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Make an estimate before every calculation, try a simple physical argument (symmetry! invariance! conservation!) before every derivation, guess the answer to every paradox and puzzle. John Wheeler's First Moral Principle from "Spacetime Physics (Taylor – Wheeler, 2 nd ed.)”
Citation preview
Cosmological constantEinstein (1917)
Universe
baryons
52768
ldquoHiggsrdquo condensate Englert-Brout Higgs (1964)
barequark
3
quark
ldquoChiralrdquo condensateNambu (1960)
quark
3
hadron
QCD Spectral Functions and DileptonsT Hatsuda (RIKEN)
Condensates hArr Elementary excitations
OutlineOutline
IQCD symmetries II Chiral order parameters
III In-medium hadronsIV Summary
ldquo The Phase Diagram of Dense QCDrdquo K Fukushima + TH Rep Prog Phys 74 (2011) 014001
ldquo Hadron Properties in the Nuclear Mediumrdquo R Hayano + TH Rev Mod Phys 82 (2010) 2949
ldquo QCD Constraints on Vector Mesons at finite T and Densityrdquo TH httpwww-rnclblgovDLSDLS_WWW_FilesDLSWorkshopdileptonhtml (1997)
Make an estimate before every calculation try a simple physical argument (symmetry invariance conservation) before every derivation guess the answer to every paradox and puzzle
John Wheelers First Moral Principle from Spacetime Physics (Taylor ndash Wheeler 2nd ed)rdquo
Symmetry realization in QCD vacuum
Chiral basis
QCD Lagrangian
classical QCD symmetry (m=0)
qqmqAtiqGGL aaa
a g )(41
Quantum QCD vacuum (m=0) Chiral condensate spontaneous mass generation
Axial anomaly quantum violation of U(1)A
Dim3 chiral condensate in QCD
Banks-Casher relation (1980)
0
0
Di Vecchia-Veneziano formula (1980)
Gell-Mann-Oakes-Renner (GOR) formula (1968)
Exam
ples
Axial rotation Axial Charge
Order parameters NOT unique
II Chiral order parameters
Order parameter = 0 (no SSB)ne 0 (SSB)
θ
σ （６００）
Spectral evidence of SSB in QCD
ltPPgt
ltSSgt
ltVVgt
ltAAgt
TH LBNL WS (1997)
ALEPH Collaboration Phys Rep 421 (2005) 191
ltVVgt - ltAAgt fromτ-decays at LEP-1 ρ V
(s)s
ρ A(s
)s
[ρV(s
)-ρA(s
)] s
Energy weighted ldquochiralrdquo sum rules from QCD (mq=0)
Dim6 chiral condensate
Koike Lee + TH NuclPhys B394 (1993) 221Kapusta and Shuryak PRD 49 (1994) 4694Klingl Kaiser and Weise NPA 624 (1997) 527
-ρpQCD(ω))
-ρpQCD(ω))= C4ltGGgt
-ρpQCD(ω))= C6ltChiral invgt +C6rsquoltchiral non-invgt
Dim4 gluon condensate
Dim6 quark and gluon condensates
Dilepton data(after Cocktail subtraction) Space-time average
(by hydro or other models)
Lattice QCD simulations (with gradient flow method)
+
Energy weighted ldquovectorrdquo sum rules from QCD (mq=0)III In-medium hadrons
TH LBNL WS (1997)Slide p31
cf GLS sum rule Adler sum rule Bjorken sum rule
QGP
Quark-Gluon Plasma
Quark superfluid
Hadronphase
Chiral symmetry is always broken at finite density
Baryon superfluid
Hadron-Quark Continuity in dense QCD （ Nc=3 Nf=3 ）
cond
ensa
tes
Continuity in the ground state Tachibana Yamamoto + TH PRD78 (rsquo08)
Vector Mesons = Gluons Baryons = Quarks
Possible fate of hadrons at high density （ Nc=3 Nf=3 ）
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
Baryons (8)Quarks (9)
Continuity in the excited state Schafer amp Wilczek PRL 82 (rsquo99)
Nonet vector mesons(heavy)
Octetvector mesons(light)
Octet gluons in CFL mg=1362Δ Gusynin amp Shovkovy NPA700 (2002) Malekzadeh amp Rischke PRD73 (2006)
TH Tachibana and Yamamoto PRD78 (2008)
Spectral continuity of vector mesons
At high density
At intermediate density
At low density
Mass formula from Finite Energy Sum Rules
IV SummaryI Chiral order parameters
not unique Dim3 condensate Dim6 condensate etc
II In-medium hadrons chiral restoration can be seen in spectral degeneracy moment analysis is important for model independence interesting possibility of hadron-quark crossover (Vector mesons = Gluons Baryons = Quarks)
Back up slides
Vector current
Current correlation function
QCD sum rules in the superconducting medium
Operator Product Expansion (OPE) up to O(1Q6)
4-quark condensate
Diquark condensate
Chiral condensate
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
baryons (8)Quarks (9)
Continuity in the excited state
Schafer and Wilczek PRL 82 (1999)
Generalized Gell-Mann-Oakes-Renner relation Yamamoto Tachibana Baym + TH PR D76 (rsquo07)
Continuity of vector mesons Tachibana Yamamoto +TH PRD78 (2008)
Explicit realization of spectral continuity
Possible fate of hadrons at high density （ Nc=3 Nf=3 ）
Vector Mesons = Gluons Baryons = Quarks
cond
ensa
tes Continuity in the ground state
Yamamoto Tachibana Baym + TH PRL97(rsquo06) PRD76 (rsquo07)
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
baryons (8)Quarks (9)
Continuity in the excited state
Schafer and Wilczek PRL 82 (1999)
Hadron-quark continuity in dense QCD
cond
ensa
tes Continuity in the ground state
Hatsuda Tachibana Yamamoto amp Baym PRL 97 (2006)
TH Slide p2(1997)
httpwww-rnclblgovDLSDLS_WWW_FilesDLSWorkshopdileptonhtml
I Why SPF is important
FLAG Collaboration update( July 26 2013) httpitpwikiunibechflag
Running masses mq(Q)
quark masses (from lattice QCD)
[MeV] (MS-bar 2GeV)
mu 216 (9)(7)
md 468 (14)(7)
ms 938 (24)
Running coupling αs(Q)=g24π
PDG (2012) httppdglblgov
I Status of QCD
Hadron masses from Lattice QCD
Improved Wilson + Iwasaki gauge action a = 009 fm L=29 fm mπ=135 MeV PACS-CS Coll Phys Rev D 81 074503 (2010)
3 accuracy
rArr L~96 fm mπ=135 MeV on K-computer underway
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
In-medium hadrons
Complex pole (even for the pion)
One-parameter example (Tne0)
For the pion f(x) and g(x) can be evaluated for small x See eg Jido Kunhihiro + TH Phys Lett B670 (2008) In general experimental inputs are really necessary Sometimes spectral function is better to be studied
Dim3 Chiral condensate in the medium
Lattice QCD (2+1)-flavorBorsanyi et al JHEP 1009 (2010)
Finite Temperature (LQCD)
Nuclear chiral perturbation Kaiser et al PRC 77 (2008)
Finite baryon density (χPT)
Mesic nuclei
2 Individual properties of NG and ldquoHiggsrdquo bosons π K η (NG) σ (Higgs) ηrsquo (anomaly)
σ2γ η2γ ηrsquo2γ
Dileptons3 Individual properties of vector bosons ρ ω and φ
Precisionsystematic studies(dispersion relation different targets hellip)
1 Spectral difference between chiral partners π-σ ρ-a1 ω-f1 etc Determination of D=6 chiral condensates in the vacuumTau-decay in nuclei
Wish list
TH Slide p7(1997)
III Exact sum rules in QCD medium
TH Slide p20(1997)
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
OutlineOutline
IQCD symmetries II Chiral order parameters
III In-medium hadronsIV Summary
ldquo The Phase Diagram of Dense QCDrdquo K Fukushima + TH Rep Prog Phys 74 (2011) 014001
ldquo Hadron Properties in the Nuclear Mediumrdquo R Hayano + TH Rev Mod Phys 82 (2010) 2949
ldquo QCD Constraints on Vector Mesons at finite T and Densityrdquo TH httpwww-rnclblgovDLSDLS_WWW_FilesDLSWorkshopdileptonhtml (1997)
Make an estimate before every calculation try a simple physical argument (symmetry invariance conservation) before every derivation guess the answer to every paradox and puzzle
John Wheelers First Moral Principle from Spacetime Physics (Taylor ndash Wheeler 2nd ed)rdquo
Symmetry realization in QCD vacuum
Chiral basis
QCD Lagrangian
classical QCD symmetry (m=0)
qqmqAtiqGGL aaa
a g )(41
Quantum QCD vacuum (m=0) Chiral condensate spontaneous mass generation
Axial anomaly quantum violation of U(1)A
Dim3 chiral condensate in QCD
Banks-Casher relation (1980)
0
0
Di Vecchia-Veneziano formula (1980)
Gell-Mann-Oakes-Renner (GOR) formula (1968)
Exam
ples
Axial rotation Axial Charge
Order parameters NOT unique
II Chiral order parameters
Order parameter = 0 (no SSB)ne 0 (SSB)
θ
σ （６００）
Spectral evidence of SSB in QCD
ltPPgt
ltSSgt
ltVVgt
ltAAgt
TH LBNL WS (1997)
ALEPH Collaboration Phys Rep 421 (2005) 191
ltVVgt - ltAAgt fromτ-decays at LEP-1 ρ V
(s)s
ρ A(s
)s
[ρV(s
)-ρA(s
)] s
Energy weighted ldquochiralrdquo sum rules from QCD (mq=0)
Dim6 chiral condensate
Koike Lee + TH NuclPhys B394 (1993) 221Kapusta and Shuryak PRD 49 (1994) 4694Klingl Kaiser and Weise NPA 624 (1997) 527
-ρpQCD(ω))
-ρpQCD(ω))= C4ltGGgt
-ρpQCD(ω))= C6ltChiral invgt +C6rsquoltchiral non-invgt
Dim4 gluon condensate
Dim6 quark and gluon condensates
Dilepton data(after Cocktail subtraction) Space-time average
(by hydro or other models)
Lattice QCD simulations (with gradient flow method)
+
Energy weighted ldquovectorrdquo sum rules from QCD (mq=0)III In-medium hadrons
TH LBNL WS (1997)Slide p31
cf GLS sum rule Adler sum rule Bjorken sum rule
QGP
Quark-Gluon Plasma
Quark superfluid
Hadronphase
Chiral symmetry is always broken at finite density
Baryon superfluid
Hadron-Quark Continuity in dense QCD （ Nc=3 Nf=3 ）
cond
ensa
tes
Continuity in the ground state Tachibana Yamamoto + TH PRD78 (rsquo08)
Vector Mesons = Gluons Baryons = Quarks
Possible fate of hadrons at high density （ Nc=3 Nf=3 ）
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
Baryons (8)Quarks (9)
Continuity in the excited state Schafer amp Wilczek PRL 82 (rsquo99)
Nonet vector mesons(heavy)
Octetvector mesons(light)
Octet gluons in CFL mg=1362Δ Gusynin amp Shovkovy NPA700 (2002) Malekzadeh amp Rischke PRD73 (2006)
TH Tachibana and Yamamoto PRD78 (2008)
Spectral continuity of vector mesons
At high density
At intermediate density
At low density
Mass formula from Finite Energy Sum Rules
IV SummaryI Chiral order parameters
not unique Dim3 condensate Dim6 condensate etc
II In-medium hadrons chiral restoration can be seen in spectral degeneracy moment analysis is important for model independence interesting possibility of hadron-quark crossover (Vector mesons = Gluons Baryons = Quarks)
Back up slides
Vector current
Current correlation function
QCD sum rules in the superconducting medium
Operator Product Expansion (OPE) up to O(1Q6)
4-quark condensate
Diquark condensate
Chiral condensate
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
baryons (8)Quarks (9)
Continuity in the excited state
Schafer and Wilczek PRL 82 (1999)
Generalized Gell-Mann-Oakes-Renner relation Yamamoto Tachibana Baym + TH PR D76 (rsquo07)
Continuity of vector mesons Tachibana Yamamoto +TH PRD78 (2008)
Explicit realization of spectral continuity
Possible fate of hadrons at high density （ Nc=3 Nf=3 ）
Vector Mesons = Gluons Baryons = Quarks
cond
ensa
tes Continuity in the ground state
Yamamoto Tachibana Baym + TH PRL97(rsquo06) PRD76 (rsquo07)
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
baryons (8)Quarks (9)
Continuity in the excited state
Schafer and Wilczek PRL 82 (1999)
Hadron-quark continuity in dense QCD
cond
ensa
tes Continuity in the ground state
Hatsuda Tachibana Yamamoto amp Baym PRL 97 (2006)
TH Slide p2(1997)
httpwww-rnclblgovDLSDLS_WWW_FilesDLSWorkshopdileptonhtml
I Why SPF is important
FLAG Collaboration update( July 26 2013) httpitpwikiunibechflag
Running masses mq(Q)
quark masses (from lattice QCD)
[MeV] (MS-bar 2GeV)
mu 216 (9)(7)
md 468 (14)(7)
ms 938 (24)
Running coupling αs(Q)=g24π
PDG (2012) httppdglblgov
I Status of QCD
Hadron masses from Lattice QCD
Improved Wilson + Iwasaki gauge action a = 009 fm L=29 fm mπ=135 MeV PACS-CS Coll Phys Rev D 81 074503 (2010)
3 accuracy
rArr L~96 fm mπ=135 MeV on K-computer underway
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
In-medium hadrons
Complex pole (even for the pion)
