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Neutrinos from Neutrinos from Gamma-Ray Bursts Gamma-Ray Bursts
Sarira SahuICN, UNAM
APCTP Focus Program on Recent Developments in Neutrino Physics and APCTP Focus Program on Recent Developments in Neutrino Physics and Astroparticle PhysicsAstroparticle Physics
June 1525, Pohang, South Korea June 1525, Pohang, South Korea
(In memory of Prof. Benjamin W. Lee)(In memory of Prof. Benjamin W. Lee)
Neutrino Energy in the Neutrino Energy in the rangerange
MeV < E < Few GeVMeV < E < Few GeV
➔Introduction to Physics of GammaRay Burst Introduction to Physics of GammaRay Burst (GRB)(GRB)➔Why to look for neutrinos ?Why to look for neutrinos ?➔High temperature and/or Density matter (Plasma)High temperature and/or Density matter (Plasma)➔Particle Propagation in a Heat Bath (Low energy)Particle Propagation in a Heat Bath (Low energy)➔ Neutrino Propagation in a medium with B=0Neutrino Propagation in a medium with B=0➔ Application to GRB FireballApplication to GRB Fireball➔ Neutrino Propagation in a medium with Neutrino Propagation in a medium with ➔ Application to GRB FireballApplication to GRB Fireball
B≠0
➔High Energy Neutrinos propagation in a mediumHigh Energy Neutrinos propagation in a medium➔ With no Magnetic field in the background (B=0)With no Magnetic field in the background (B=0)➔ With Magnetic Field in the backgroundWith Magnetic Field in the background➔ Application to Physics of magnetar and GRB Application to Physics of magnetar and GRB PhysicsPhysics➔ MultiGeV Neutrinos From GRBsMultiGeV Neutrinos From GRBs➔ SummarySummary
Physics of Gamma-Ray Bursts & fireball Model
Physics of GammaRay Physics of GammaRay Bursts & Fireball ModelBursts & Fireball Model
What are GRBs ?What are GRBs ?
These are flashes of nonthermal bursts of low energy (~100 KeV1 MeV) photons.Release about erg in few seconds, making them the most luminous object in the Universe.They occur at cosmological distance, homogeneous distribution in the sky.
1051 −1055
T. Piran, 1999, 2000, Zhang, Meszaros, 2003
The burst duration ranges from several micro seconds toseveral hundred seconds with complicated and irregular structure.
No two grbs are the same. Some are short, some are long, some are weak, some are strong, some have many spikes, some have none, each unlike the other one.
Spectrum
NonthermalPowerLawN(E) dE ∝ E−
≃ 2
Fluence: F= ∫ flux. dt
Type of GRBsType of GRBs
Short - Hard (Short - Hard (≤ 2 sec) about 25%≤ 2 sec) about 25%Long - Soft (> 2 sec) 75%Long - Soft (> 2 sec) 75%Long GRBs are produced due to core col-lapse of massive stars (Hypernovae)Probably coalescence of compact bia-naries are responsible for the short-hard bursts (observation of afterglow from GRBs 050709, 050709b, 050724)/MagnetarsMeszaroes 2006, Zhang & meszaroes 2003
What are Fireballs ?What are Fireballs ?Sudden release of copious amount of Gamma-Rays into a compact region with a size ~100-1000 Km creates an opaque fireball due to pair creation.
The optical depth is very high ( ) so photons can not escape freely.
The fireball expands relativistically with a Lorentz Factor ~100 – 1000 under its own pressure and cools adiabatically. The radiation emerges freely to ISM when optical depth is ≈ 1.
e e−
≃1013
Irrespective of the nature of the Irrespective of the nature of the progenitorprogenitor
Gamma-Ray emission due to collision of Gamma-Ray emission due to collision of internal shocks (shells); relativistic outinternal shocks (shells); relativistic out--flow from the source ?flow from the source ?TheThe Fireball Model Fireball Model explains the explains the
temporal structure of the bursts and non-temporal structure of the bursts and non-thermal spectral behavior.thermal spectral behavior.Expanding fireball runs into the surroundExpanding fireball runs into the surrounding ISM to give afterglow.ing ISM to give afterglow.
EeV neutrinos from external shocks
(Waxman & Bahcall 2000)(Dermer 2002)
(KM 2007)
PeV neutrinos from internal shocks
HL GRBs (Waxman & Bahcall 1997)
LL GRBs(KM et al. 2006)
(Gupta & Zhang 2006)
MeV neutrinosat collapse
TeV neutrinosfrom inside the star
(Meszaros & Waxman 2001)(Schneider et al. 02)
( Razzaque et al. 2003)(Fabio, KM, et al. 07)
Meszaros (2001)
PeVEeV neutrinos from flares
(KM &Nagataki 2006)
High Density/Temperature PlasmaHigh Density/Temperature PlasmaEarly UniverseEarly UniverseNeutron StarNeutron StarGRB FireballGRB FireballAccretion Disk................Accretion Disk................Modified Particle PropertiesModified Particle Propertiesin the medium; new phenomenain the medium; new phenomena
●Effect of Heat bath on particle properties Effect of Heat bath on particle properties
●Massive Photon (Plasmon)Massive Photon (Plasmon)●Cherenkov radiation (Refractive Index > 1)Cherenkov radiation (Refractive Index > 1)●Plasmon decay ( )Plasmon decay ( )●Massless neutrino acquires an effective massMassless neutrino acquires an effective mass●MSW effect of neutrinos flavor conversionMSW effect of neutrinos flavor conversionModification of dispersion relation in the Modification of dispersion relation in the medium with and without magnetic field.medium with and without magnetic field.
