400 GeV) asymp25 Crab
bull 3rd low-peaked VHE blazar after BL Lac amp W comae
bull Host galaxy detected Z=031+-008 =gt 3rd farthest VHE emitter for which the spectral index has been measured
S5 0716+714Trigger in April
2008
Clear signal 68σNew
discoveryarXiv09072386
18
Deformation of the SED
PKS 0447-439 z=020 HESS 20091ES 1011+496 z=021 MAGIC 20071ES 0414+009 z=029 HESS amp Fermi 2009S5 0716+71 z=031plusmn008 MAGIC 20091ES 0502+675 z=034 VERITAS 20093C 66A z=044 VERITAS 2009 3C 279 z=054 MAGIC 2008
hellipand more new sources are coming into the game (VERITAS HESS MAGIC)
19
Other possible explanationsrelated to new physics
bull Kifune 2001 Violation of the Lorentz invariance
bull We should keep in mind thatndash Extraordinary claims require extraordinary evidence
bull New Scientist SciAm blognews hellip and then
ndash Claims must be followed upbull What else do we expect
bull Fundamental implications of unexpected findings
bull Are we seeing a part of the same big picture
2
222 1 ss E
EO
E
EEpc
20
Conclusions
bull The existence of a very light ALP predicted by many extensions of the SM naturally explains the observed transparency of the VHE gamma-ray sky
bull As a bonus it explains why only the most distant AGN seem to demand an unconventional emission spectrum
bull The DaRMa prediction in particular concerns the spectral change of observed AGN flux at VHE and becomes observable if the TeV band is carefully probed
bull It can be tested with IACTs with Fermi and with EAS
21
rdquoA textbook example of the merging of
particle physics and astronomy into the
modern field of astroparticle
physicsrdquo
22
BACKUP
23
PROPAGATION OVER ONE DOMAIN
We work in the short-wavelength approximation so
the beam with energy E is formally a 3-level non
relativistic quantum system described by the wave
equation
with
24
and mixing matrix
which in the presence of absorption becomes
with
25
Hence the conversion probability reads
in terms of the propagation matrix We find
that a nonvanishing conversion probability over the
WHOLE range requires
with
26
In the present situation we have
and so the mixing matrix reduces to
Following Csaki et al ICAP 05 (2003) 005 we
get the explicit form of the propagation matrix
27
PROPAGATION OVER MANY DOMAINS
When all domains are considered at once one has to
allow for the randomness of the direction of B in the
n-th domain Let be the direction of B in the n-th
domain with respect to a FIXED fiducial direction for
all domains and denote by the evolution
matrix in the n-th domain
Then the overall beam propagation is described by
28
We evaluate by numerically
computing and iterating the result
times by randomly choosing each time
We repeat this procedure 5000 times and next
average all these realizations of the propagation
process over all random angles So the PHYSICAL
propagation matrix of the beam is
29
Assuming that the initial state of the beam is
unpolarized and fully made of photons the initial
beam state is
So we finally get
30
Ideal case z = 1 ndash EBL of Franceschini et al
16
Sanchez-Condersquo et al (DA FARE)
17
Experimental input from more sources at high z MAGIC S5 0716+714
bull After trigger MAGIC observed 26h April 28 Swift reports flux about 50 larger
than that observed in 2007
Apr 29 ATel 1500 MAGIC reports 68 discovery Apr 23-25 F(gt400 GeV) asymp25 Crab
bull 3rd low-peaked VHE blazar after BL Lac amp W comae
bull Host galaxy detected Z=031+-008 =gt 3rd farthest VHE emitter for which the spectral index has been measured
S5 0716+714Trigger in April
2008
Clear signal 68σNew
discoveryarXiv09072386
18
Deformation of the SED
PKS 0447-439 z=020 HESS 20091ES 1011+496 z=021 MAGIC 20071ES 0414+009 z=029 HESS amp Fermi 2009S5 0716+71 z=031plusmn008 MAGIC 20091ES 0502+675 z=034 VERITAS 20093C 66A z=044 VERITAS 2009 3C 279 z=054 MAGIC 2008
hellipand more new sources are coming into the game (VERITAS HESS MAGIC)
19
Other possible explanationsrelated to new physics
bull Kifune 2001 Violation of the Lorentz invariance
bull We should keep in mind thatndash Extraordinary claims require extraordinary evidence
bull New Scientist SciAm blognews hellip and then
ndash Claims must be followed upbull What else do we expect
bull Fundamental implications of unexpected findings
bull Are we seeing a part of the same big picture
2
222 1 ss E
EO
E
EEpc
20
Conclusions