One-parameter example (Tne0)
For the pion f(x) and g(x) can be evaluated for small x See eg Jido Kunhihiro + TH Phys Lett B670 (2008) In general experimental inputs are really necessary Sometimes spectral function is better to be studied
Dim3 Chiral condensate in the medium
Lattice QCD (2+1)-flavorBorsanyi et al JHEP 1009 (2010)
Finite Temperature (LQCD)
Nuclear chiral perturbation Kaiser et al PRC 77 (2008)
Finite baryon density (χPT)
Mesic nuclei
2 Individual properties of NG and ldquoHiggsrdquo bosons π K η (NG) σ (Higgs) ηrsquo (anomaly)
σ2γ η2γ ηrsquo2γ
Dileptons3 Individual properties of vector bosons ρ ω and φ
Precisionsystematic studies(dispersion relation different targets hellip)
1 Spectral difference between chiral partners π-σ ρ-a1 ω-f1 etc Determination of D=6 chiral condensates in the vacuumTau-decay in nuclei
Wish list
TH Slide p7(1997)
III Exact sum rules in QCD medium
TH Slide p20(1997)
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
Make an estimate before every calculation try a simple physical argument (symmetry invariance conservation) before every derivation guess the answer to every paradox and puzzle
John Wheelers First Moral Principle from Spacetime Physics (Taylor ndash Wheeler 2nd ed)rdquo
Symmetry realization in QCD vacuum
Chiral basis
QCD Lagrangian
classical QCD symmetry (m=0)
qqmqAtiqGGL aaa
a g )(41
Quantum QCD vacuum (m=0) Chiral condensate spontaneous mass generation
Axial anomaly quantum violation of U(1)A
Dim3 chiral condensate in QCD
Banks-Casher relation (1980)
0
0
Di Vecchia-Veneziano formula (1980)
Gell-Mann-Oakes-Renner (GOR) formula (1968)
Exam
ples
Axial rotation Axial Charge
Order parameters NOT unique
II Chiral order parameters
Order parameter = 0 (no SSB)ne 0 (SSB)
θ
σ （６００）
Spectral evidence of SSB in QCD
ltPPgt
ltSSgt
ltVVgt
ltAAgt
TH LBNL WS (1997)
ALEPH Collaboration Phys Rep 421 (2005) 191
ltVVgt - ltAAgt fromτ-decays at LEP-1 ρ V
(s)s
ρ A(s
)s
[ρV(s
)-ρA(s
)] s
Energy weighted ldquochiralrdquo sum rules from QCD (mq=0)
Dim6 chiral condensate
Koike Lee + TH NuclPhys B394 (1993) 221Kapusta and Shuryak PRD 49 (1994) 4694Klingl Kaiser and Weise NPA 624 (1997) 527
-ρpQCD(ω))
-ρpQCD(ω))= C4ltGGgt
-ρpQCD(ω))= C6ltChiral invgt +C6rsquoltchiral non-invgt
Dim4 gluon condensate
Dim6 quark and gluon condensates
Dilepton data(after Cocktail subtraction) Space-time average
(by hydro or other models)
Lattice QCD simulations (with gradient flow method)
+
Energy weighted ldquovectorrdquo sum rules from QCD (mq=0)III In-medium hadrons
TH LBNL WS (1997)Slide p31
cf GLS sum rule Adler sum rule Bjorken sum rule
QGP
Quark-Gluon Plasma
Quark superfluid
Hadronphase
Chiral symmetry is always broken at finite density
Baryon superfluid
Hadron-Quark Continuity in dense QCD （ Nc=3 Nf=3 ）
cond
ensa
tes
Continuity in the ground state Tachibana Yamamoto + TH PRD78 (rsquo08)
Vector Mesons = Gluons Baryons = Quarks
Possible fate of hadrons at high density （ Nc=3 Nf=3 ）
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
Baryons (8)Quarks (9)
Continuity in the excited state Schafer amp Wilczek PRL 82 (rsquo99)
Nonet vector mesons(heavy)
Octetvector mesons(light)
Octet gluons in CFL mg=1362Δ Gusynin amp Shovkovy NPA700 (2002) Malekzadeh amp Rischke PRD73 (2006)
TH Tachibana and Yamamoto PRD78 (2008)
Spectral continuity of vector mesons
At high density
At intermediate density
At low density
Mass formula from Finite Energy Sum Rules
IV SummaryI Chiral order parameters
not unique Dim3 condensate Dim6 condensate etc
II In-medium hadrons chiral restoration can be seen in spectral degeneracy moment analysis is important for model independence interesting possibility of hadron-quark crossover (Vector mesons = Gluons Baryons = Quarks)
Back up slides
Vector current
Current correlation function
QCD sum rules in the superconducting medium
Operator Product Expansion (OPE) up to O(1Q6)
4-quark condensate
Diquark condensate
Chiral condensate
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
baryons (8)Quarks (9)
Continuity in the excited state
Schafer and Wilczek PRL 82 (1999)
Generalized Gell-Mann-Oakes-Renner relation Yamamoto Tachibana Baym + TH PR D76 (rsquo07)
Continuity of vector mesons Tachibana Yamamoto +TH PRD78 (2008)
Explicit realization of spectral continuity
Possible fate of hadrons at high density （ Nc=3 Nf=3 ）
Vector Mesons = Gluons Baryons = Quarks
cond
ensa
tes Continuity in the ground state
Yamamoto Tachibana Baym + TH PRL97(rsquo06) PRD76 (rsquo07)
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
baryons (8)Quarks (9)
Continuity in the excited state
Schafer and Wilczek PRL 82 (1999)
Hadron-quark continuity in dense QCD
cond
ensa
tes Continuity in the ground state
Hatsuda Tachibana Yamamoto amp Baym PRL 97 (2006)
TH Slide p2(1997)
httpwww-rnclblgovDLSDLS_WWW_FilesDLSWorkshopdileptonhtml
I Why SPF is important
FLAG Collaboration update( July 26 2013) httpitpwikiunibechflag
Running masses mq(Q)
quark masses (from lattice QCD)
[MeV] (MS-bar 2GeV)
mu 216 (9)(7)
md 468 (14)(7)
ms 938 (24)
Running coupling αs(Q)=g24π
PDG (2012) httppdglblgov
I Status of QCD
Hadron masses from Lattice QCD
Improved Wilson + Iwasaki gauge action a = 009 fm L=29 fm mπ=135 MeV PACS-CS Coll Phys Rev D 81 074503 (2010)
3 accuracy
rArr L~96 fm mπ=135 MeV on K-computer underway
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
In-medium hadrons
Complex pole (even for the pion)
One-parameter example (Tne0)
For the pion f(x) and g(x) can be evaluated for small x See eg Jido Kunhihiro + TH Phys Lett B670 (2008) In general experimental inputs are really necessary Sometimes spectral function is better to be studied
Dim3 Chiral condensate in the medium
Lattice QCD (2+1)-flavorBorsanyi et al JHEP 1009 (2010)
Finite Temperature (LQCD)
Nuclear chiral perturbation Kaiser et al PRC 77 (2008)
Finite baryon density (χPT)
Mesic nuclei
2 Individual properties of NG and ldquoHiggsrdquo bosons π K η (NG) σ (Higgs) ηrsquo (anomaly)
σ2γ η2γ ηrsquo2γ
Dileptons3 Individual properties of vector bosons ρ ω and φ
Precisionsystematic studies(dispersion relation different targets hellip)
1 Spectral difference between chiral partners π-σ ρ-a1 ω-f1 etc Determination of D=6 chiral condensates in the vacuumTau-decay in nuclei
Wish list
TH Slide p7(1997)
III Exact sum rules in QCD medium
TH Slide p20(1997)
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
Symmetry realization in QCD vacuum
Chiral basis
QCD Lagrangian
classical QCD symmetry (m=0)
qqmqAtiqGGL aaa
a g )(41
Quantum QCD vacuum (m=0) Chiral condensate spontaneous mass generation
Axial anomaly quantum violation of U(1)A
Dim3 chiral condensate in QCD
Banks-Casher relation (1980)
0
0
Di Vecchia-Veneziano formula (1980)
Gell-Mann-Oakes-Renner (GOR) formula (1968)
Exam
ples
Axial rotation Axial Charge
Order parameters NOT unique
II Chiral order parameters
Order parameter = 0 (no SSB)ne 0 (SSB)
θ
σ （６００）
Spectral evidence of SSB in QCD
ltPPgt
ltSSgt
ltVVgt
ltAAgt
TH LBNL WS (1997)
ALEPH Collaboration Phys Rep 421 (2005) 191
ltVVgt - ltAAgt fromτ-decays at LEP-1 ρ V
(s)s
ρ A(s
)s
[ρV(s
)-ρA(s
)] s
Energy weighted ldquochiralrdquo sum rules from QCD (mq=0)
Dim6 chiral condensate
Koike Lee + TH NuclPhys B394 (1993) 221Kapusta and Shuryak PRD 49 (1994) 4694Klingl Kaiser and Weise NPA 624 (1997) 527
-ρpQCD(ω))
-ρpQCD(ω))= C4ltGGgt
-ρpQCD(ω))= C6ltChiral invgt +C6rsquoltchiral non-invgt
Dim4 gluon condensate
Dim6 quark and gluon condensates
Dilepton data(after Cocktail subtraction) Space-time average
(by hydro or other models)
Lattice QCD simulations (with gradient flow method)
+
Energy weighted ldquovectorrdquo sum rules from QCD (mq=0)III In-medium hadrons
TH LBNL WS (1997)Slide p31
cf GLS sum rule Adler sum rule Bjorken sum rule
QGP
Quark-Gluon Plasma
Quark superfluid
Hadronphase
Chiral symmetry is always broken at finite density
Baryon superfluid
Hadron-Quark Continuity in dense QCD （ Nc=3 Nf=3 ）
cond
ensa
tes
Continuity in the ground state Tachibana Yamamoto + TH PRD78 (rsquo08)
Vector Mesons = Gluons Baryons = Quarks
Possible fate of hadrons at high density （ Nc=3 Nf=3 ）
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
Baryons (8)Quarks (9)
Continuity in the excited state Schafer amp Wilczek PRL 82 (rsquo99)
Nonet vector mesons(heavy)
Octetvector mesons(light)
Octet gluons in CFL mg=1362Δ Gusynin amp Shovkovy NPA700 (2002) Malekzadeh amp Rischke PRD73 (2006)
TH Tachibana and Yamamoto PRD78 (2008)
Spectral continuity of vector mesons
At high density
At intermediate density
At low density
Mass formula from Finite Energy Sum Rules
IV SummaryI Chiral order parameters
not unique Dim3 condensate Dim6 condensate etc
II In-medium hadrons chiral restoration can be seen in spectral degeneracy moment analysis is important for model independence interesting possibility of hadron-quark crossover (Vector mesons = Gluons Baryons = Quarks)
Back up slides
Vector current
Current correlation function
QCD sum rules in the superconducting medium
Operator Product Expansion (OPE) up to O(1Q6)
4-quark condensate
Diquark condensate
Chiral condensate
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
baryons (8)Quarks (9)
Continuity in the excited state
Schafer and Wilczek PRL 82 (1999)
Generalized Gell-Mann-Oakes-Renner relation Yamamoto Tachibana Baym + TH PR D76 (rsquo07)
Continuity of vector mesons Tachibana Yamamoto +TH PRD78 (2008)
Explicit realization of spectral continuity
Possible fate of hadrons at high density （ Nc=3 Nf=3 ）
Vector Mesons = Gluons Baryons = Quarks
cond
ensa
tes Continuity in the ground state
Yamamoto Tachibana Baym + TH PRL97(rsquo06) PRD76 (rsquo07)
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
baryons (8)Quarks (9)
Continuity in the excited state
Schafer and Wilczek PRL 82 (1999)
Hadron-quark continuity in dense QCD
cond
ensa
tes Continuity in the ground state
Hatsuda Tachibana Yamamoto amp Baym PRL 97 (2006)
TH Slide p2(1997)
httpwww-rnclblgovDLSDLS_WWW_FilesDLSWorkshopdileptonhtml
I Why SPF is important
FLAG Collaboration update( July 26 2013) httpitpwikiunibechflag
Running masses mq(Q)
quark masses (from lattice QCD)
[MeV] (MS-bar 2GeV)
mu 216 (9)(7)
md 468 (14)(7)
ms 938 (24)
Running coupling αs(Q)=g24π
PDG (2012) httppdglblgov
I Status of QCD
Hadron masses from Lattice QCD
Improved Wilson + Iwasaki gauge action a = 009 fm L=29 fm mπ=135 MeV PACS-CS Coll Phys Rev D 81 074503 (2010)
3 accuracy
rArr L~96 fm mπ=135 MeV on K-computer underway
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
In-medium hadrons
Complex pole (even for the pion)
One-parameter example (Tne0)
For the pion f(x) and g(x) can be evaluated for small x See eg Jido Kunhihiro + TH Phys Lett B670 (2008) In general experimental inputs are really necessary Sometimes spectral function is better to be studied
Dim3 Chiral condensate in the medium
Lattice QCD (2+1)-flavorBorsanyi et al JHEP 1009 (2010)
Finite Temperature (LQCD)
Nuclear chiral perturbation Kaiser et al PRC 77 (2008)
Finite baryon density (χPT)
Mesic nuclei
2 Individual properties of NG and ldquoHiggsrdquo bosons π K η (NG) σ (Higgs) ηrsquo (anomaly)
σ2γ η2γ ηrsquo2γ
Dileptons3 Individual properties of vector bosons ρ ω and φ
Precisionsystematic studies(dispersion relation different targets hellip)