p2−m2≠0
L
Neutrino Propagation in Neutrino Propagation in a Medium without a Medium without
Magnetic fieldMagnetic field
Effective Potential of a Neutrino in the medium
Constituent of the medium Forward Scattering Amplitude Same as considering the Real Part of the Neutrino Self-Energy Imaginary part corresponds to the Damping
DependsDepends
To calculate the selfenergyTo calculate the selfenergy
Thermal Field Theory has to be usedThermal Field Theory has to be usedReal Time Finite Temperature Field TheoryReal Time Finite Temperature Field Theory Imaginary Time Formalism Imaginary Time Formalism Thermo Field DynamicsThermo Field DynamicsAll the calculations are done using All the calculations are done using the medium at restthe medium at restThe Feynman diagrams which will contribute to the neutrino selfenergy are (Real Part Only) (Real Part Only)Kapusta 93, Niemi 84, Weldon 83, Nieves 93
To drder 1/M^4 (M-Vector Boson Mass) correction to the neutrino self energy in a medium.
−i W k =g2
2R∫ d 4 p
24[ S e p D
q]L
−i Z=−ig2cosW
C V
−C A
5 i Dq=0
× ∫ d 4 p
24−1Tr [
−ig2cosW
CV
f−C A
f5 i SF p]
Wolfenstein 79, Pal 89, Bravo 07, Notzold 88
− =akbu , ℜ=R L u=1,0
det 1akbu=0
−∣k∣=−b
V eff=−b
V e≃2GF N [
122sin2W Le
12−2sin2W L p−
12
Ln2 LeL
L−1
12cos2W
74T3M W
2
]
La=N a−N a
N
V=V e−V
=2GF N [ LeL e−L
−7 4 3
2
T 2
M W2 ]
In the Early Universe, For electron neutrino goes to muon neutrino the potential is
V=V e−V
=2GF N [Le−743
2 T 2
M W2 ]
In the charge neutral GRB fireball
If the asymmetry in the Early Universe then it is exactly same as the GRB fireball
Le=L
For antineutrinos will be replaced by LaLa
Bravo 07, Sahu 05
Mimic Early Universe
Neutrino Oscillation in GRB FireballNeutrino Oscillation in GRB Fireball
Sources for the MeV neutrinos:Neutrinos of about 520 MeV are generated due to the stellar collapse or merger event that trigger the burst. Nucleon bremsstrahlung,
In the Fireball,
All have energy in the MeV range.Some of these neutrinos will propagate through the fireball.
And
NN NN
e e−
pe− ne
Kumar 99, Janka 99
MeV MeV neutrinoneutrinoss
at collapseat collapse
NN NN
e e
−
pe− n e
EeV neutrinos from external shocks
(Waxman & Bahcall 2000)(Dermer 2002)
(KM 2007)
MeV neutrinosat collapse
Meszaros (2001)
PeVEeV neutrinos from flares
(KM &Nagataki 2006)
MultiGeV
Neutrino oscillations:Neutrino oscillations:In a relativistic and non degenerate plasma, the effective potential experience by a electron neutrino is
e e−
By a muon neutrino
V e≃ 2 GF N Le−7
[4 ] [3 ]
2 T 2
MW2 . V
,≃ 2 GF N L
, .
Oscillation processesOscillation processes
e , , e s , , s
Baryon Load in the fireball:
Computer simulation suggests baryon loadhas to be very small (outstanding problem)
~ 10−8 M ⊙ − 10−5 M ⊙
Otherwise the expansion is Newtonian & NO GRBFireball has to expand relativistically !!!Consistent with the OBSERVATION.
Piran 99
V ≃ 1.02×10−12 T MeV3 [± Le− 6.14 ×10−9 T MeV
2 ] MeV. ± ,
P t =
2 sin2 2
2 sin2 t
2 . =m2
2 E
= V−cos 2 2
2 sin2 2 is the neutrino energy ( 520 MeV), ө is the mixing angleE
Neutrino potential:
Probability of conversion after a time t
Resonance condition
V = cos2
Le 6.14×10−9 T MeV2
Lres ≃ 2 48EMeV
m2 sin 2cm
T MeV5
0.2×108 m2 cos 2 EMeV
M baryon ~ 2.23×10−4 R73 T MeV
3 Le M⊙
At resonance:
We assume:
Assumptions
The fireball is spherical with radius R~1001000 KM
It is charge neutral & having equal number of protons and neutrons.