bull The existence of a very light ALP predicted by many extensions of the SM naturally explains the observed transparency of the VHE gamma-ray sky
bull As a bonus it explains why only the most distant AGN seem to demand an unconventional emission spectrum
bull The DaRMa prediction in particular concerns the spectral change of observed AGN flux at VHE and becomes observable if the TeV band is carefully probed
bull It can be tested with IACTs with Fermi and with EAS
21
rdquoA textbook example of the merging of
particle physics and astronomy into the
modern field of astroparticle
physicsrdquo
22
BACKUP
23
PROPAGATION OVER ONE DOMAIN
We work in the short-wavelength approximation so
the beam with energy E is formally a 3-level non
relativistic quantum system described by the wave
equation
with
24
and mixing matrix
which in the presence of absorption becomes
with
25
Hence the conversion probability reads
in terms of the propagation matrix We find
that a nonvanishing conversion probability over the
WHOLE range requires
with
26
In the present situation we have
and so the mixing matrix reduces to
Following Csaki et al ICAP 05 (2003) 005 we
get the explicit form of the propagation matrix
27
PROPAGATION OVER MANY DOMAINS
When all domains are considered at once one has to
allow for the randomness of the direction of B in the
n-th domain Let be the direction of B in the n-th
domain with respect to a FIXED fiducial direction for
all domains and denote by the evolution
matrix in the n-th domain
Then the overall beam propagation is described by
28
We evaluate by numerically
computing and iterating the result
times by randomly choosing each time
We repeat this procedure 5000 times and next
average all these realizations of the propagation
process over all random angles So the PHYSICAL
propagation matrix of the beam is
29
Assuming that the initial state of the beam is
unpolarized and fully made of photons the initial
beam state is
So we finally get
30
Ideal case z = 1 ndash EBL of Franceschini et al
17
Experimental input from more sources at high z MAGIC S5 0716+714
bull After trigger MAGIC observed 26h April 28 Swift reports flux about 50 larger
than that observed in 2007
Apr 29 ATel 1500 MAGIC reports 68 discovery Apr 23-25 F(gt400 GeV) asymp25 Crab
bull 3rd low-peaked VHE blazar after BL Lac amp W comae
bull Host galaxy detected Z=031+-008 =gt 3rd farthest VHE emitter for which the spectral index has been measured
S5 0716+714Trigger in April
2008
Clear signal 68σNew
discoveryarXiv09072386
18
Deformation of the SED
PKS 0447-439 z=020 HESS 20091ES 1011+496 z=021 MAGIC 20071ES 0414+009 z=029 HESS amp Fermi 2009S5 0716+71 z=031plusmn008 MAGIC 20091ES 0502+675 z=034 VERITAS 20093C 66A z=044 VERITAS 2009 3C 279 z=054 MAGIC 2008
hellipand more new sources are coming into the game (VERITAS HESS MAGIC)
19
Other possible explanationsrelated to new physics
bull Kifune 2001 Violation of the Lorentz invariance
bull We should keep in mind thatndash Extraordinary claims require extraordinary evidence
bull New Scientist SciAm blognews hellip and then
ndash Claims must be followed upbull What else do we expect
bull Fundamental implications of unexpected findings
bull Are we seeing a part of the same big picture
2
222 1 ss E
EO
E
EEpc
20
Conclusions
bull The existence of a very light ALP predicted by many extensions of the SM naturally explains the observed transparency of the VHE gamma-ray sky
bull As a bonus it explains why only the most distant AGN seem to demand an unconventional emission spectrum
bull The DaRMa prediction in particular concerns the spectral change of observed AGN flux at VHE and becomes observable if the TeV band is carefully probed
bull It can be tested with IACTs with Fermi and with EAS
21
rdquoA textbook example of the merging of
particle physics and astronomy into the
modern field of astroparticle
physicsrdquo
22
BACKUP
23
PROPAGATION OVER ONE DOMAIN
We work in the short-wavelength approximation so
the beam with energy E is formally a 3-level non
relativistic quantum system described by the wave
equation
with
24
and mixing matrix
which in the presence of absorption becomes
with
25
Hence the conversion probability reads
in terms of the propagation matrix We find
that a nonvanishing conversion probability over the
WHOLE range requires
with
26
In the present situation we have
and so the mixing matrix reduces to