1 Spectral difference between chiral partners π-σ ρ-a1 ω-f1 etc Determination of D=6 chiral condensates in the vacuumTau-decay in nuclei
Wish list
TH Slide p7(1997)
III Exact sum rules in QCD medium
TH Slide p20(1997)
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
Dim3 chiral condensate in QCD
Banks-Casher relation (1980)
0
0
Di Vecchia-Veneziano formula (1980)
Gell-Mann-Oakes-Renner (GOR) formula (1968)
Exam
ples
Axial rotation Axial Charge
Order parameters NOT unique
II Chiral order parameters
Order parameter = 0 (no SSB)ne 0 (SSB)
θ
σ （６００）
Spectral evidence of SSB in QCD
ltPPgt
ltSSgt
ltVVgt
ltAAgt
TH LBNL WS (1997)
ALEPH Collaboration Phys Rep 421 (2005) 191
ltVVgt - ltAAgt fromτ-decays at LEP-1 ρ V
(s)s
ρ A(s
)s
[ρV(s
)-ρA(s
)] s
Energy weighted ldquochiralrdquo sum rules from QCD (mq=0)
Dim6 chiral condensate
Koike Lee + TH NuclPhys B394 (1993) 221Kapusta and Shuryak PRD 49 (1994) 4694Klingl Kaiser and Weise NPA 624 (1997) 527
-ρpQCD(ω))
-ρpQCD(ω))= C4ltGGgt
-ρpQCD(ω))= C6ltChiral invgt +C6rsquoltchiral non-invgt
Dim4 gluon condensate
Dim6 quark and gluon condensates
Dilepton data(after Cocktail subtraction) Space-time average
(by hydro or other models)
Lattice QCD simulations (with gradient flow method)
+
Energy weighted ldquovectorrdquo sum rules from QCD (mq=0)III In-medium hadrons
TH LBNL WS (1997)Slide p31
cf GLS sum rule Adler sum rule Bjorken sum rule
QGP
Quark-Gluon Plasma
Quark superfluid
Hadronphase
Chiral symmetry is always broken at finite density
Baryon superfluid
Hadron-Quark Continuity in dense QCD （ Nc=3 Nf=3 ）
cond
ensa
tes
Continuity in the ground state Tachibana Yamamoto + TH PRD78 (rsquo08)
Vector Mesons = Gluons Baryons = Quarks
Possible fate of hadrons at high density （ Nc=3 Nf=3 ）
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
Baryons (8)Quarks (9)
Continuity in the excited state Schafer amp Wilczek PRL 82 (rsquo99)
Nonet vector mesons(heavy)
Octetvector mesons(light)
Octet gluons in CFL mg=1362Δ Gusynin amp Shovkovy NPA700 (2002) Malekzadeh amp Rischke PRD73 (2006)
TH Tachibana and Yamamoto PRD78 (2008)
Spectral continuity of vector mesons
At high density
At intermediate density
At low density
Mass formula from Finite Energy Sum Rules
IV SummaryI Chiral order parameters
not unique Dim3 condensate Dim6 condensate etc
II In-medium hadrons chiral restoration can be seen in spectral degeneracy moment analysis is important for model independence interesting possibility of hadron-quark crossover (Vector mesons = Gluons Baryons = Quarks)
Back up slides
Vector current
Current correlation function
QCD sum rules in the superconducting medium
Operator Product Expansion (OPE) up to O(1Q6)
4-quark condensate
Diquark condensate
Chiral condensate
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
baryons (8)Quarks (9)
Continuity in the excited state
Schafer and Wilczek PRL 82 (1999)
Generalized Gell-Mann-Oakes-Renner relation Yamamoto Tachibana Baym + TH PR D76 (rsquo07)
Continuity of vector mesons Tachibana Yamamoto +TH PRD78 (2008)
Explicit realization of spectral continuity
Possible fate of hadrons at high density （ Nc=3 Nf=3 ）
Vector Mesons = Gluons Baryons = Quarks
cond
ensa
tes Continuity in the ground state
Yamamoto Tachibana Baym + TH PRL97(rsquo06) PRD76 (rsquo07)
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
baryons (8)Quarks (9)
Continuity in the excited state
Schafer and Wilczek PRL 82 (1999)
Hadron-quark continuity in dense QCD
cond
ensa
tes Continuity in the ground state
Hatsuda Tachibana Yamamoto amp Baym PRL 97 (2006)
TH Slide p2(1997)
httpwww-rnclblgovDLSDLS_WWW_FilesDLSWorkshopdileptonhtml
I Why SPF is important
FLAG Collaboration update( July 26 2013) httpitpwikiunibechflag
Running masses mq(Q)
quark masses (from lattice QCD)
[MeV] (MS-bar 2GeV)
mu 216 (9)(7)
md 468 (14)(7)
ms 938 (24)
Running coupling αs(Q)=g24π
PDG (2012) httppdglblgov
I Status of QCD
Hadron masses from Lattice QCD
Improved Wilson + Iwasaki gauge action a = 009 fm L=29 fm mπ=135 MeV PACS-CS Coll Phys Rev D 81 074503 (2010)
3 accuracy
rArr L~96 fm mπ=135 MeV on K-computer underway
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
In-medium hadrons
Complex pole (even for the pion)
One-parameter example (Tne0)
For the pion f(x) and g(x) can be evaluated for small x See eg Jido Kunhihiro + TH Phys Lett B670 (2008) In general experimental inputs are really necessary Sometimes spectral function is better to be studied
Dim3 Chiral condensate in the medium
Lattice QCD (2+1)-flavorBorsanyi et al JHEP 1009 (2010)
Finite Temperature (LQCD)
Nuclear chiral perturbation Kaiser et al PRC 77 (2008)
Finite baryon density (χPT)
Mesic nuclei
2 Individual properties of NG and ldquoHiggsrdquo bosons π K η (NG) σ (Higgs) ηrsquo (anomaly)
σ2γ η2γ ηrsquo2γ
Dileptons3 Individual properties of vector bosons ρ ω and φ
Precisionsystematic studies(dispersion relation different targets hellip)
1 Spectral difference between chiral partners π-σ ρ-a1 ω-f1 etc Determination of D=6 chiral condensates in the vacuumTau-decay in nuclei
Wish list
TH Slide p7(1997)
III Exact sum rules in QCD medium
TH Slide p20(1997)
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
Exam
ples
Axial rotation Axial Charge
Order parameters NOT unique
II Chiral order parameters
Order parameter = 0 (no SSB)ne 0 (SSB)
θ
σ （６００）
Spectral evidence of SSB in QCD
ltPPgt
ltSSgt
ltVVgt
ltAAgt
TH LBNL WS (1997)
ALEPH Collaboration Phys Rep 421 (2005) 191
ltVVgt - ltAAgt fromτ-decays at LEP-1 ρ V
(s)s
ρ A(s
)s
[ρV(s
)-ρA(s
)] s
Energy weighted ldquochiralrdquo sum rules from QCD (mq=0)
Dim6 chiral condensate
Koike Lee + TH NuclPhys B394 (1993) 221Kapusta and Shuryak PRD 49 (1994) 4694Klingl Kaiser and Weise NPA 624 (1997) 527
-ρpQCD(ω))
-ρpQCD(ω))= C4ltGGgt
-ρpQCD(ω))= C6ltChiral invgt +C6rsquoltchiral non-invgt
Dim4 gluon condensate
Dim6 quark and gluon condensates
Dilepton data(after Cocktail subtraction) Space-time average
(by hydro or other models)
Lattice QCD simulations (with gradient flow method)
+
Energy weighted ldquovectorrdquo sum rules from QCD (mq=0)III In-medium hadrons
TH LBNL WS (1997)Slide p31
cf GLS sum rule Adler sum rule Bjorken sum rule
QGP
Quark-Gluon Plasma
Quark superfluid
Hadronphase
Chiral symmetry is always broken at finite density
Baryon superfluid
Hadron-Quark Continuity in dense QCD （ Nc=3 Nf=3 ）
cond
ensa
tes
Continuity in the ground state Tachibana Yamamoto + TH PRD78 (rsquo08)
Vector Mesons = Gluons Baryons = Quarks
Possible fate of hadrons at high density （ Nc=3 Nf=3 ）
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
Baryons (8)Quarks (9)
Continuity in the excited state Schafer amp Wilczek PRL 82 (rsquo99)
Nonet vector mesons(heavy)
Octetvector mesons(light)
Octet gluons in CFL mg=1362Δ Gusynin amp Shovkovy NPA700 (2002) Malekzadeh amp Rischke PRD73 (2006)
TH Tachibana and Yamamoto PRD78 (2008)
Spectral continuity of vector mesons
At high density
At intermediate density
At low density
Mass formula from Finite Energy Sum Rules
IV SummaryI Chiral order parameters
not unique Dim3 condensate Dim6 condensate etc
II In-medium hadrons chiral restoration can be seen in spectral degeneracy moment analysis is important for model independence interesting possibility of hadron-quark crossover (Vector mesons = Gluons Baryons = Quarks)
Back up slides
Vector current
Current correlation function
QCD sum rules in the superconducting medium
Operator Product Expansion (OPE) up to O(1Q6)
4-quark condensate
Diquark condensate
Chiral condensate
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
baryons (8)Quarks (9)
Continuity in the excited state
Schafer and Wilczek PRL 82 (1999)
Generalized Gell-Mann-Oakes-Renner relation Yamamoto Tachibana Baym + TH PR D76 (rsquo07)
Continuity of vector mesons Tachibana Yamamoto +TH PRD78 (2008)
Explicit realization of spectral continuity
Possible fate of hadrons at high density （ Nc=3 Nf=3 ）
Vector Mesons = Gluons Baryons = Quarks
cond
ensa
tes Continuity in the ground state
Yamamoto Tachibana Baym + TH PRL97(rsquo06) PRD76 (rsquo07)
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
baryons (8)Quarks (9)
Continuity in the excited state
Schafer and Wilczek PRL 82 (1999)
Hadron-quark continuity in dense QCD
cond
ensa
tes Continuity in the ground state
Hatsuda Tachibana Yamamoto amp Baym PRL 97 (2006)
TH Slide p2(1997)
httpwww-rnclblgovDLSDLS_WWW_FilesDLSWorkshopdileptonhtml
I Why SPF is important
FLAG Collaboration update( July 26 2013) httpitpwikiunibechflag
Running masses mq(Q)
quark masses (from lattice QCD)
[MeV] (MS-bar 2GeV)
mu 216 (9)(7)
md 468 (14)(7)
ms 938 (24)
Running coupling αs(Q)=g24π
PDG (2012) httppdglblgov
I Status of QCD
Hadron masses from Lattice QCD
Improved Wilson + Iwasaki gauge action a = 009 fm L=29 fm mπ=135 MeV PACS-CS Coll Phys Rev D 81 074503 (2010)
3 accuracy
rArr L~96 fm mπ=135 MeV on K-computer underway
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
In-medium hadrons
Complex pole (even for the pion)
One-parameter example (Tne0)
For the pion f(x) and g(x) can be evaluated for small x See eg Jido Kunhihiro + TH Phys Lett B670 (2008) In general experimental inputs are really necessary Sometimes spectral function is better to be studied
Dim3 Chiral condensate in the medium
Lattice QCD (2+1)-flavorBorsanyi et al JHEP 1009 (2010)
Finite Temperature (LQCD)
Nuclear chiral perturbation Kaiser et al PRC 77 (2008)
Finite baryon density (χPT)
Mesic nuclei
2 Individual properties of NG and ldquoHiggsrdquo bosons π K η (NG) σ (Higgs) ηrsquo (anomaly)
σ2γ η2γ ηrsquo2γ
Dileptons3 Individual properties of vector bosons ρ ω and φ
Precisionsystematic studies(dispersion relation different targets hellip)
1 Spectral difference between chiral partners π-σ ρ-a1 ω-f1 etc Determination of D=6 chiral condensates in the vacuumTau-decay in nuclei
Wish list
TH Slide p7(1997)
III Exact sum rules in QCD medium
TH Slide p20(1997)
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
σ （６００）
Spectral evidence of SSB in QCD
ltPPgt
ltSSgt
ltVVgt
ltAAgt
TH LBNL WS (1997)
ALEPH Collaboration Phys Rep 421 (2005) 191
ltVVgt - ltAAgt fromτ-decays at LEP-1 ρ V
(s)s
ρ A(s
)s
[ρV(s
)-ρA(s
)] s
Energy weighted ldquochiralrdquo sum rules from QCD (mq=0)
Dim6 chiral condensate
Koike Lee + TH NuclPhys B394 (1993) 221Kapusta and Shuryak PRD 49 (1994) 4694Klingl Kaiser and Weise NPA 624 (1997) 527
-ρpQCD(ω))
-ρpQCD(ω))= C4ltGGgt
-ρpQCD(ω))= C6ltChiral invgt +C6rsquoltchiral non-invgt
Dim4 gluon condensate
Dim6 quark and gluon condensates
Dilepton data(after Cocktail subtraction) Space-time average
(by hydro or other models)
Lattice QCD simulations (with gradient flow method)
+
Energy weighted ldquovectorrdquo sum rules from QCD (mq=0)III In-medium hadrons
TH LBNL WS (1997)Slide p31
cf GLS sum rule Adler sum rule Bjorken sum rule
QGP
Quark-Gluon Plasma
Quark superfluid
Hadronphase
Chiral symmetry is always broken at finite density
Baryon superfluid
Hadron-Quark Continuity in dense QCD （ Nc=3 Nf=3 ）
cond
ensa
tes
Continuity in the ground state Tachibana Yamamoto + TH PRD78 (rsquo08)
Vector Mesons = Gluons Baryons = Quarks
Possible fate of hadrons at high density （ Nc=3 Nf=3 ）
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
Baryons (8)Quarks (9)
Continuity in the excited state Schafer amp Wilczek PRL 82 (rsquo99)