T.Piran, Phys. Rep. 314,575 (1999)
Derishev et al., A&A 345, L51 (1999); APJ 521, 640 (1999)
Solar neutrinos:
SNO + KamLAND (reactor) SNO Collaboration, PRL 92, 181301 (2004) KamLAND Collaboration, hepex/0406035
6×10−5 eV 2 m2
10−4 eV2 0.8 sin2 0.98,
Best fit is at
m2~ 7.1 × 10−5 eV 2, sin2 ~ 0.83
Le ≃0.5 × 10−5 T MeV−3 EMeV
−1 ,
M baryon ~ 0.23×10−9 R73 M⊙ M baryon ~ 0.58×10−10 R7
3 M ⊙
Lres ~ 211Km L res ~ 845 Km
EMeV = 5 EMeV = 20
T MeV 2.8
Probably very few or NO resonant oscillations take place within the fireball and most of the neutrinos will come out.
Atmospheric Neutrinos:
SuperKamiokande: SK Collaboration, PRL 93, 101801 (2004)
1.9 ×10−3 eV 2 m2
3.0 ×10−3 eV20.9 sin2 2 1.0,
We take Average Value
m2~ 2.5 × 10−3 eV 2 , sin2 2 ~ 0.9
Le ≃0.98 × 10−4 T MeV−3 E MeV
−1
M baryon ~ 0.44×10−8 R73 M⊙ M baryon ~ 0.11×10−8 R7
3 M⊙Lres ~ 5 Km Lres ~ 21 Km
EMeV = 5EMeV = 20
T MeV 5gives
Neutrinos can have many resonant oscillations within the fireball.
Reactor Neutrinos:Liquid Scintillator Neutrino Detector (LSND) & KARMEN 2, combined Analysis: Phys. Rev D66, 013001 (2002)
0.45 eV 2 m2
1 eV 2 , 2×10−3 sin2 2 7×10−3
We consider
m2~ 0.5 eV 2 , sin 2 ~ 0.07
M baryon ~ 0.3×10−5 R73 M⊙
M baryon ~ 0.7×10−6 R73 M⊙Lres 1 Km
Lres 1.4 Km
EMeV = 5 EMeV = 20
T MeV 18
Neutrinos will oscillate several times before coming out of the fireball. Sahu 05
Gives
Neutrino oscillation is possible
If.....Neutrino mass square difference & mixing angle are in the
Atmospheric and/or Reactor expt. ranges
for SOLARMay be just............
Is it possible to detect these neutrinos....
Unfortunately not with the present generation detectors.........Similar to SN1987A burst but very very far, flux is very small
GRB NeutrinosGRB NeutrinosPartIIPartII
Neutrino Propagation in Neutrino Propagation in a Medium with Magnetic a Medium with Magnetic
fieldfield
Magnetic Field in the Jet Outflow
It is believed that non-thermal emission is due to synchrotron emission/inverse Compton scattering. For synchrotron emission strong magnetic field is required. There is no way to estimate the magnetic field from the first principle.
Large magnetic field is expected if the progenitor is highly magnetized. Also amplification of small field due to turbulent dynamo mechanism, compression or shearing.
Decrease of Magnetic field due to expansion at larger radii.
Magnetic Field in .......Recently it has been suggested that,
emission in GRBs cab be explained through Compton-drag process and no magnetic field is needed (APJ 529, 2000; APJ 511, 1999, APJ 491, L15, 1997)
Despite all these, there is no satisfactory explanation for the existence of strong field.
We use Magnetic field as a parameter here.
Neutrino in the presence of a Magnetic fieldNeutrino in the presence of a Magnetic field
Calculation of neutrino-self energy in the presence of a magnetic field to order 1/M^4_W
−i W k =∫ d 4 p
24−ig
2 L i S l p
−ig
2 L i W q
¿
−i T k =−g
2cosW
2
R i Z 0∫ d 4 p
24Tr [ cVc A5 i S l p ]
−i Z k =∫ d 4 p
24
−ig
2cosW
2
L i S l p L i Z q
Elizalde 02, Erdas 98, Bravo 08
k =R a ∥ k ∥a ⊥ k ⊥
bu
c b L
u=1,0 b
=0, b
S l p=S l0 pS l
p
iS l0 p=∫0
∞
e p , sG p , sds
S l p=i p.u∫
−∞
∞
e p , s G p , sds
p , s=i s p ∥2 −ml
2−tan z
zp ⊥2
p ∥2= p0
2− p3
2 p ⊥2= p1
2 p2
2 z=eBsSchwinger 51
G p , s=sec2 z [ Ai B5m l cos2 z−i 3sin z cos z ]
A= p−sin2 z p.u u− p.b b
3=5
bu
B=sin z cos z p.u b− p.bu
W q=−1
q2−M W2 [ g−
1
M W2 qq
ie2
F ]2ieF
q2−M W22
−1
q2−M W2 /
1
M W2 qq
ie2
F
W q=
g
M W2 1
q2
M W2 −
M W4
3 ie F
2M W4 q2≪M W
2 ,=0
In the unitary gauge and low momentum limit
V eff=b−c cosa ∥ −a ⊥ ∣k∣sin2
The is the angle between the magnetic field and the momentum of the neutrino