Following Csaki et al ICAP 05 (2003) 005 we
get the explicit form of the propagation matrix
27
PROPAGATION OVER MANY DOMAINS
When all domains are considered at once one has to
allow for the randomness of the direction of B in the
n-th domain Let be the direction of B in the n-th
domain with respect to a FIXED fiducial direction for
all domains and denote by the evolution
matrix in the n-th domain
Then the overall beam propagation is described by
28
We evaluate by numerically
computing and iterating the result
times by randomly choosing each time
We repeat this procedure 5000 times and next
average all these realizations of the propagation
process over all random angles So the PHYSICAL
propagation matrix of the beam is
29
Assuming that the initial state of the beam is
unpolarized and fully made of photons the initial
beam state is
So we finally get
30
Ideal case z = 1 ndash EBL of Franceschini et al
18
Deformation of the SED
PKS 0447-439 z=020 HESS 20091ES 1011+496 z=021 MAGIC 20071ES 0414+009 z=029 HESS amp Fermi 2009S5 0716+71 z=031plusmn008 MAGIC 20091ES 0502+675 z=034 VERITAS 20093C 66A z=044 VERITAS 2009 3C 279 z=054 MAGIC 2008
hellipand more new sources are coming into the game (VERITAS HESS MAGIC)
19
Other possible explanationsrelated to new physics
bull Kifune 2001 Violation of the Lorentz invariance
bull We should keep in mind thatndash Extraordinary claims require extraordinary evidence
bull New Scientist SciAm blognews hellip and then
ndash Claims must be followed upbull What else do we expect
bull Fundamental implications of unexpected findings
bull Are we seeing a part of the same big picture
2
222 1 ss E
EO
E
EEpc
20
Conclusions
bull The existence of a very light ALP predicted by many extensions of the SM naturally explains the observed transparency of the VHE gamma-ray sky
bull As a bonus it explains why only the most distant AGN seem to demand an unconventional emission spectrum
bull The DaRMa prediction in particular concerns the spectral change of observed AGN flux at VHE and becomes observable if the TeV band is carefully probed
bull It can be tested with IACTs with Fermi and with EAS
21
rdquoA textbook example of the merging of
particle physics and astronomy into the
modern field of astroparticle
physicsrdquo
22
BACKUP
23
PROPAGATION OVER ONE DOMAIN
We work in the short-wavelength approximation so
the beam with energy E is formally a 3-level non
relativistic quantum system described by the wave
equation
with
24
and mixing matrix
which in the presence of absorption becomes
with
25
Hence the conversion probability reads
in terms of the propagation matrix We find
that a nonvanishing conversion probability over the
WHOLE range requires
with
26
In the present situation we have
and so the mixing matrix reduces to
Following Csaki et al ICAP 05 (2003) 005 we
get the explicit form of the propagation matrix
27
PROPAGATION OVER MANY DOMAINS
When all domains are considered at once one has to
allow for the randomness of the direction of B in the
n-th domain Let be the direction of B in the n-th
domain with respect to a FIXED fiducial direction for
all domains and denote by the evolution
matrix in the n-th domain
Then the overall beam propagation is described by
28
We evaluate by numerically
computing and iterating the result
times by randomly choosing each time
We repeat this procedure 5000 times and next
average all these realizations of the propagation
process over all random angles So the PHYSICAL
propagation matrix of the beam is
29
Assuming that the initial state of the beam is
unpolarized and fully made of photons the initial
beam state is
So we finally get
30
Ideal case z = 1 ndash EBL of Franceschini et al
19
Other possible explanationsrelated to new physics
bull Kifune 2001 Violation of the Lorentz invariance
bull We should keep in mind thatndash Extraordinary claims require extraordinary evidence
bull New Scientist SciAm blognews hellip and then
ndash Claims must be followed upbull What else do we expect
bull Fundamental implications of unexpected findings
bull Are we seeing a part of the same big picture
2
222 1 ss E
EO
E
EEpc
20
Conclusions
bull The existence of a very light ALP predicted by many extensions of the SM naturally explains the observed transparency of the VHE gamma-ray sky
bull As a bonus it explains why only the most distant AGN seem to demand an unconventional emission spectrum