Nonet vector mesons(heavy)
Octetvector mesons(light)
Octet gluons in CFL mg=1362Δ Gusynin amp Shovkovy NPA700 (2002) Malekzadeh amp Rischke PRD73 (2006)
TH Tachibana and Yamamoto PRD78 (2008)
Spectral continuity of vector mesons
At high density
At intermediate density
At low density
Mass formula from Finite Energy Sum Rules
IV SummaryI Chiral order parameters
not unique Dim3 condensate Dim6 condensate etc
II In-medium hadrons chiral restoration can be seen in spectral degeneracy moment analysis is important for model independence interesting possibility of hadron-quark crossover (Vector mesons = Gluons Baryons = Quarks)
Back up slides
Vector current
Current correlation function
QCD sum rules in the superconducting medium
Operator Product Expansion (OPE) up to O(1Q6)
4-quark condensate
Diquark condensate
Chiral condensate
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
baryons (8)Quarks (9)
Continuity in the excited state
Schafer and Wilczek PRL 82 (1999)
Generalized Gell-Mann-Oakes-Renner relation Yamamoto Tachibana Baym + TH PR D76 (rsquo07)
Continuity of vector mesons Tachibana Yamamoto +TH PRD78 (2008)
Explicit realization of spectral continuity
Possible fate of hadrons at high density （ Nc=3 Nf=3 ）
Vector Mesons = Gluons Baryons = Quarks
cond
ensa
tes Continuity in the ground state
Yamamoto Tachibana Baym + TH PRL97(rsquo06) PRD76 (rsquo07)
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
baryons (8)Quarks (9)
Continuity in the excited state
Schafer and Wilczek PRL 82 (1999)
Hadron-quark continuity in dense QCD
cond
ensa
tes Continuity in the ground state
Hatsuda Tachibana Yamamoto amp Baym PRL 97 (2006)
TH Slide p2(1997)
httpwww-rnclblgovDLSDLS_WWW_FilesDLSWorkshopdileptonhtml
I Why SPF is important
FLAG Collaboration update( July 26 2013) httpitpwikiunibechflag
Running masses mq(Q)
quark masses (from lattice QCD)
[MeV] (MS-bar 2GeV)
mu 216 (9)(7)
md 468 (14)(7)
ms 938 (24)
Running coupling αs(Q)=g24π
PDG (2012) httppdglblgov
I Status of QCD
Hadron masses from Lattice QCD
Improved Wilson + Iwasaki gauge action a = 009 fm L=29 fm mπ=135 MeV PACS-CS Coll Phys Rev D 81 074503 (2010)
3 accuracy
rArr L~96 fm mπ=135 MeV on K-computer underway
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
In-medium hadrons
Complex pole (even for the pion)
One-parameter example (Tne0)
For the pion f(x) and g(x) can be evaluated for small x See eg Jido Kunhihiro + TH Phys Lett B670 (2008) In general experimental inputs are really necessary Sometimes spectral function is better to be studied
Dim3 Chiral condensate in the medium
Lattice QCD (2+1)-flavorBorsanyi et al JHEP 1009 (2010)
Finite Temperature (LQCD)
Nuclear chiral perturbation Kaiser et al PRC 77 (2008)
Finite baryon density (χPT)
Mesic nuclei
2 Individual properties of NG and ldquoHiggsrdquo bosons π K η (NG) σ (Higgs) ηrsquo (anomaly)
σ2γ η2γ ηrsquo2γ
Dileptons3 Individual properties of vector bosons ρ ω and φ
Precisionsystematic studies(dispersion relation different targets hellip)
1 Spectral difference between chiral partners π-σ ρ-a1 ω-f1 etc Determination of D=6 chiral condensates in the vacuumTau-decay in nuclei
Wish list
TH Slide p7(1997)
III Exact sum rules in QCD medium
TH Slide p20(1997)
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
ALEPH Collaboration Phys Rep 421 (2005) 191
ltVVgt - ltAAgt fromτ-decays at LEP-1 ρ V
(s)s
ρ A(s
)s
[ρV(s
)-ρA(s
)] s
Energy weighted ldquochiralrdquo sum rules from QCD (mq=0)
Dim6 chiral condensate
Koike Lee + TH NuclPhys B394 (1993) 221Kapusta and Shuryak PRD 49 (1994) 4694Klingl Kaiser and Weise NPA 624 (1997) 527
-ρpQCD(ω))
-ρpQCD(ω))= C4ltGGgt
-ρpQCD(ω))= C6ltChiral invgt +C6rsquoltchiral non-invgt
Dim4 gluon condensate
Dim6 quark and gluon condensates
Dilepton data(after Cocktail subtraction) Space-time average
(by hydro or other models)
Lattice QCD simulations (with gradient flow method)
+
Energy weighted ldquovectorrdquo sum rules from QCD (mq=0)III In-medium hadrons
TH LBNL WS (1997)Slide p31
cf GLS sum rule Adler sum rule Bjorken sum rule
QGP
Quark-Gluon Plasma
Quark superfluid
Hadronphase
Chiral symmetry is always broken at finite density
Baryon superfluid
Hadron-Quark Continuity in dense QCD （ Nc=3 Nf=3 ）
cond
ensa
tes
Continuity in the ground state Tachibana Yamamoto + TH PRD78 (rsquo08)
Vector Mesons = Gluons Baryons = Quarks
Possible fate of hadrons at high density （ Nc=3 Nf=3 ）
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
Baryons (8)Quarks (9)
Continuity in the excited state Schafer amp Wilczek PRL 82 (rsquo99)
Nonet vector mesons(heavy)
Octetvector mesons(light)
Octet gluons in CFL mg=1362Δ Gusynin amp Shovkovy NPA700 (2002) Malekzadeh amp Rischke PRD73 (2006)
TH Tachibana and Yamamoto PRD78 (2008)
Spectral continuity of vector mesons
At high density
At intermediate density
At low density
Mass formula from Finite Energy Sum Rules
IV SummaryI Chiral order parameters
not unique Dim3 condensate Dim6 condensate etc
II In-medium hadrons chiral restoration can be seen in spectral degeneracy moment analysis is important for model independence interesting possibility of hadron-quark crossover (Vector mesons = Gluons Baryons = Quarks)
Back up slides
Vector current
Current correlation function
QCD sum rules in the superconducting medium
Operator Product Expansion (OPE) up to O(1Q6)
4-quark condensate
Diquark condensate
Chiral condensate
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
baryons (8)Quarks (9)
Continuity in the excited state
Schafer and Wilczek PRL 82 (1999)
Generalized Gell-Mann-Oakes-Renner relation Yamamoto Tachibana Baym + TH PR D76 (rsquo07)
Continuity of vector mesons Tachibana Yamamoto +TH PRD78 (2008)
Explicit realization of spectral continuity
Possible fate of hadrons at high density （ Nc=3 Nf=3 ）
Vector Mesons = Gluons Baryons = Quarks
cond
ensa
tes Continuity in the ground state
Yamamoto Tachibana Baym + TH PRL97(rsquo06) PRD76 (rsquo07)
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
baryons (8)Quarks (9)
Continuity in the excited state
Schafer and Wilczek PRL 82 (1999)
Hadron-quark continuity in dense QCD
cond
ensa
tes Continuity in the ground state
Hatsuda Tachibana Yamamoto amp Baym PRL 97 (2006)
TH Slide p2(1997)
httpwww-rnclblgovDLSDLS_WWW_FilesDLSWorkshopdileptonhtml
I Why SPF is important
FLAG Collaboration update( July 26 2013) httpitpwikiunibechflag
Running masses mq(Q)
quark masses (from lattice QCD)
[MeV] (MS-bar 2GeV)
mu 216 (9)(7)
md 468 (14)(7)
ms 938 (24)
Running coupling αs(Q)=g24π
PDG (2012) httppdglblgov
I Status of QCD
Hadron masses from Lattice QCD
Improved Wilson + Iwasaki gauge action a = 009 fm L=29 fm mπ=135 MeV PACS-CS Coll Phys Rev D 81 074503 (2010)
3 accuracy
rArr L~96 fm mπ=135 MeV on K-computer underway
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
In-medium hadrons
Complex pole (even for the pion)
One-parameter example (Tne0)
For the pion f(x) and g(x) can be evaluated for small x See eg Jido Kunhihiro + TH Phys Lett B670 (2008) In general experimental inputs are really necessary Sometimes spectral function is better to be studied
Dim3 Chiral condensate in the medium
Lattice QCD (2+1)-flavorBorsanyi et al JHEP 1009 (2010)
Finite Temperature (LQCD)
Nuclear chiral perturbation Kaiser et al PRC 77 (2008)
Finite baryon density (χPT)
Mesic nuclei
2 Individual properties of NG and ldquoHiggsrdquo bosons π K η (NG) σ (Higgs) ηrsquo (anomaly)
σ2γ η2γ ηrsquo2γ
Dileptons3 Individual properties of vector bosons ρ ω and φ
Precisionsystematic studies(dispersion relation different targets hellip)
1 Spectral difference between chiral partners π-σ ρ-a1 ω-f1 etc Determination of D=6 chiral condensates in the vacuumTau-decay in nuclei
Wish list
TH Slide p7(1997)
III Exact sum rules in QCD medium
TH Slide p20(1997)
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
Energy weighted ldquochiralrdquo sum rules from QCD (mq=0)
Dim6 chiral condensate
Koike Lee + TH NuclPhys B394 (1993) 221Kapusta and Shuryak PRD 49 (1994) 4694Klingl Kaiser and Weise NPA 624 (1997) 527
-ρpQCD(ω))
-ρpQCD(ω))= C4ltGGgt
-ρpQCD(ω))= C6ltChiral invgt +C6rsquoltchiral non-invgt
Dim4 gluon condensate
Dim6 quark and gluon condensates
Dilepton data(after Cocktail subtraction) Space-time average
(by hydro or other models)
Lattice QCD simulations (with gradient flow method)
+
Energy weighted ldquovectorrdquo sum rules from QCD (mq=0)III In-medium hadrons
TH LBNL WS (1997)Slide p31
cf GLS sum rule Adler sum rule Bjorken sum rule
QGP
Quark-Gluon Plasma
Quark superfluid
Hadronphase
Chiral symmetry is always broken at finite density
Baryon superfluid
Hadron-Quark Continuity in dense QCD （ Nc=3 Nf=3 ）
cond
ensa
tes
Continuity in the ground state Tachibana Yamamoto + TH PRD78 (rsquo08)
Vector Mesons = Gluons Baryons = Quarks
Possible fate of hadrons at high density （ Nc=3 Nf=3 ）
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
Baryons (8)Quarks (9)
Continuity in the excited state Schafer amp Wilczek PRL 82 (rsquo99)
Nonet vector mesons(heavy)
Octetvector mesons(light)
Octet gluons in CFL mg=1362Δ Gusynin amp Shovkovy NPA700 (2002) Malekzadeh amp Rischke PRD73 (2006)
TH Tachibana and Yamamoto PRD78 (2008)
Spectral continuity of vector mesons
At high density
At intermediate density
At low density
Mass formula from Finite Energy Sum Rules
IV SummaryI Chiral order parameters
not unique Dim3 condensate Dim6 condensate etc
II In-medium hadrons chiral restoration can be seen in spectral degeneracy moment analysis is important for model independence interesting possibility of hadron-quark crossover (Vector mesons = Gluons Baryons = Quarks)
Back up slides
Vector current
Current correlation function
QCD sum rules in the superconducting medium
Operator Product Expansion (OPE) up to O(1Q6)
4-quark condensate
Diquark condensate
Chiral condensate
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
baryons (8)Quarks (9)
Continuity in the excited state
Schafer and Wilczek PRL 82 (1999)
Generalized Gell-Mann-Oakes-Renner relation Yamamoto Tachibana Baym + TH PR D76 (rsquo07)
Continuity of vector mesons Tachibana Yamamoto +TH PRD78 (2008)
Explicit realization of spectral continuity
Possible fate of hadrons at high density （ Nc=3 Nf=3 ）
Vector Mesons = Gluons Baryons = Quarks
cond
ensa
tes Continuity in the ground state
Yamamoto Tachibana Baym + TH PRL97(rsquo06) PRD76 (rsquo07)
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
baryons (8)Quarks (9)
Continuity in the excited state
Schafer and Wilczek PRL 82 (1999)
Hadron-quark continuity in dense QCD
cond
ensa
tes Continuity in the ground state
Hatsuda Tachibana Yamamoto amp Baym PRL 97 (2006)
TH Slide p2(1997)
httpwww-rnclblgovDLSDLS_WWW_FilesDLSWorkshopdileptonhtml
I Why SPF is important
FLAG Collaboration update( July 26 2013) httpitpwikiunibechflag
Running masses mq(Q)
quark masses (from lattice QCD)
[MeV] (MS-bar 2GeV)
mu 216 (9)(7)
md 468 (14)(7)
ms 938 (24)
Running coupling αs(Q)=g24π
PDG (2012) httppdglblgov
I Status of QCD
Hadron masses from Lattice QCD
Improved Wilson + Iwasaki gauge action a = 009 fm L=29 fm mπ=135 MeV PACS-CS Coll Phys Rev D 81 074503 (2010)
3 accuracy
rArr L~96 fm mπ=135 MeV on K-computer underway
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
In-medium hadrons
Complex pole (even for the pion)