b=g 2 N l− N l
2 M W2 2cV
2 ml2
2 M W2
g 2 eB
2 M W2 N l
2− N l
2
g 2
2 M W2 [N l
− N l−
22
k 2
M Z2 ⟨El
B⟩N l
⟨E l
B⟩ N l
]
−g2 eB
M W2 ∫2
∞ dp 2
2 2∑n=2
∞
∑=±2
[k 2
E l , n
p22
ml2
2 ,2
n , 2k 2 E l , n] f l , nf l ,n
Garcia 08
c=g 2N l
0− N l
0
4M W2
1−c Aml2
2M W2
g 2eB
4M W4N l− N l
−g2 eB
M W4 ∫0
∞ dp322
∑n=0
∞
∑=±1
[k 0 E l ,n−ml2
E l , n
,1n ,0
k 3 p32
E l ,n
] f l , nf l , n
a ⊥ =−g 2eB
M W4 ∫0
∞ dp32
2∑n=0
∞
∑=±1
H2E l , n
m l2
E l ,n
f l , n f l , n
g 2
4M W2 [ k 3N l
0− N l0k 0 N l− N lN l
− N l23 ⟨E l
B ⟩ N l⟨E l
B ⟩ N l ]
H=eB 2n1−
a ∥ =−g 2 eB
M W4 ∫0
∞ dp32
2∑n=0
∞
∑=±1
m l2
E l ,n
f l ,nf l ,n
g 2
4M W2 [ k 3N l
0− N l
0k 0 N l− N lN l
− N l23 ⟨E l
B⟩ N l
⟨E l
B⟩ N l
]
●If neutrino is moving along the magnetic field ●If the magnetic field is very strong, only lowest Landau levels are filled n=0●If the magnetic field is very weak
a ∥ −a ⊥ sin2=0
V eff ≃b−c
SelfEnergy of the neutrino in a medium in the presence of a classical uniform Magnetic field calculated.
The calculation is carried out in the unitary gauge, where unphysical Higgs Contributions does not appear.
Magnetic field is Weak compared to the WBoson mass only, but not for electron mass.
For B>0 limit our results matches with the result in a matter background.
Neutrino oscillation in the magnetized GRB fireball Neutrino oscillation in the magnetized GRB fireball arXiv:0904.0138 With Nissim Fraija and Y. Y. Keum
In the presence of a magnetic field (weak)In the presence of a magnetic field (weak)
V =b−c cos Is the angle between K and B and for
phi=0 we have
V = 2GFm3
2 [ 1− 2−
4
2
mM W
2 E
m 3− 4 ]
N e0− N e
0=
m3
2
BBc∑ l=0
∞
−1l sinh K 1 =m3
2 1
N e− N e=m3
2
BBc∑ l=0
∞
−1l sinh [ 2 K 2 −BBc
K 1 ]= m3
2 1
Nissim 09
3=∑ l=0
∞
−1l cosh [ 3 2−14
BBc
K 0 16 2 K 1
]
4=∑ l=0
∞
−1l cosh1 2 [ K 0
2
K 1
]
= l1 ;= m l1
The Resonance condition is The Resonance condition is
1− 2−3.196×10−11 E MeV 3− 4=2.26
m2
E MeV
cos 2
m2≃7.1×10−5eV 2 ; sin22≃0.69B/Bc = 0.1
5 MeV
10
20
30
L_e ~5 x10^{8}2x 10^{7}L_{res} ~ 210842kmM_b ~10^{10} M_sun10^{8} Msun
SNOSNO
Le≃7×10−7−−2×10−7
520 MeV520 MeV
Lres≃5.2km−−21 km
M b≃4.24×10−9−−4.54×10−8
5 MeV5 MeV
10 MeV10 MeV
m2~2.5×10−3 eV 2 ; sin22~0.9
SuperKamioKande SuperKamioKande
5 MeV5 MeV
10 MeV10 MeV
Le≃3.28×10−6−−4.77×10−4
Lres≃0.4 km−1.4 km
M b≃ .3210−7M sun−−2.87×10−6 M sun
m2~0.5 eV 2 ; sin22~0.0049LSNDLSND
W
With SuperK and LSND Neutrino parametersResonant Oscillation is PossibleWith SNO (Solar) May be just so
The Magnetic field effect changes the Lepton Asymmetry and the Baryon Load of the fireball
Effective Potential for Highly relativistic Effective Potential for Highly relativistic neutrinos in a weakly magnetized neutrinos in a weakly magnetized
medium and their oscillationmedium and their oscillation
EPJC 58, 608 (2008) with WY. P. Hwang
We have calculated the effective potential experienced by highly relativistic neutrinos in a weakly magnetized electronpositron plasma, where momentum dependence finite width correction to the Wpropagator is considered to account for the threshold effect. Magnetars are believed to be sources of TeVPeV neutrinos which are produced due to photomeson and proton proton interaction in their atmosphere.We have studied the resonant oscillation process
of the highly relativisticneutrinos in SGR 180620 atmosphere which is a magnetar. It is shown that, for high energy neutrinos propagating within the magnetar atmosphere, the resonance condition can never be satisfied. On the other hand if GeV neutrinos are produced deep inside the magnetar atmosphere, where the temperature is about 50 keV or more, then these neutrinos can undergo resonant oscillation.