bull The DaRMa prediction in particular concerns the spectral change of observed AGN flux at VHE and becomes observable if the TeV band is carefully probed
bull It can be tested with IACTs with Fermi and with EAS
21
rdquoA textbook example of the merging of
particle physics and astronomy into the
modern field of astroparticle
physicsrdquo
22
BACKUP
23
PROPAGATION OVER ONE DOMAIN
We work in the short-wavelength approximation so
the beam with energy E is formally a 3-level non
relativistic quantum system described by the wave
equation
with
24
and mixing matrix
which in the presence of absorption becomes
with
25
Hence the conversion probability reads
in terms of the propagation matrix We find
that a nonvanishing conversion probability over the
WHOLE range requires
with
26
In the present situation we have
and so the mixing matrix reduces to
Following Csaki et al ICAP 05 (2003) 005 we
get the explicit form of the propagation matrix
27
PROPAGATION OVER MANY DOMAINS
When all domains are considered at once one has to
allow for the randomness of the direction of B in the
n-th domain Let be the direction of B in the n-th
domain with respect to a FIXED fiducial direction for
all domains and denote by the evolution
matrix in the n-th domain
Then the overall beam propagation is described by
28
We evaluate by numerically
computing and iterating the result
times by randomly choosing each time
We repeat this procedure 5000 times and next
average all these realizations of the propagation
process over all random angles So the PHYSICAL
propagation matrix of the beam is
29
Assuming that the initial state of the beam is
unpolarized and fully made of photons the initial
beam state is
So we finally get
30
Ideal case z = 1 ndash EBL of Franceschini et al
20
Conclusions
bull The existence of a very light ALP predicted by many extensions of the SM naturally explains the observed transparency of the VHE gamma-ray sky
bull As a bonus it explains why only the most distant AGN seem to demand an unconventional emission spectrum
bull The DaRMa prediction in particular concerns the spectral change of observed AGN flux at VHE and becomes observable if the TeV band is carefully probed
bull It can be tested with IACTs with Fermi and with EAS
21
rdquoA textbook example of the merging of
particle physics and astronomy into the
modern field of astroparticle
physicsrdquo
22
BACKUP
23
PROPAGATION OVER ONE DOMAIN
We work in the short-wavelength approximation so
the beam with energy E is formally a 3-level non
relativistic quantum system described by the wave
equation
with
24
and mixing matrix
which in the presence of absorption becomes
with
25
Hence the conversion probability reads
in terms of the propagation matrix We find
that a nonvanishing conversion probability over the
WHOLE range requires
with
26
In the present situation we have
and so the mixing matrix reduces to
Following Csaki et al ICAP 05 (2003) 005 we
get the explicit form of the propagation matrix
27
PROPAGATION OVER MANY DOMAINS
When all domains are considered at once one has to
allow for the randomness of the direction of B in the
n-th domain Let be the direction of B in the n-th
domain with respect to a FIXED fiducial direction for
all domains and denote by the evolution
matrix in the n-th domain
Then the overall beam propagation is described by
28
We evaluate by numerically
computing and iterating the result
times by randomly choosing each time
We repeat this procedure 5000 times and next
average all these realizations of the propagation
process over all random angles So the PHYSICAL
propagation matrix of the beam is
29
Assuming that the initial state of the beam is
unpolarized and fully made of photons the initial
beam state is
So we finally get
30
Ideal case z = 1 ndash EBL of Franceschini et al
21
rdquoA textbook example of the merging of
particle physics and astronomy into the
modern field of astroparticle
physicsrdquo
22
BACKUP
23
PROPAGATION OVER ONE DOMAIN
We work in the short-wavelength approximation so
the beam with energy E is formally a 3-level non
relativistic quantum system described by the wave
equation
with
24
and mixing matrix
which in the presence of absorption becomes
with
25
Hence the conversion probability reads
in terms of the propagation matrix We find
that a nonvanishing conversion probability over the
WHOLE range requires