One-parameter example (Tne0)
For the pion f(x) and g(x) can be evaluated for small x See eg Jido Kunhihiro + TH Phys Lett B670 (2008) In general experimental inputs are really necessary Sometimes spectral function is better to be studied
Dim3 Chiral condensate in the medium
Lattice QCD (2+1)-flavorBorsanyi et al JHEP 1009 (2010)
Finite Temperature (LQCD)
Nuclear chiral perturbation Kaiser et al PRC 77 (2008)
Finite baryon density (χPT)
Mesic nuclei
2 Individual properties of NG and ldquoHiggsrdquo bosons π K η (NG) σ (Higgs) ηrsquo (anomaly)
σ2γ η2γ ηrsquo2γ
Dileptons3 Individual properties of vector bosons ρ ω and φ
Precisionsystematic studies(dispersion relation different targets hellip)
1 Spectral difference between chiral partners π-σ ρ-a1 ω-f1 etc Determination of D=6 chiral condensates in the vacuumTau-decay in nuclei
Wish list
TH Slide p7(1997)
III Exact sum rules in QCD medium
TH Slide p20(1997)
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
-ρpQCD(ω))
-ρpQCD(ω))= C4ltGGgt
-ρpQCD(ω))= C6ltChiral invgt +C6rsquoltchiral non-invgt
Dim4 gluon condensate
Dim6 quark and gluon condensates
Dilepton data(after Cocktail subtraction) Space-time average
(by hydro or other models)
Lattice QCD simulations (with gradient flow method)
+
Energy weighted ldquovectorrdquo sum rules from QCD (mq=0)III In-medium hadrons
TH LBNL WS (1997)Slide p31
cf GLS sum rule Adler sum rule Bjorken sum rule
QGP
Quark-Gluon Plasma
Quark superfluid
Hadronphase
Chiral symmetry is always broken at finite density
Baryon superfluid
Hadron-Quark Continuity in dense QCD （ Nc=3 Nf=3 ）
cond
ensa
tes
Continuity in the ground state Tachibana Yamamoto + TH PRD78 (rsquo08)
Vector Mesons = Gluons Baryons = Quarks
Possible fate of hadrons at high density （ Nc=3 Nf=3 ）
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
Baryons (8)Quarks (9)
Continuity in the excited state Schafer amp Wilczek PRL 82 (rsquo99)
Nonet vector mesons(heavy)
Octetvector mesons(light)
Octet gluons in CFL mg=1362Δ Gusynin amp Shovkovy NPA700 (2002) Malekzadeh amp Rischke PRD73 (2006)
TH Tachibana and Yamamoto PRD78 (2008)
Spectral continuity of vector mesons
At high density
At intermediate density
At low density
Mass formula from Finite Energy Sum Rules
IV SummaryI Chiral order parameters
not unique Dim3 condensate Dim6 condensate etc
II In-medium hadrons chiral restoration can be seen in spectral degeneracy moment analysis is important for model independence interesting possibility of hadron-quark crossover (Vector mesons = Gluons Baryons = Quarks)
Back up slides
Vector current
Current correlation function
QCD sum rules in the superconducting medium
Operator Product Expansion (OPE) up to O(1Q6)
4-quark condensate
Diquark condensate
Chiral condensate
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
baryons (8)Quarks (9)
Continuity in the excited state
Schafer and Wilczek PRL 82 (1999)
Generalized Gell-Mann-Oakes-Renner relation Yamamoto Tachibana Baym + TH PR D76 (rsquo07)
Continuity of vector mesons Tachibana Yamamoto +TH PRD78 (2008)
Explicit realization of spectral continuity
Possible fate of hadrons at high density （ Nc=3 Nf=3 ）
Vector Mesons = Gluons Baryons = Quarks
cond
ensa
tes Continuity in the ground state
Yamamoto Tachibana Baym + TH PRL97(rsquo06) PRD76 (rsquo07)
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
baryons (8)Quarks (9)
Continuity in the excited state
Schafer and Wilczek PRL 82 (1999)
Hadron-quark continuity in dense QCD
cond
ensa
tes Continuity in the ground state
Hatsuda Tachibana Yamamoto amp Baym PRL 97 (2006)
TH Slide p2(1997)
httpwww-rnclblgovDLSDLS_WWW_FilesDLSWorkshopdileptonhtml
I Why SPF is important
FLAG Collaboration update( July 26 2013) httpitpwikiunibechflag
Running masses mq(Q)
quark masses (from lattice QCD)
[MeV] (MS-bar 2GeV)
mu 216 (9)(7)
md 468 (14)(7)
ms 938 (24)
Running coupling αs(Q)=g24π
PDG (2012) httppdglblgov
I Status of QCD
Hadron masses from Lattice QCD
Improved Wilson + Iwasaki gauge action a = 009 fm L=29 fm mπ=135 MeV PACS-CS Coll Phys Rev D 81 074503 (2010)
3 accuracy
rArr L~96 fm mπ=135 MeV on K-computer underway
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
In-medium hadrons
Complex pole (even for the pion)
One-parameter example (Tne0)
For the pion f(x) and g(x) can be evaluated for small x See eg Jido Kunhihiro + TH Phys Lett B670 (2008) In general experimental inputs are really necessary Sometimes spectral function is better to be studied
Dim3 Chiral condensate in the medium
Lattice QCD (2+1)-flavorBorsanyi et al JHEP 1009 (2010)
Finite Temperature (LQCD)
Nuclear chiral perturbation Kaiser et al PRC 77 (2008)
Finite baryon density (χPT)
Mesic nuclei
2 Individual properties of NG and ldquoHiggsrdquo bosons π K η (NG) σ (Higgs) ηrsquo (anomaly)
σ2γ η2γ ηrsquo2γ
Dileptons3 Individual properties of vector bosons ρ ω and φ
Precisionsystematic studies(dispersion relation different targets hellip)
1 Spectral difference between chiral partners π-σ ρ-a1 ω-f1 etc Determination of D=6 chiral condensates in the vacuumTau-decay in nuclei
Wish list
TH Slide p7(1997)
III Exact sum rules in QCD medium
TH Slide p20(1997)
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
TH LBNL WS (1997)Slide p31
cf GLS sum rule Adler sum rule Bjorken sum rule
QGP
Quark-Gluon Plasma
Quark superfluid
Hadronphase
Chiral symmetry is always broken at finite density
Baryon superfluid
Hadron-Quark Continuity in dense QCD （ Nc=3 Nf=3 ）
cond
ensa
tes
Continuity in the ground state Tachibana Yamamoto + TH PRD78 (rsquo08)
Vector Mesons = Gluons Baryons = Quarks
Possible fate of hadrons at high density （ Nc=3 Nf=3 ）
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
Baryons (8)Quarks (9)
Continuity in the excited state Schafer amp Wilczek PRL 82 (rsquo99)
Nonet vector mesons(heavy)
Octetvector mesons(light)
Octet gluons in CFL mg=1362Δ Gusynin amp Shovkovy NPA700 (2002) Malekzadeh amp Rischke PRD73 (2006)
TH Tachibana and Yamamoto PRD78 (2008)
Spectral continuity of vector mesons
At high density
At intermediate density
At low density
Mass formula from Finite Energy Sum Rules
IV SummaryI Chiral order parameters
not unique Dim3 condensate Dim6 condensate etc
II In-medium hadrons chiral restoration can be seen in spectral degeneracy moment analysis is important for model independence interesting possibility of hadron-quark crossover (Vector mesons = Gluons Baryons = Quarks)
Back up slides
Vector current
Current correlation function
QCD sum rules in the superconducting medium
Operator Product Expansion (OPE) up to O(1Q6)
4-quark condensate
Diquark condensate
Chiral condensate
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
baryons (8)Quarks (9)
Continuity in the excited state
Schafer and Wilczek PRL 82 (1999)
Generalized Gell-Mann-Oakes-Renner relation Yamamoto Tachibana Baym + TH PR D76 (rsquo07)
Continuity of vector mesons Tachibana Yamamoto +TH PRD78 (2008)
Explicit realization of spectral continuity
Possible fate of hadrons at high density （ Nc=3 Nf=3 ）
Vector Mesons = Gluons Baryons = Quarks
cond
ensa
tes Continuity in the ground state
Yamamoto Tachibana Baym + TH PRL97(rsquo06) PRD76 (rsquo07)
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
baryons (8)Quarks (9)
Continuity in the excited state
Schafer and Wilczek PRL 82 (1999)
Hadron-quark continuity in dense QCD
cond
ensa
tes Continuity in the ground state
Hatsuda Tachibana Yamamoto amp Baym PRL 97 (2006)
TH Slide p2(1997)
httpwww-rnclblgovDLSDLS_WWW_FilesDLSWorkshopdileptonhtml
I Why SPF is important
FLAG Collaboration update( July 26 2013) httpitpwikiunibechflag
Running masses mq(Q)
quark masses (from lattice QCD)
[MeV] (MS-bar 2GeV)
mu 216 (9)(7)
md 468 (14)(7)
ms 938 (24)
Running coupling αs(Q)=g24π
PDG (2012) httppdglblgov
I Status of QCD
Hadron masses from Lattice QCD
Improved Wilson + Iwasaki gauge action a = 009 fm L=29 fm mπ=135 MeV PACS-CS Coll Phys Rev D 81 074503 (2010)
3 accuracy
rArr L~96 fm mπ=135 MeV on K-computer underway
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
In-medium hadrons
Complex pole (even for the pion)
One-parameter example (Tne0)
For the pion f(x) and g(x) can be evaluated for small x See eg Jido Kunhihiro + TH Phys Lett B670 (2008) In general experimental inputs are really necessary Sometimes spectral function is better to be studied
Dim3 Chiral condensate in the medium
Lattice QCD (2+1)-flavorBorsanyi et al JHEP 1009 (2010)
Finite Temperature (LQCD)
Nuclear chiral perturbation Kaiser et al PRC 77 (2008)
Finite baryon density (χPT)
Mesic nuclei
2 Individual properties of NG and ldquoHiggsrdquo bosons π K η (NG) σ (Higgs) ηrsquo (anomaly)
σ2γ η2γ ηrsquo2γ
Dileptons3 Individual properties of vector bosons ρ ω and φ
Precisionsystematic studies(dispersion relation different targets hellip)
1 Spectral difference between chiral partners π-σ ρ-a1 ω-f1 etc Determination of D=6 chiral condensates in the vacuumTau-decay in nuclei
Wish list
TH Slide p7(1997)
III Exact sum rules in QCD medium
TH Slide p20(1997)
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
QGP
Quark-Gluon Plasma
Quark superfluid
Hadronphase
Chiral symmetry is always broken at finite density
Baryon superfluid
Hadron-Quark Continuity in dense QCD （ Nc=3 Nf=3 ）
cond
ensa
tes
Continuity in the ground state Tachibana Yamamoto + TH PRD78 (rsquo08)
Vector Mesons = Gluons Baryons = Quarks
Possible fate of hadrons at high density （ Nc=3 Nf=3 ）
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
Baryons (8)Quarks (9)
Continuity in the excited state Schafer amp Wilczek PRL 82 (rsquo99)
Nonet vector mesons(heavy)
Octetvector mesons(light)
Octet gluons in CFL mg=1362Δ Gusynin amp Shovkovy NPA700 (2002) Malekzadeh amp Rischke PRD73 (2006)
TH Tachibana and Yamamoto PRD78 (2008)
Spectral continuity of vector mesons
At high density
At intermediate density
At low density
Mass formula from Finite Energy Sum Rules
IV SummaryI Chiral order parameters
not unique Dim3 condensate Dim6 condensate etc
II In-medium hadrons chiral restoration can be seen in spectral degeneracy moment analysis is important for model independence interesting possibility of hadron-quark crossover (Vector mesons = Gluons Baryons = Quarks)
Back up slides
Vector current
Current correlation function
QCD sum rules in the superconducting medium
Operator Product Expansion (OPE) up to O(1Q6)
4-quark condensate
Diquark condensate
Chiral condensate
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
baryons (8)Quarks (9)
Continuity in the excited state
Schafer and Wilczek PRL 82 (1999)
Generalized Gell-Mann-Oakes-Renner relation Yamamoto Tachibana Baym + TH PR D76 (rsquo07)
Continuity of vector mesons Tachibana Yamamoto +TH PRD78 (2008)
Explicit realization of spectral continuity
Possible fate of hadrons at high density （ Nc=3 Nf=3 ）
Vector Mesons = Gluons Baryons = Quarks
cond
ensa
tes Continuity in the ground state
Yamamoto Tachibana Baym + TH PRL97(rsquo06) PRD76 (rsquo07)
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
baryons (8)Quarks (9)
Continuity in the excited state
Schafer and Wilczek PRL 82 (1999)
Hadron-quark continuity in dense QCD
cond
ensa
tes Continuity in the ground state
Hatsuda Tachibana Yamamoto amp Baym PRL 97 (2006)
TH Slide p2(1997)
httpwww-rnclblgovDLSDLS_WWW_FilesDLSWorkshopdileptonhtml