e ,
The coherent forward scattering of low energy neutrinos in The coherent forward scattering of low energy neutrinos in a medium give the matter potentiala medium give the matter potential
V e=2GF N e−N e
This is derived by considering the contact interaction and assuming the momentum transfer smaller than the vector boson mass. For q² ~M²this is no more valid. In this case the energy limit is
E≃M W2/2me≃10
7GeV
W q=−g
q2−M [W ]2
iW MW
W q=−g
q2−M [W ]2 iq2W /MW
Using finite temperature temperature field theory as a tool to calculate the neutrino self energy in a background medium in the presence of a magnetic field, we get
¿
24
¿
d 4 p¿
k =−g2∫ ¿
k=g2
2 ∫d 4 p
24 R S l p LW
q
i S p =∫0
∞
ds e p , sG p , s
=R L=akbu
cb
¿
The dispersion relation of the neutrino in the The dispersion relation of the neutrino in the background is given bybackground is given by
k0−k≃b−c cos
V e=V = 1− 12 e B
me Tcos 2GF N e f sW −N e f −sW
f ±sW =1± sW
1± sW2 sW
2W2 sW=2E me /MW
2
W=W / M W≃0.0266
Reduction due to B field, B~0.01me^2/e, T=0.05 me, 10% reduction Konstandin 06, Sahu 08
The discontinuity in function function f(sw) st sW=1 corresponds to The discontinuity in function function f(sw) st sW=1 corresponds to Wboson production.Wboson production.The calculation of the effective potential of the neutrino in the e+e The calculation of the effective potential of the neutrino in the e+e background.background.Threshold behavior forThreshold behavior for
ee W ee− W−
Application in MagnetarsApplication in Magnetars
SGR 180620SGR 180620
2727thth of October 2004 in our galaxy of October 2004 in our galaxy with ~ 15 Kpc distancewith ~ 15 Kpc distance
E≃3×1046 erg 0.1 sec
Presence of baryons in the fireball are responsiblePresence of baryons in the fireball are responsible for the production of high energy neutrinos throughfor the production of high energy neutrinos through
p , pp
Neutrino oscillation in magnetar atmosphere
P t =2 sin2
2 sin2
t2
=V − cos2 2sin2 2
= m2
2E
V= cos2
Resonance conditionResonance condition
At resonance, the length isAt resonance, the length is
l res=2.5×1010 E ,14 cm
m2 sin 2
On the surface of the magnetar, the photon number On the surface of the magnetar, the photon number density is density is
n≃9.73×1029L47.5 r0, 6
−2 cm−3
T~313keV
By equating the e+eannihilation rate to the local By equating the e+eannihilation rate to the local expansion rate, the remaining pair is given byexpansion rate, the remaining pair is given by
T≃18KeV
N≃6.1×1044 E 46.53 / 4 r 0, 6
−1 / 2 t−11 / 4
Pair temperature is Pair temperature is
at a distance r_{+}at a distance r_{+}
r± ~2.1×109 cm
Piran 05
Number density of photon at this point is
n≃1.8×1026 cm−3
Number density of pair isNumber density of pair is
N e≃2.2×1030 T
me 3 /2
e−me /T cm−3≃6.8×1015cm−3¿
r± ¿
≃2.1×109 cm
The radius is
2 r±
m2cos2 ≃1.7×10−7
Analysis is done by considering the large and small mixingAnalysis is done by considering the large and small mixing
Large Mixing range
We get
Samall Mixing range
We get
The l_res obtained are much larger than r_(+) and the Temp also will be very small at l_res. So High Energy Neutrinos will never satisfy the resonance condition and no supression of their flux due to matter and magnetic field effect.
0.64≤sin22≤0.96
2.8×10−7 eV 2≤ m
2 ≤8.5×10−7 eV 2 , E=1014eV
3.16×1016 cm≤ l res ≤1.1×1017 cm
2×10−3≤sin22≤7×10−3
m
2~10−7 eV 2
l res ~1018cm
2.8×10−7 eV 2≤ m
2 ≤8.5×10−7 eV 2 , E=1014eV
3.16×1016 cm≤ l res ≤1.1×1017 cm
But if the Neutrinos are of GeV energy or less, Temp ~ 50 keV or moreFor large mixing we get:
Resonant oscillation is possible if GeV neutrinos are produced deep inside the Magnetar atmosphere where Temperature is of Order 50 keV or so.
10−3eV 2≤ m
2 3.1×10−3eV 2
6.7×107 cm≤ l res ≤3×108cm r±
300keV18 keV
E =1014eV 1GeV
X= log [ m
2] , Y=log [ sin22 ]
Electromagnetic Effects of neutrinosElectromagnetic Effects of neutrinos
About the electromagnetic properties of a medium that consists of a matter background (electron gas) and a neutrino gas that moves as a whole relative to the electron gas.