with
26
In the present situation we have
and so the mixing matrix reduces to
Following Csaki et al ICAP 05 (2003) 005 we
get the explicit form of the propagation matrix
27
PROPAGATION OVER MANY DOMAINS
When all domains are considered at once one has to
allow for the randomness of the direction of B in the
n-th domain Let be the direction of B in the n-th
domain with respect to a FIXED fiducial direction for
all domains and denote by the evolution
matrix in the n-th domain
Then the overall beam propagation is described by
28
We evaluate by numerically
computing and iterating the result
times by randomly choosing each time
We repeat this procedure 5000 times and next
average all these realizations of the propagation
process over all random angles So the PHYSICAL
propagation matrix of the beam is
29
Assuming that the initial state of the beam is
unpolarized and fully made of photons the initial
beam state is
So we finally get
30
Ideal case z = 1 ndash EBL of Franceschini et al
22
BACKUP
23
PROPAGATION OVER ONE DOMAIN
We work in the short-wavelength approximation so
the beam with energy E is formally a 3-level non
relativistic quantum system described by the wave
equation
with
24
and mixing matrix
which in the presence of absorption becomes
with
25
Hence the conversion probability reads
in terms of the propagation matrix We find
that a nonvanishing conversion probability over the
WHOLE range requires
with
26
In the present situation we have
and so the mixing matrix reduces to
Following Csaki et al ICAP 05 (2003) 005 we
get the explicit form of the propagation matrix
27
PROPAGATION OVER MANY DOMAINS
When all domains are considered at once one has to
allow for the randomness of the direction of B in the
n-th domain Let be the direction of B in the n-th
domain with respect to a FIXED fiducial direction for
all domains and denote by the evolution
matrix in the n-th domain
Then the overall beam propagation is described by
28
We evaluate by numerically
computing and iterating the result
times by randomly choosing each time
We repeat this procedure 5000 times and next
average all these realizations of the propagation
process over all random angles So the PHYSICAL
propagation matrix of the beam is
29
Assuming that the initial state of the beam is
unpolarized and fully made of photons the initial
beam state is
So we finally get
30
Ideal case z = 1 ndash EBL of Franceschini et al
23
PROPAGATION OVER ONE DOMAIN
We work in the short-wavelength approximation so
the beam with energy E is formally a 3-level non
relativistic quantum system described by the wave
equation
with
24
and mixing matrix
which in the presence of absorption becomes
with
25
Hence the conversion probability reads
in terms of the propagation matrix We find
that a nonvanishing conversion probability over the
WHOLE range requires
with
26
In the present situation we have
and so the mixing matrix reduces to
Following Csaki et al ICAP 05 (2003) 005 we
get the explicit form of the propagation matrix
27
PROPAGATION OVER MANY DOMAINS
When all domains are considered at once one has to
allow for the randomness of the direction of B in the
n-th domain Let be the direction of B in the n-th
domain with respect to a FIXED fiducial direction for
all domains and denote by the evolution
matrix in the n-th domain
Then the overall beam propagation is described by
28
We evaluate by numerically
computing and iterating the result
times by randomly choosing each time
We repeat this procedure 5000 times and next
average all these realizations of the propagation
process over all random angles So the PHYSICAL
propagation matrix of the beam is
29
Assuming that the initial state of the beam is
unpolarized and fully made of photons the initial
beam state is
So we finally get
30
Ideal case z = 1 ndash EBL of Franceschini et al
24
and mixing matrix
which in the presence of absorption becomes
with
25
Hence the conversion probability reads
in terms of the propagation matrix We find
that a nonvanishing conversion probability over the
WHOLE range requires
with
26
In the present situation we have
and so the mixing matrix reduces to
Following Csaki et al ICAP 05 (2003) 005 we
get the explicit form of the propagation matrix
27
PROPAGATION OVER MANY DOMAINS
When all domains are considered at once one has to
allow for the randomness of the direction of B in the