I Why SPF is important
FLAG Collaboration update( July 26 2013) httpitpwikiunibechflag
Running masses mq(Q)
quark masses (from lattice QCD)
[MeV] (MS-bar 2GeV)
mu 216 (9)(7)
md 468 (14)(7)
ms 938 (24)
Running coupling αs(Q)=g24π
PDG (2012) httppdglblgov
I Status of QCD
Hadron masses from Lattice QCD
Improved Wilson + Iwasaki gauge action a = 009 fm L=29 fm mπ=135 MeV PACS-CS Coll Phys Rev D 81 074503 (2010)
3 accuracy
rArr L~96 fm mπ=135 MeV on K-computer underway
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
In-medium hadrons
Complex pole (even for the pion)
One-parameter example (Tne0)
For the pion f(x) and g(x) can be evaluated for small x See eg Jido Kunhihiro + TH Phys Lett B670 (2008) In general experimental inputs are really necessary Sometimes spectral function is better to be studied
Dim3 Chiral condensate in the medium
Lattice QCD (2+1)-flavorBorsanyi et al JHEP 1009 (2010)
Finite Temperature (LQCD)
Nuclear chiral perturbation Kaiser et al PRC 77 (2008)
Finite baryon density (χPT)
Mesic nuclei
2 Individual properties of NG and ldquoHiggsrdquo bosons π K η (NG) σ (Higgs) ηrsquo (anomaly)
σ2γ η2γ ηrsquo2γ
Dileptons3 Individual properties of vector bosons ρ ω and φ
Precisionsystematic studies(dispersion relation different targets hellip)
1 Spectral difference between chiral partners π-σ ρ-a1 ω-f1 etc Determination of D=6 chiral condensates in the vacuumTau-decay in nuclei
Wish list
TH Slide p7(1997)
III Exact sum rules in QCD medium
TH Slide p20(1997)
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
cond
ensa
tes
Continuity in the ground state Tachibana Yamamoto + TH PRD78 (rsquo08)
Vector Mesons = Gluons Baryons = Quarks
Possible fate of hadrons at high density （ Nc=3 Nf=3 ）
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
Baryons (8)Quarks (9)
Continuity in the excited state Schafer amp Wilczek PRL 82 (rsquo99)
Nonet vector mesons(heavy)
Octetvector mesons(light)
Octet gluons in CFL mg=1362Δ Gusynin amp Shovkovy NPA700 (2002) Malekzadeh amp Rischke PRD73 (2006)
TH Tachibana and Yamamoto PRD78 (2008)
Spectral continuity of vector mesons
At high density
At intermediate density
At low density
Mass formula from Finite Energy Sum Rules
IV SummaryI Chiral order parameters
not unique Dim3 condensate Dim6 condensate etc
II In-medium hadrons chiral restoration can be seen in spectral degeneracy moment analysis is important for model independence interesting possibility of hadron-quark crossover (Vector mesons = Gluons Baryons = Quarks)
Back up slides
Vector current
Current correlation function
QCD sum rules in the superconducting medium
Operator Product Expansion (OPE) up to O(1Q6)
4-quark condensate
Diquark condensate
Chiral condensate
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
baryons (8)Quarks (9)
Continuity in the excited state
Schafer and Wilczek PRL 82 (1999)
Generalized Gell-Mann-Oakes-Renner relation Yamamoto Tachibana Baym + TH PR D76 (rsquo07)
Continuity of vector mesons Tachibana Yamamoto +TH PRD78 (2008)
Explicit realization of spectral continuity
Possible fate of hadrons at high density （ Nc=3 Nf=3 ）
Vector Mesons = Gluons Baryons = Quarks
cond
ensa
tes Continuity in the ground state
Yamamoto Tachibana Baym + TH PRL97(rsquo06) PRD76 (rsquo07)
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
baryons (8)Quarks (9)
Continuity in the excited state
Schafer and Wilczek PRL 82 (1999)
Hadron-quark continuity in dense QCD
cond
ensa
tes Continuity in the ground state
Hatsuda Tachibana Yamamoto amp Baym PRL 97 (2006)
TH Slide p2(1997)
httpwww-rnclblgovDLSDLS_WWW_FilesDLSWorkshopdileptonhtml
I Why SPF is important
FLAG Collaboration update( July 26 2013) httpitpwikiunibechflag
Running masses mq(Q)
quark masses (from lattice QCD)
[MeV] (MS-bar 2GeV)
mu 216 (9)(7)
md 468 (14)(7)
ms 938 (24)
Running coupling αs(Q)=g24π
PDG (2012) httppdglblgov
I Status of QCD
Hadron masses from Lattice QCD
Improved Wilson + Iwasaki gauge action a = 009 fm L=29 fm mπ=135 MeV PACS-CS Coll Phys Rev D 81 074503 (2010)
3 accuracy
rArr L~96 fm mπ=135 MeV on K-computer underway
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
In-medium hadrons
Complex pole (even for the pion)
One-parameter example (Tne0)
For the pion f(x) and g(x) can be evaluated for small x See eg Jido Kunhihiro + TH Phys Lett B670 (2008) In general experimental inputs are really necessary Sometimes spectral function is better to be studied
Dim3 Chiral condensate in the medium
Lattice QCD (2+1)-flavorBorsanyi et al JHEP 1009 (2010)
Finite Temperature (LQCD)
Nuclear chiral perturbation Kaiser et al PRC 77 (2008)
Finite baryon density (χPT)
Mesic nuclei
2 Individual properties of NG and ldquoHiggsrdquo bosons π K η (NG) σ (Higgs) ηrsquo (anomaly)
σ2γ η2γ ηrsquo2γ
Dileptons3 Individual properties of vector bosons ρ ω and φ
Precisionsystematic studies(dispersion relation different targets hellip)
1 Spectral difference between chiral partners π-σ ρ-a1 ω-f1 etc Determination of D=6 chiral condensates in the vacuumTau-decay in nuclei
Wish list
TH Slide p7(1997)
III Exact sum rules in QCD medium
TH Slide p20(1997)
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
Nonet vector mesons(heavy)
Octetvector mesons(light)
Octet gluons in CFL mg=1362Δ Gusynin amp Shovkovy NPA700 (2002) Malekzadeh amp Rischke PRD73 (2006)
TH Tachibana and Yamamoto PRD78 (2008)
Spectral continuity of vector mesons
At high density
At intermediate density
At low density
Mass formula from Finite Energy Sum Rules
IV SummaryI Chiral order parameters
not unique Dim3 condensate Dim6 condensate etc
II In-medium hadrons chiral restoration can be seen in spectral degeneracy moment analysis is important for model independence interesting possibility of hadron-quark crossover (Vector mesons = Gluons Baryons = Quarks)
Back up slides
Vector current
Current correlation function
QCD sum rules in the superconducting medium
Operator Product Expansion (OPE) up to O(1Q6)
4-quark condensate
Diquark condensate
Chiral condensate
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
baryons (8)Quarks (9)
Continuity in the excited state
Schafer and Wilczek PRL 82 (1999)
Generalized Gell-Mann-Oakes-Renner relation Yamamoto Tachibana Baym + TH PR D76 (rsquo07)
Continuity of vector mesons Tachibana Yamamoto +TH PRD78 (2008)
Explicit realization of spectral continuity
Possible fate of hadrons at high density （ Nc=3 Nf=3 ）
Vector Mesons = Gluons Baryons = Quarks
cond
ensa
tes Continuity in the ground state
Yamamoto Tachibana Baym + TH PRL97(rsquo06) PRD76 (rsquo07)
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
baryons (8)Quarks (9)
Continuity in the excited state
Schafer and Wilczek PRL 82 (1999)
Hadron-quark continuity in dense QCD
cond
ensa
tes Continuity in the ground state
Hatsuda Tachibana Yamamoto amp Baym PRL 97 (2006)
TH Slide p2(1997)
httpwww-rnclblgovDLSDLS_WWW_FilesDLSWorkshopdileptonhtml
I Why SPF is important
FLAG Collaboration update( July 26 2013) httpitpwikiunibechflag
Running masses mq(Q)
quark masses (from lattice QCD)
[MeV] (MS-bar 2GeV)
mu 216 (9)(7)
md 468 (14)(7)
ms 938 (24)
Running coupling αs(Q)=g24π
PDG (2012) httppdglblgov
I Status of QCD
Hadron masses from Lattice QCD
Improved Wilson + Iwasaki gauge action a = 009 fm L=29 fm mπ=135 MeV PACS-CS Coll Phys Rev D 81 074503 (2010)
3 accuracy
rArr L~96 fm mπ=135 MeV on K-computer underway
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
In-medium hadrons
Complex pole (even for the pion)
One-parameter example (Tne0)
For the pion f(x) and g(x) can be evaluated for small x See eg Jido Kunhihiro + TH Phys Lett B670 (2008) In general experimental inputs are really necessary Sometimes spectral function is better to be studied
Dim3 Chiral condensate in the medium
Lattice QCD (2+1)-flavorBorsanyi et al JHEP 1009 (2010)
Finite Temperature (LQCD)
Nuclear chiral perturbation Kaiser et al PRC 77 (2008)
Finite baryon density (χPT)
Mesic nuclei
2 Individual properties of NG and ldquoHiggsrdquo bosons π K η (NG) σ (Higgs) ηrsquo (anomaly)
σ2γ η2γ ηrsquo2γ
Dileptons3 Individual properties of vector bosons ρ ω and φ
Precisionsystematic studies(dispersion relation different targets hellip)
1 Spectral difference between chiral partners π-σ ρ-a1 ω-f1 etc Determination of D=6 chiral condensates in the vacuumTau-decay in nuclei
Wish list
TH Slide p7(1997)
III Exact sum rules in QCD medium
TH Slide p20(1997)
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
At high density
At intermediate density
At low density
Mass formula from Finite Energy Sum Rules
IV SummaryI Chiral order parameters
not unique Dim3 condensate Dim6 condensate etc
II In-medium hadrons chiral restoration can be seen in spectral degeneracy moment analysis is important for model independence interesting possibility of hadron-quark crossover (Vector mesons = Gluons Baryons = Quarks)
Back up slides
Vector current
Current correlation function
QCD sum rules in the superconducting medium
Operator Product Expansion (OPE) up to O(1Q6)
4-quark condensate
Diquark condensate
Chiral condensate
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
baryons (8)Quarks (9)
Continuity in the excited state
Schafer and Wilczek PRL 82 (1999)
Generalized Gell-Mann-Oakes-Renner relation Yamamoto Tachibana Baym + TH PR D76 (rsquo07)
Continuity of vector mesons Tachibana Yamamoto +TH PRD78 (2008)
Explicit realization of spectral continuity
Possible fate of hadrons at high density （ Nc=3 Nf=3 ）
Vector Mesons = Gluons Baryons = Quarks
cond
ensa
tes Continuity in the ground state
Yamamoto Tachibana Baym + TH PRL97(rsquo06) PRD76 (rsquo07)
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
baryons (8)Quarks (9)
Continuity in the excited state
Schafer and Wilczek PRL 82 (1999)
Hadron-quark continuity in dense QCD
cond
ensa
tes Continuity in the ground state
Hatsuda Tachibana Yamamoto amp Baym PRL 97 (2006)
TH Slide p2(1997)
httpwww-rnclblgovDLSDLS_WWW_FilesDLSWorkshopdileptonhtml
I Why SPF is important
FLAG Collaboration update( July 26 2013) httpitpwikiunibechflag
Running masses mq(Q)
quark masses (from lattice QCD)
[MeV] (MS-bar 2GeV)
mu 216 (9)(7)
md 468 (14)(7)
ms 938 (24)
Running coupling αs(Q)=g24π
PDG (2012) httppdglblgov
I Status of QCD
Hadron masses from Lattice QCD
Improved Wilson + Iwasaki gauge action a = 009 fm L=29 fm mπ=135 MeV PACS-CS Coll Phys Rev D 81 074503 (2010)
3 accuracy
rArr L~96 fm mπ=135 MeV on K-computer underway
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
In-medium hadrons
Complex pole (even for the pion)
One-parameter example (Tne0)
For the pion f(x) and g(x) can be evaluated for small x See eg Jido Kunhihiro + TH Phys Lett B670 (2008) In general experimental inputs are really necessary Sometimes spectral function is better to be studied
Dim3 Chiral condensate in the medium
Lattice QCD (2+1)-flavorBorsanyi et al JHEP 1009 (2010)
Finite Temperature (LQCD)
Nuclear chiral perturbation Kaiser et al PRC 77 (2008)
Finite baryon density (χPT)
Mesic nuclei
2 Individual properties of NG and ldquoHiggsrdquo bosons π K η (NG) σ (Higgs) ηrsquo (anomaly)
σ2γ η2γ ηrsquo2γ
Dileptons3 Individual properties of vector bosons ρ ω and φ
Precisionsystematic studies(dispersion relation different targets hellip)