Nieves 05
The quantity of interest is the photon selfenergy and from this other macroscopic quantities of physical interest can be determined
In an isotropic medium the most general parametrization of the photon polarization tensor is
=T RL QP P
Consistent with gauge invariance
R= g−Q , Q=u u
u2,=q.u
u= gu , g=g−q q
q2Q=2
−q2
P=iQq u u
=1,0 .
T , L , P scalar functions of Q and . related to dielectric and magnetic permeability functions of the medium
T , L
Activity Constant related to the natural optical activity p
Arises as a result of Parity (P), CP as well as CPT asymmetric effects.
ExampleWeak Interactions violate P and CP at some levelNormal matter is CPTasymmetricActivity Constant is present in all normal matter
In a background if n−n≠0, p≠0
Standard Bing Bang predicts relic neutrino background comparable to CMB radiation. Light from all astrophysical sources travel through this background before reaching to us and if it induces some optical activity , interesting physical effects on Light can be observed.
We compute the photon selfenergy in the
Electron background at rest
and Neutrino background moving
u=1,0
v=v0, V
Both electron and neutrino/antineutrino backgrounds are contributing to the photon polarization tensor
Photon self energy can be expressed as
=T RL QP PP' P
'
Due to neutrino background
Static background Moving background anisotropic
P =i
Q q u P ' =
iQ q v' , v'
=v−uu.v
Mimic Mag. Field
are finite for limit , participate in Macroscopic effects in long wavelength and staticlimit.
P , ' P q0
A class of diagrams which contribute to the photon A class of diagrams which contribute to the photon selfenergy in the presence of a neutrino background areselfenergy in the presence of a neutrino background are
=
e
e
Purely neutrino Purely neutrino backgroundbackground neutrinoneutrino
+electron+electron
One loop diagrams for theelectron selfenergy in a neutrino gas
e = v vA5
V=2 GF [ aeZ=e , , n
−nne
−ne ]
A=2 GF [ beZ=e , , n
−n−ne
−ne ]
Proportional to the difference of neutrino number density
n−n≠0
Pe
= −4 e2A Q [ I1u.v I 2 ]
P' e
= −4 e2A Q I 2
I1=u.vQ2∫
d3 p23 2 E
∂ f e fe
∂E [ q2 p.u−q.u p.q
q22 p.q ]q−q
I2=2 me2∫
d3 p23 2 E
∂∂E [ 1
2 E f e fe
q22p.q ]q−q
T≃Te ,L≃L
e P≃0, q0
i=− ie 2∫ d 4 p
24Tr [ i S e pq i S e p ]
The expressions for and allows us to evaluate and for situations of interest for physical applications
Pe
P' e
I 1 I 2
We consider the regime ≫v Q
Degenerate electron gas
Pe=− e2
32 A pF3
EF3 Q u.v
P' e=− e2
22 A pF
EF
QA=232 GF T 3
=
−
n
−
n
−e
−e
n
MACROSCOPIC ELECTRODYNAMICS
The presence of neutrino gas influence the electromagnetic properties of the system in the static and long wavelength limit q------>0.
We assume the neutrino gas is at rest with respect to the electron gas
v=u , P
'=0
For simplicity
2−Q2
−T±P =0
2−Q2− T±P∓
QV ' P =0 Q∥V
With Finite velocity
F=−i q A−A q
The equation of motion can be written as
−iq F= jext j
ind
We obtain the Maxwell equation
i Q×Bi E=jextj ind
jind=− A
Induced current
The induced current is
j ind=i [1− l E1−
1 Q×Bi
2
Q p
B ]where 1−t=
T
2 , 1−l=
L
q2 , p= p
2
1=1
2
Q2 l− tDielectric constant
Magnetic permeability
Evaluation of Magnetic Field:
i Q×Bi E=j ind
Consider the initial evaluation of magnetic perturbationin the medium
In the long wavelength limit
No external source
1i
≫V QAverage velocity of the background particles
Also
Conductivityof the mediumAll these finally give
=−
2
Q p=−
p
Q
Where
∂ B∂ t
=2∇
2 B ∇×BInduction Equation of Magnetohydrodynamics
An equation of same form was obtained in PRL 92, 131301 (2004) by different method and suggesting a new mechanism for generation of largescale magnetic field in the early Universe as a consequence of neutrinoplasma interaction. The mechanism can result in the selfexcitation of an almost constant magnetic perturbation.
Consider a plane wave magnetic field
B=B ei Q .x− t e
=i Q−
Q2
, = ±
The sign of depends on the sign of the neutrinoantineutrino asymmetry. But one will be damped and another will grow.
B~e∓Q/ ∣∣±Q/ t
Qmax=∣∣
2will grow provided Q∣∣
The mode with max. growth implies
Growth (decay) of Magnetic field
=
2
4,
−1≃
e2
42 T
=2×10−20
2 TGeV
5
GeV
This is the growth rate of the field
Applications:Growth of Magnetic field in Astrophysical objects Where there are JETSAGN, QUASAR, MICROQUASAR,NASCANT NEUTRON STARS,PULSAR, GRB
Internal & External Shocks implies promt & afterglow
Optical activity of the neutrino gas
Photon that propagate through a gas of neutrinos with non zero chemical potential, the left handed and righthanded polarization modes acquire different dispersions.