n-th domain Let be the direction of B in the n-th
domain with respect to a FIXED fiducial direction for
all domains and denote by the evolution
matrix in the n-th domain
Then the overall beam propagation is described by
28
We evaluate by numerically
computing and iterating the result
times by randomly choosing each time
We repeat this procedure 5000 times and next
average all these realizations of the propagation
process over all random angles So the PHYSICAL
propagation matrix of the beam is
29
Assuming that the initial state of the beam is
unpolarized and fully made of photons the initial
beam state is
So we finally get
30
Ideal case z = 1 ndash EBL of Franceschini et al
25
Hence the conversion probability reads
in terms of the propagation matrix We find
that a nonvanishing conversion probability over the
WHOLE range requires
with
26
In the present situation we have
and so the mixing matrix reduces to
Following Csaki et al ICAP 05 (2003) 005 we
get the explicit form of the propagation matrix
27
PROPAGATION OVER MANY DOMAINS
When all domains are considered at once one has to
allow for the randomness of the direction of B in the
n-th domain Let be the direction of B in the n-th
domain with respect to a FIXED fiducial direction for
all domains and denote by the evolution
matrix in the n-th domain
Then the overall beam propagation is described by
28
We evaluate by numerically
computing and iterating the result
times by randomly choosing each time
We repeat this procedure 5000 times and next
average all these realizations of the propagation
process over all random angles So the PHYSICAL
propagation matrix of the beam is
29
Assuming that the initial state of the beam is
unpolarized and fully made of photons the initial
beam state is
So we finally get
30
Ideal case z = 1 ndash EBL of Franceschini et al
26
In the present situation we have
and so the mixing matrix reduces to
Following Csaki et al ICAP 05 (2003) 005 we
get the explicit form of the propagation matrix
27
PROPAGATION OVER MANY DOMAINS
When all domains are considered at once one has to
allow for the randomness of the direction of B in the
n-th domain Let be the direction of B in the n-th
domain with respect to a FIXED fiducial direction for
all domains and denote by the evolution
matrix in the n-th domain
Then the overall beam propagation is described by
28
We evaluate by numerically
computing and iterating the result
times by randomly choosing each time
We repeat this procedure 5000 times and next
average all these realizations of the propagation
process over all random angles So the PHYSICAL
propagation matrix of the beam is
29
Assuming that the initial state of the beam is
unpolarized and fully made of photons the initial
beam state is
So we finally get
30
Ideal case z = 1 ndash EBL of Franceschini et al
27
PROPAGATION OVER MANY DOMAINS
When all domains are considered at once one has to
allow for the randomness of the direction of B in the
n-th domain Let be the direction of B in the n-th
domain with respect to a FIXED fiducial direction for
all domains and denote by the evolution
matrix in the n-th domain
Then the overall beam propagation is described by
28
We evaluate by numerically
computing and iterating the result
times by randomly choosing each time
We repeat this procedure 5000 times and next
average all these realizations of the propagation
process over all random angles So the PHYSICAL
propagation matrix of the beam is
29
Assuming that the initial state of the beam is
unpolarized and fully made of photons the initial
beam state is
So we finally get
30
Ideal case z = 1 ndash EBL of Franceschini et al
28
We evaluate by numerically
computing and iterating the result
times by randomly choosing each time
We repeat this procedure 5000 times and next
average all these realizations of the propagation
process over all random angles So the PHYSICAL
propagation matrix of the beam is
29
Assuming that the initial state of the beam is
unpolarized and fully made of photons the initial
beam state is
So we finally get
30
Ideal case z = 1 ndash EBL of Franceschini et al
29
Assuming that the initial state of the beam is
unpolarized and fully made of photons the initial
beam state is
So we finally get
30
Ideal case z = 1 ndash EBL of Franceschini et al
30
Ideal case z = 1 ndash EBL of Franceschini et al
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