1 Spectral difference between chiral partners π-σ ρ-a1 ω-f1 etc Determination of D=6 chiral condensates in the vacuumTau-decay in nuclei
Wish list
TH Slide p7(1997)
III Exact sum rules in QCD medium
TH Slide p20(1997)
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
IV SummaryI Chiral order parameters
not unique Dim3 condensate Dim6 condensate etc
II In-medium hadrons chiral restoration can be seen in spectral degeneracy moment analysis is important for model independence interesting possibility of hadron-quark crossover (Vector mesons = Gluons Baryons = Quarks)
Back up slides
Vector current
Current correlation function
QCD sum rules in the superconducting medium
Operator Product Expansion (OPE) up to O(1Q6)
4-quark condensate
Diquark condensate
Chiral condensate
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
baryons (8)Quarks (9)
Continuity in the excited state
Schafer and Wilczek PRL 82 (1999)
Generalized Gell-Mann-Oakes-Renner relation Yamamoto Tachibana Baym + TH PR D76 (rsquo07)
Continuity of vector mesons Tachibana Yamamoto +TH PRD78 (2008)
Explicit realization of spectral continuity
Possible fate of hadrons at high density （ Nc=3 Nf=3 ）
Vector Mesons = Gluons Baryons = Quarks
cond
ensa
tes Continuity in the ground state
Yamamoto Tachibana Baym + TH PRL97(rsquo06) PRD76 (rsquo07)
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
baryons (8)Quarks (9)
Continuity in the excited state
Schafer and Wilczek PRL 82 (1999)
Hadron-quark continuity in dense QCD
cond
ensa
tes Continuity in the ground state
Hatsuda Tachibana Yamamoto amp Baym PRL 97 (2006)
TH Slide p2(1997)
httpwww-rnclblgovDLSDLS_WWW_FilesDLSWorkshopdileptonhtml
I Why SPF is important
FLAG Collaboration update( July 26 2013) httpitpwikiunibechflag
Running masses mq(Q)
quark masses (from lattice QCD)
[MeV] (MS-bar 2GeV)
mu 216 (9)(7)
md 468 (14)(7)
ms 938 (24)
Running coupling αs(Q)=g24π
PDG (2012) httppdglblgov
I Status of QCD
Hadron masses from Lattice QCD
Improved Wilson + Iwasaki gauge action a = 009 fm L=29 fm mπ=135 MeV PACS-CS Coll Phys Rev D 81 074503 (2010)
3 accuracy
rArr L~96 fm mπ=135 MeV on K-computer underway
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
In-medium hadrons
Complex pole (even for the pion)
One-parameter example (Tne0)
For the pion f(x) and g(x) can be evaluated for small x See eg Jido Kunhihiro + TH Phys Lett B670 (2008) In general experimental inputs are really necessary Sometimes spectral function is better to be studied
Dim3 Chiral condensate in the medium
Lattice QCD (2+1)-flavorBorsanyi et al JHEP 1009 (2010)
Finite Temperature (LQCD)
Nuclear chiral perturbation Kaiser et al PRC 77 (2008)
Finite baryon density (χPT)
Mesic nuclei
2 Individual properties of NG and ldquoHiggsrdquo bosons π K η (NG) σ (Higgs) ηrsquo (anomaly)
σ2γ η2γ ηrsquo2γ
Dileptons3 Individual properties of vector bosons ρ ω and φ
Precisionsystematic studies(dispersion relation different targets hellip)
1 Spectral difference between chiral partners π-σ ρ-a1 ω-f1 etc Determination of D=6 chiral condensates in the vacuumTau-decay in nuclei
Wish list
TH Slide p7(1997)
III Exact sum rules in QCD medium
TH Slide p20(1997)
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
Back up slides
Vector current
Current correlation function
QCD sum rules in the superconducting medium
Operator Product Expansion (OPE) up to O(1Q6)
4-quark condensate
Diquark condensate
Chiral condensate
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
baryons (8)Quarks (9)
Continuity in the excited state
Schafer and Wilczek PRL 82 (1999)
Generalized Gell-Mann-Oakes-Renner relation Yamamoto Tachibana Baym + TH PR D76 (rsquo07)
Continuity of vector mesons Tachibana Yamamoto +TH PRD78 (2008)
Explicit realization of spectral continuity
Possible fate of hadrons at high density （ Nc=3 Nf=3 ）
Vector Mesons = Gluons Baryons = Quarks
cond
ensa
tes Continuity in the ground state
Yamamoto Tachibana Baym + TH PRL97(rsquo06) PRD76 (rsquo07)
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
baryons (8)Quarks (9)
Continuity in the excited state
Schafer and Wilczek PRL 82 (1999)
Hadron-quark continuity in dense QCD
cond
ensa
tes Continuity in the ground state
Hatsuda Tachibana Yamamoto amp Baym PRL 97 (2006)
TH Slide p2(1997)
httpwww-rnclblgovDLSDLS_WWW_FilesDLSWorkshopdileptonhtml
I Why SPF is important
FLAG Collaboration update( July 26 2013) httpitpwikiunibechflag
Running masses mq(Q)
quark masses (from lattice QCD)
[MeV] (MS-bar 2GeV)
mu 216 (9)(7)
md 468 (14)(7)
ms 938 (24)
Running coupling αs(Q)=g24π
PDG (2012) httppdglblgov
I Status of QCD
Hadron masses from Lattice QCD
Improved Wilson + Iwasaki gauge action a = 009 fm L=29 fm mπ=135 MeV PACS-CS Coll Phys Rev D 81 074503 (2010)
3 accuracy
rArr L~96 fm mπ=135 MeV on K-computer underway
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
In-medium hadrons
Complex pole (even for the pion)
One-parameter example (Tne0)
For the pion f(x) and g(x) can be evaluated for small x See eg Jido Kunhihiro + TH Phys Lett B670 (2008) In general experimental inputs are really necessary Sometimes spectral function is better to be studied
Dim3 Chiral condensate in the medium
Lattice QCD (2+1)-flavorBorsanyi et al JHEP 1009 (2010)
Finite Temperature (LQCD)
Nuclear chiral perturbation Kaiser et al PRC 77 (2008)
Finite baryon density (χPT)
Mesic nuclei
2 Individual properties of NG and ldquoHiggsrdquo bosons π K η (NG) σ (Higgs) ηrsquo (anomaly)
σ2γ η2γ ηrsquo2γ
Dileptons3 Individual properties of vector bosons ρ ω and φ
Precisionsystematic studies(dispersion relation different targets hellip)
1 Spectral difference between chiral partners π-σ ρ-a1 ω-f1 etc Determination of D=6 chiral condensates in the vacuumTau-decay in nuclei
Wish list
TH Slide p7(1997)
III Exact sum rules in QCD medium
TH Slide p20(1997)
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
Vector current
Current correlation function
QCD sum rules in the superconducting medium
Operator Product Expansion (OPE) up to O(1Q6)
4-quark condensate
Diquark condensate
Chiral condensate
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
baryons (8)Quarks (9)
Continuity in the excited state
Schafer and Wilczek PRL 82 (1999)
Generalized Gell-Mann-Oakes-Renner relation Yamamoto Tachibana Baym + TH PR D76 (rsquo07)
Continuity of vector mesons Tachibana Yamamoto +TH PRD78 (2008)
Explicit realization of spectral continuity
Possible fate of hadrons at high density （ Nc=3 Nf=3 ）
Vector Mesons = Gluons Baryons = Quarks
cond
ensa
tes Continuity in the ground state
Yamamoto Tachibana Baym + TH PRL97(rsquo06) PRD76 (rsquo07)
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
baryons (8)Quarks (9)
Continuity in the excited state
Schafer and Wilczek PRL 82 (1999)
Hadron-quark continuity in dense QCD
cond
ensa
tes Continuity in the ground state
Hatsuda Tachibana Yamamoto amp Baym PRL 97 (2006)
TH Slide p2(1997)
httpwww-rnclblgovDLSDLS_WWW_FilesDLSWorkshopdileptonhtml
I Why SPF is important
FLAG Collaboration update( July 26 2013) httpitpwikiunibechflag
Running masses mq(Q)
quark masses (from lattice QCD)
[MeV] (MS-bar 2GeV)
mu 216 (9)(7)
md 468 (14)(7)
ms 938 (24)
Running coupling αs(Q)=g24π
PDG (2012) httppdglblgov
I Status of QCD
Hadron masses from Lattice QCD
Improved Wilson + Iwasaki gauge action a = 009 fm L=29 fm mπ=135 MeV PACS-CS Coll Phys Rev D 81 074503 (2010)
3 accuracy
rArr L~96 fm mπ=135 MeV on K-computer underway
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
In-medium hadrons
Complex pole (even for the pion)
One-parameter example (Tne0)
For the pion f(x) and g(x) can be evaluated for small x See eg Jido Kunhihiro + TH Phys Lett B670 (2008) In general experimental inputs are really necessary Sometimes spectral function is better to be studied
Dim3 Chiral condensate in the medium
Lattice QCD (2+1)-flavorBorsanyi et al JHEP 1009 (2010)
Finite Temperature (LQCD)
Nuclear chiral perturbation Kaiser et al PRC 77 (2008)
Finite baryon density (χPT)
Mesic nuclei
2 Individual properties of NG and ldquoHiggsrdquo bosons π K η (NG) σ (Higgs) ηrsquo (anomaly)
σ2γ η2γ ηrsquo2γ
Dileptons3 Individual properties of vector bosons ρ ω and φ
Precisionsystematic studies(dispersion relation different targets hellip)
1 Spectral difference between chiral partners π-σ ρ-a1 ω-f1 etc Determination of D=6 chiral condensates in the vacuumTau-decay in nuclei
Wish list
TH Slide p7(1997)
III Exact sum rules in QCD medium
TH Slide p20(1997)
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
baryons (8)Quarks (9)
Continuity in the excited state
Schafer and Wilczek PRL 82 (1999)
Generalized Gell-Mann-Oakes-Renner relation Yamamoto Tachibana Baym + TH PR D76 (rsquo07)
Continuity of vector mesons Tachibana Yamamoto +TH PRD78 (2008)
Explicit realization of spectral continuity
Possible fate of hadrons at high density （ Nc=3 Nf=3 ）
Vector Mesons = Gluons Baryons = Quarks
cond
ensa
tes Continuity in the ground state
Yamamoto Tachibana Baym + TH PRL97(rsquo06) PRD76 (rsquo07)
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
baryons (8)Quarks (9)
Continuity in the excited state
Schafer and Wilczek PRL 82 (1999)
Hadron-quark continuity in dense QCD
cond
ensa
tes Continuity in the ground state
Hatsuda Tachibana Yamamoto amp Baym PRL 97 (2006)
TH Slide p2(1997)
httpwww-rnclblgovDLSDLS_WWW_FilesDLSWorkshopdileptonhtml
I Why SPF is important
FLAG Collaboration update( July 26 2013) httpitpwikiunibechflag
Running masses mq(Q)
quark masses (from lattice QCD)
[MeV] (MS-bar 2GeV)
mu 216 (9)(7)
md 468 (14)(7)
ms 938 (24)
Running coupling αs(Q)=g24π
PDG (2012) httppdglblgov
I Status of QCD
Hadron masses from Lattice QCD
Improved Wilson + Iwasaki gauge action a = 009 fm L=29 fm mπ=135 MeV PACS-CS Coll Phys Rev D 81 074503 (2010)
3 accuracy
rArr L~96 fm mπ=135 MeV on K-computer underway
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
In-medium hadrons
Complex pole (even for the pion)
One-parameter example (Tne0)
For the pion f(x) and g(x) can be evaluated for small x See eg Jido Kunhihiro + TH Phys Lett B670 (2008) In general experimental inputs are really necessary Sometimes spectral function is better to be studied
Dim3 Chiral condensate in the medium
Lattice QCD (2+1)-flavorBorsanyi et al JHEP 1009 (2010)
Finite Temperature (LQCD)
Nuclear chiral perturbation Kaiser et al PRC 77 (2008)
Finite baryon density (χPT)
Mesic nuclei
2 Individual properties of NG and ldquoHiggsrdquo bosons π K η (NG) σ (Higgs) ηrsquo (anomaly)
σ2γ η2γ ηrsquo2γ
Dileptons3 Individual properties of vector bosons ρ ω and φ
Precisionsystematic studies(dispersion relation different targets hellip)
1 Spectral difference between chiral partners π-σ ρ-a1 ω-f1 etc Determination of D=6 chiral condensates in the vacuumTau-decay in nuclei
Wish list
TH Slide p7(1997)
III Exact sum rules in QCD medium
TH Slide p20(1997)
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
Low High
(8) amp H rsquo (8) amp HNGs
Vectors
Fermions
excitation
V (9)gluons (8)
baryons (8)Quarks (9)
Continuity in the excited state
Schafer and Wilczek PRL 82 (1999)
Hadron-quark continuity in dense QCD
cond
ensa
tes Continuity in the ground state
Hatsuda Tachibana Yamamoto amp Baym PRL 97 (2006)
TH Slide p2(1997)
httpwww-rnclblgovDLSDLS_WWW_FilesDLSWorkshopdileptonhtml
I Why SPF is important
FLAG Collaboration update( July 26 2013) httpitpwikiunibechflag