Due to CP and CPTodd terms induced by neutrino.
Differential time delay
V g± =
∂±
∂Q, t= l
V g−
lV g
− Group velocity
To study the Effect of Velocity dependent term
Wavelength independent Optical rotation
l ∝Q− −Q lIndependent of the wavelength of the propagating wave.
It is like Faraday rotation due to magnetic field
l ∝2
Polarization dependent bending of light
=2 G M
b 1V
2 −1
V−
2
Growth of magnetic perturbation
Growth + anisotropic effect P'
We showed
n−n≠0In a medium with Optically active one
Multi GeV neutrinos from the fireballMulti GeV neutrinos from the fireball
Bahcall & Meszaros Mechanism, 2000
Neutrons can also contribute to the baryonic Neutrons can also contribute to the baryonic component as protons.component as protons.Initial stage of the relativistic flow e, p, n all are Initial stage of the relativistic flow e, p, n all are coupled. p,n through nuclear elastic scattering.coupled. p,n through nuclear elastic scattering.Expansion of the fireballdynamical Expansion of the fireballdynamical decoupling, neutrons and protons have decoupling, neutrons and protons have different velocities, inelastic scattering—pion different velocities, inelastic scattering—pion productionneutrinos productionneutrinos
MeV MeV neutrinoneutrinoss
at collapseat collapse
NN NN
e e
−
pe− n e
Bac, Mes 2000Mes, Rees 2000525 GeV
Neutrons and protons are coupled untilComoving np scatting timelonger than the comoving expansion time
tnp´~
1
np´ c
texp´ ~r / c t np
´ texp´
np´=
L1 4 r2m p c3
nn´/ np
´=
Neutron, proton decoupling during the coasting/ accelerating regime depends on the critical value of the dimensionless entropy
= [ L
4 mp c3 ro 1 ]1 / 4
=3.9×102L521 / 4 ro7
−1 / 4[1] /2−1 /4
i ≤
ii ≥
Two conditions:Two conditions:
i ≤
t np´≥ texp
´ at a radius
rnp / ro= / 3
This radius is beyond the saturation radius
r s / ro~
Here both n & p coast with even after decoupling they coast together due to inertia and the relative velocity is small to have inelastic scattering.
~=const.
ii ≥
Decoupling condition is satisfied
tnp´≥ t exp
´ at a radius
rnp / ro= / −1 /3
Beyond this radius proton can still continue to accelerate with p≃r / ro
Neutrons coast with
nf≃3×102L52
1 /4 ro7−1 / 4 [1 ] / 2−1 / 4 /
−1 / 3
Drift velocity is sufficient to have inelastic scattering and production of pions.
v rel cpion production threthold
´140MeV
At this point tnp´~ texp
´ , rnp≃rpionosphere radius
pn p p−
− e− e
pn nn
e e
pn pno
PRL 85, 1362 (2000)
N n=
1 E
mp c2
~0.83×1053E53 21 400
Total number of neutrons in the fireball Total number of neutrons in the fireball
Pion formation takes place below the ү
-photosphere because, ≪T
=3×10−26 cm2
T =6.65×10−25 cm2
Photons from pion decay has energy
~70 nf
1 z MeV≃10 GeV
Fluence of this photon which is emitted from the skin depth of the photosphere on Earth:
N ~N n P / 4 D p2~10−5 cm2
NeutrinosNeutrinos e e~5 GeV
~10 GeV
Event rate on Earth (km^3 detector)Event rate on Earth (km^3 detector)R =
N t
4 Dp2 Rb Nn
R ~7E53N t39 Rb3 21
4 /3
h652 2−21 z−1 z / year
Burst rate within a Hubble distance/year
Target proton
Distance to the GRB
Coincident with the electromagnetic flashes within 10 sec diff. Followed by120 MeV electron antineutrinos from neutron decay.
The neutrino production The neutrino production
depends ondepends on
Neutron fraction in the Neutron fraction in the fireballfireballdimensionless entropy of the dimensionless entropy of the fireballfireball
Multi-GeV neutrinos from Internal Multi-GeV neutrinos from Internal Dissipation in FireballDissipation in Fireball
Meszaros & Rees mechanism 2000
Below the radiation photosphere internal shocks can lead to the rapid diffusion of neutrons both parallel and perpendicular to the radial direction .
In this case inelastic collision of neutrons with protons can give rise to about 3 GeV neutrinos. Both below and above the critical value of the entropy
, sh ~ 120 , sh ~ 120
In realistic flow there should be inhomogeneities intemporal or angular component. Both types of inhomogeneities implies presence of density gradients and thus the possibility of neutrons to diffuse from one region to another.During this period when the neutron encounter proton with a relative velocity of order v=0.6 c or more this corresponds to the CM energy more than 140 MeV, leading to pion formation and then neutrinos.
To occur with significant probability
l ´~np
´
−1≃ l inhomo
They produce 225 GeV neutrinos
These mechanisms operateEven for low neutron density in the outflowInelastic collision with optical depth > 1 can convert proton to neutron and vice versa.
In ICECUBE, BAIKAL...the predicated event rates are of order 315/ year with sufficiently packed photo tubes. (3050 times)
APJ 541, L5 (2000)
Role of Neutron in GRBs
Changes the dynamics of the fireball (Derishev et. al.)
Dynamical decoupling of the neutron from the rest of the shell will give rise to inelastic n-p scattering and lead to the emission of observable multi-GeV (5-10 GeV) neutrinos (Bahcall, Mészáros, PRL 2000; Mészáros, Rees, APJ 2000).
Role of Neutron in GRBs
Changes the dynamics of the fireball (Derishev et. al.)
Dynamical decoupling of the neutron from the rest of the shell will give rise to inelastic n-p scattering and lead to the emission of observable multi-GeV (5-10 GeV) neutrinos (Bahcall, Mészáros, PRL 2000; Mészáros, Rees, APJ 2000).
Is baryon number a good symmetry of Nature ?
It is believed that Baryon number is not a good symmetry of Nature (Universe is matter dominated) and it require baryon number violating interactions: proton decay,& oscillation (no success so far), oscillation occurs due to ΔB=2 transition
The existence of baryon number violating processes generic prediction of GUT to unify the fundamental forces.
n n
oscillation mechanismn n
N n=12
N n mE
2
=0.6×10−25 N n BG −2
m=n n−1 n n ≃109 sec.
In the presence of a magnetic field, neutrons energy levels are splitted by an amount ΔE=gμB and this is responsible for the oscillation. Due to oscillation, the number of anti-neutron is with
Number of anti-neutron at a distance r from the source is
neutron to proton ration and due to neutron decay.
protons, neutrons and electrons are coupled with the radiation in the expanding jet outflow until the Compton scattering time scale and the elastic n-p scattering time scale are shorter than the co-moving plasma expansion time scale
N n≃12 1 E
m p
e−r / r mE
2
=2×1027 BG
−2
21 E53
100e−r /r
≃1 e−r /r
tTh'≃n p
'Th
−1
tnp'≃n p
'np
−1
t exp'≃r /
np~3×10−26 cm2
np1
rnpLnp
14m p2
~6×1010L52
11002 100
cm
rr npr gives r6×1010 cm 1016 cm
r
The neutrons and protons are coupled until the opacity , which corresponds to neutron, proton decoupling radius The np coupling radius lies So we can neglect the effect of neutron beta decay. Decay of with in the fireball
n pe e
Produced anti-neutron will annihilate with the protons in the background through (also ppbar annihilation) Pion decay
nn
−
0
nn
−
nn0
0
±
±
± e± e e
0
The neutral pion decay will give photons of energies 45 and 71 GeVs.
The optical depth , so GeVs photons will degrade by pair production and can not escape.
The total amount of energy released in annihilation is
A major fraction of it will be in the form of neutrinos.
≫1
n n
n n=2m p N n≃6×1024 E53
100 BG −2
21 erg
Proton anti-proton annihilation, each pion carry energy
Average energy carried by muons is 80% and rest is by neutrinos. in the pion decay.
In muon decay ~1/3 energy is carried by each particle. Average energy of neutrino in muon decay the co-moving frame. In observer frame normalizing at z=1
Energy of muon neutrinos due to pion decay
1.88 GeV /k
, '≃0.5 GeV /k
,≃75 GeV
k
30021z
, k=3,2, 25−37.5 GeV
, ≃56 GeV
k
30021z
, 19−28 GeV
Neutrino Event RateShort and Long GRBs rate within a Hubble
radius of per year, number of events per year in a detector with protons is By considering Earth as the detector with protons and a magnetic field of in the jet outflow the event rate is
Rb~105 Rb5
N t
R~ N t
4D2 Rb Nn
1051 10−6G
R~4h702 Rb5
E53
100N t51300 B
10−6G −2
21 3−222z−21z year−1
Production of neutrinos and anti-neutrinos due to nnbar/ppbar annihilation is inversely proportional to the square of the mag. filed. So if nnbar oscillation exist in the GRBs outflow, mag. field can't be arbitrarily strong or weak.
Very Weak filed enhance neutrino production and take away huge energy.
Is it possible to observe these neutrinos?
May be in future, the Extreme Universe Space Observatory (EUSO) will be able to see it !
OutlookNo other process can give rise to neutrinos
inbetween source and the n-p decoupling radius.
19-38 GeV neutrinos will be produced much before the 5-10 GeV neutrinos due to dynamical decoupling of neutrons
It will tell about the nature of the progenitor of GRBs.
Observation of these multi-GeV neutrinos will be unique signature of Physics Beyond the Standard Model.
t~rnp /2~4.10−6 s
Summary:
We have studied the neutrino propagation in a medium, where we found :
The interaction of neutrino background with an electron background can give rise to the growth of magnetic field.
Resonant Oscillation of MeV neutrinos in the GRB medium with/without Magnetic field and calculation of Baryon Load and Lepton asymmetry.
Possibility of Resonant Oscillation of neutrinos in the Magnetar Atmosphere.