Running masses mq(Q)
quark masses (from lattice QCD)
[MeV] (MS-bar 2GeV)
mu 216 (9)(7)
md 468 (14)(7)
ms 938 (24)
Running coupling αs(Q)=g24π
PDG (2012) httppdglblgov
I Status of QCD
Hadron masses from Lattice QCD
Improved Wilson + Iwasaki gauge action a = 009 fm L=29 fm mπ=135 MeV PACS-CS Coll Phys Rev D 81 074503 (2010)
3 accuracy
rArr L~96 fm mπ=135 MeV on K-computer underway
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
In-medium hadrons
Complex pole (even for the pion)
One-parameter example (Tne0)
For the pion f(x) and g(x) can be evaluated for small x See eg Jido Kunhihiro + TH Phys Lett B670 (2008) In general experimental inputs are really necessary Sometimes spectral function is better to be studied
Dim3 Chiral condensate in the medium
Lattice QCD (2+1)-flavorBorsanyi et al JHEP 1009 (2010)
Finite Temperature (LQCD)
Nuclear chiral perturbation Kaiser et al PRC 77 (2008)
Finite baryon density (χPT)
Mesic nuclei
2 Individual properties of NG and ldquoHiggsrdquo bosons π K η (NG) σ (Higgs) ηrsquo (anomaly)
σ2γ η2γ ηrsquo2γ
Dileptons3 Individual properties of vector bosons ρ ω and φ
Precisionsystematic studies(dispersion relation different targets hellip)
1 Spectral difference between chiral partners π-σ ρ-a1 ω-f1 etc Determination of D=6 chiral condensates in the vacuumTau-decay in nuclei
Wish list
TH Slide p7(1997)
III Exact sum rules in QCD medium
TH Slide p20(1997)
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
TH Slide p2(1997)
httpwww-rnclblgovDLSDLS_WWW_FilesDLSWorkshopdileptonhtml
I Why SPF is important
FLAG Collaboration update( July 26 2013) httpitpwikiunibechflag
Running masses mq(Q)
quark masses (from lattice QCD)
[MeV] (MS-bar 2GeV)
mu 216 (9)(7)
md 468 (14)(7)
ms 938 (24)
Running coupling αs(Q)=g24π
PDG (2012) httppdglblgov
I Status of QCD
Hadron masses from Lattice QCD
Improved Wilson + Iwasaki gauge action a = 009 fm L=29 fm mπ=135 MeV PACS-CS Coll Phys Rev D 81 074503 (2010)
3 accuracy
rArr L~96 fm mπ=135 MeV on K-computer underway
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
In-medium hadrons
Complex pole (even for the pion)
One-parameter example (Tne0)
For the pion f(x) and g(x) can be evaluated for small x See eg Jido Kunhihiro + TH Phys Lett B670 (2008) In general experimental inputs are really necessary Sometimes spectral function is better to be studied
Dim3 Chiral condensate in the medium
Lattice QCD (2+1)-flavorBorsanyi et al JHEP 1009 (2010)
Finite Temperature (LQCD)
Nuclear chiral perturbation Kaiser et al PRC 77 (2008)
Finite baryon density (χPT)
Mesic nuclei
2 Individual properties of NG and ldquoHiggsrdquo bosons π K η (NG) σ (Higgs) ηrsquo (anomaly)
σ2γ η2γ ηrsquo2γ
Dileptons3 Individual properties of vector bosons ρ ω and φ
Precisionsystematic studies(dispersion relation different targets hellip)
1 Spectral difference between chiral partners π-σ ρ-a1 ω-f1 etc Determination of D=6 chiral condensates in the vacuumTau-decay in nuclei
Wish list
TH Slide p7(1997)
III Exact sum rules in QCD medium
TH Slide p20(1997)
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
httpwww-rnclblgovDLSDLS_WWW_FilesDLSWorkshopdileptonhtml
I Why SPF is important
FLAG Collaboration update( July 26 2013) httpitpwikiunibechflag
Running masses mq(Q)
quark masses (from lattice QCD)
[MeV] (MS-bar 2GeV)
mu 216 (9)(7)
md 468 (14)(7)
ms 938 (24)
Running coupling αs(Q)=g24π
PDG (2012) httppdglblgov
I Status of QCD
Hadron masses from Lattice QCD
Improved Wilson + Iwasaki gauge action a = 009 fm L=29 fm mπ=135 MeV PACS-CS Coll Phys Rev D 81 074503 (2010)
3 accuracy
rArr L~96 fm mπ=135 MeV on K-computer underway
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
In-medium hadrons
Complex pole (even for the pion)
One-parameter example (Tne0)
For the pion f(x) and g(x) can be evaluated for small x See eg Jido Kunhihiro + TH Phys Lett B670 (2008) In general experimental inputs are really necessary Sometimes spectral function is better to be studied
Dim3 Chiral condensate in the medium
Lattice QCD (2+1)-flavorBorsanyi et al JHEP 1009 (2010)
Finite Temperature (LQCD)
Nuclear chiral perturbation Kaiser et al PRC 77 (2008)
Finite baryon density (χPT)
Mesic nuclei
2 Individual properties of NG and ldquoHiggsrdquo bosons π K η (NG) σ (Higgs) ηrsquo (anomaly)
σ2γ η2γ ηrsquo2γ
Dileptons3 Individual properties of vector bosons ρ ω and φ
Precisionsystematic studies(dispersion relation different targets hellip)
1 Spectral difference between chiral partners π-σ ρ-a1 ω-f1 etc Determination of D=6 chiral condensates in the vacuumTau-decay in nuclei
Wish list
TH Slide p7(1997)
III Exact sum rules in QCD medium
TH Slide p20(1997)
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
FLAG Collaboration update( July 26 2013) httpitpwikiunibechflag
Running masses mq(Q)
quark masses (from lattice QCD)
[MeV] (MS-bar 2GeV)
mu 216 (9)(7)
md 468 (14)(7)
ms 938 (24)
Running coupling αs(Q)=g24π
PDG (2012) httppdglblgov
I Status of QCD
Hadron masses from Lattice QCD
Improved Wilson + Iwasaki gauge action a = 009 fm L=29 fm mπ=135 MeV PACS-CS Coll Phys Rev D 81 074503 (2010)
3 accuracy
rArr L~96 fm mπ=135 MeV on K-computer underway
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
In-medium hadrons
Complex pole (even for the pion)
One-parameter example (Tne0)
For the pion f(x) and g(x) can be evaluated for small x See eg Jido Kunhihiro + TH Phys Lett B670 (2008) In general experimental inputs are really necessary Sometimes spectral function is better to be studied
Dim3 Chiral condensate in the medium
Lattice QCD (2+1)-flavorBorsanyi et al JHEP 1009 (2010)
Finite Temperature (LQCD)
Nuclear chiral perturbation Kaiser et al PRC 77 (2008)
Finite baryon density (χPT)
Mesic nuclei
2 Individual properties of NG and ldquoHiggsrdquo bosons π K η (NG) σ (Higgs) ηrsquo (anomaly)
σ2γ η2γ ηrsquo2γ
Dileptons3 Individual properties of vector bosons ρ ω and φ
Precisionsystematic studies(dispersion relation different targets hellip)
1 Spectral difference between chiral partners π-σ ρ-a1 ω-f1 etc Determination of D=6 chiral condensates in the vacuumTau-decay in nuclei
Wish list
TH Slide p7(1997)
III Exact sum rules in QCD medium
TH Slide p20(1997)
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
Hadron masses from Lattice QCD
Improved Wilson + Iwasaki gauge action a = 009 fm L=29 fm mπ=135 MeV PACS-CS Coll Phys Rev D 81 074503 (2010)
3 accuracy
rArr L~96 fm mπ=135 MeV on K-computer underway
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
In-medium hadrons
Complex pole (even for the pion)
One-parameter example (Tne0)
For the pion f(x) and g(x) can be evaluated for small x See eg Jido Kunhihiro + TH Phys Lett B670 (2008) In general experimental inputs are really necessary Sometimes spectral function is better to be studied
Dim3 Chiral condensate in the medium
Lattice QCD (2+1)-flavorBorsanyi et al JHEP 1009 (2010)
Finite Temperature (LQCD)
Nuclear chiral perturbation Kaiser et al PRC 77 (2008)
Finite baryon density (χPT)
Mesic nuclei
2 Individual properties of NG and ldquoHiggsrdquo bosons π K η (NG) σ (Higgs) ηrsquo (anomaly)
σ2γ η2γ ηrsquo2γ
Dileptons3 Individual properties of vector bosons ρ ω and φ
Precisionsystematic studies(dispersion relation different targets hellip)
1 Spectral difference between chiral partners π-σ ρ-a1 ω-f1 etc Determination of D=6 chiral condensates in the vacuumTau-decay in nuclei
Wish list
TH Slide p7(1997)
III Exact sum rules in QCD medium
TH Slide p20(1997)
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
In-medium hadrons
Complex pole (even for the pion)
One-parameter example (Tne0)
For the pion f(x) and g(x) can be evaluated for small x See eg Jido Kunhihiro + TH Phys Lett B670 (2008) In general experimental inputs are really necessary Sometimes spectral function is better to be studied
Dim3 Chiral condensate in the medium
Lattice QCD (2+1)-flavorBorsanyi et al JHEP 1009 (2010)
Finite Temperature (LQCD)
Nuclear chiral perturbation Kaiser et al PRC 77 (2008)
Finite baryon density (χPT)
Mesic nuclei
2 Individual properties of NG and ldquoHiggsrdquo bosons π K η (NG) σ (Higgs) ηrsquo (anomaly)
σ2γ η2γ ηrsquo2γ
Dileptons3 Individual properties of vector bosons ρ ω and φ
Precisionsystematic studies(dispersion relation different targets hellip)
1 Spectral difference between chiral partners π-σ ρ-a1 ω-f1 etc Determination of D=6 chiral condensates in the vacuumTau-decay in nuclei
Wish list
TH Slide p7(1997)
III Exact sum rules in QCD medium
TH Slide p20(1997)
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
In-medium hadrons
Complex pole (even for the pion)
One-parameter example (Tne0)
For the pion f(x) and g(x) can be evaluated for small x See eg Jido Kunhihiro + TH Phys Lett B670 (2008) In general experimental inputs are really necessary Sometimes spectral function is better to be studied
Dim3 Chiral condensate in the medium
Lattice QCD (2+1)-flavorBorsanyi et al JHEP 1009 (2010)
Finite Temperature (LQCD)
Nuclear chiral perturbation Kaiser et al PRC 77 (2008)
Finite baryon density (χPT)
Mesic nuclei
2 Individual properties of NG and ldquoHiggsrdquo bosons π K η (NG) σ (Higgs) ηrsquo (anomaly)
σ2γ η2γ ηrsquo2γ
Dileptons3 Individual properties of vector bosons ρ ω and φ
Precisionsystematic studies(dispersion relation different targets hellip)
1 Spectral difference between chiral partners π-σ ρ-a1 ω-f1 etc Determination of D=6 chiral condensates in the vacuumTau-decay in nuclei
Wish list
TH Slide p7(1997)
III Exact sum rules in QCD medium
TH Slide p20(1997)
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
Dim3 Chiral condensate in the medium
Lattice QCD (2+1)-flavorBorsanyi et al JHEP 1009 (2010)
Finite Temperature (LQCD)
Nuclear chiral perturbation Kaiser et al PRC 77 (2008)
Finite baryon density (χPT)
Mesic nuclei
2 Individual properties of NG and ldquoHiggsrdquo bosons π K η (NG) σ (Higgs) ηrsquo (anomaly)
σ2γ η2γ ηrsquo2γ
Dileptons3 Individual properties of vector bosons ρ ω and φ
Precisionsystematic studies(dispersion relation different targets hellip)
1 Spectral difference between chiral partners π-σ ρ-a1 ω-f1 etc Determination of D=6 chiral condensates in the vacuumTau-decay in nuclei
Wish list
TH Slide p7(1997)
III Exact sum rules in QCD medium
TH Slide p20(1997)
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
Mesic nuclei
2 Individual properties of NG and ldquoHiggsrdquo bosons π K η (NG) σ (Higgs) ηrsquo (anomaly)
σ2γ η2γ ηrsquo2γ
Dileptons3 Individual properties of vector bosons ρ ω and φ
Precisionsystematic studies(dispersion relation different targets hellip)
1 Spectral difference between chiral partners π-σ ρ-a1 ω-f1 etc Determination of D=6 chiral condensates in the vacuumTau-decay in nuclei
Wish list
TH Slide p7(1997)
III Exact sum rules in QCD medium
TH Slide p20(1997)
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
TH Slide p7(1997)
III Exact sum rules in QCD medium
TH Slide p20(1997)
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
III Exact sum rules in QCD medium
TH Slide p20(1997)
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
Nambu-Goldstone bosons
Other hadrons
Examples
QCDSR from Commutatorby Hayata PRD88 (2013)
Gell-Mann-Oakes-Renner relation (1968)
QCDSR from OPE by SVD (1979)
III In-medium hadrons
In-vacuum
