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.)”
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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
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)
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
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Slide 11
Slide 12
Slide 13
Slide 14
Slide 15
Slide 16
Slide 17
Slide 18
Slide 19
Slide 20
Slide 21
Slide 22
Slide 23
Slide 24
Slide 25
Slide 26
Slide 27
Slide 28
Slide 29
Slide 30
Slide 31
Slide 32
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
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)
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
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Slide 11
Slide 12
Slide 13
Slide 14
Slide 15
Slide 16
Slide 17
Slide 18
Slide 19
Slide 20
Slide 21
Slide 22
Slide 23
Slide 24
Slide 25
Slide 26
Slide 27
Slide 28
Slide 29
Slide 30
Slide 31
Slide 32
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
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)
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
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Slide 11
Slide 12
Slide 13
Slide 14
Slide 15
Slide 16
Slide 17
Slide 18
Slide 19
Slide 20
Slide 21
Slide 22
Slide 23
Slide 24
Slide 25
Slide 26
Slide 27
Slide 28
Slide 29
Slide 30
Slide 31
Slide 32
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
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)
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
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Slide 11
Slide 12
Slide 13
Slide 14
Slide 15
Slide 16
Slide 17
Slide 18
Slide 19
Slide 20
Slide 21
Slide 22
Slide 23
Slide 24
Slide 25
Slide 26
Slide 27
Slide 28
Slide 29
Slide 30
Slide 31
Slide 32
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
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)
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
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Slide 11
Slide 12
Slide 13
Slide 14
Slide 15
Slide 16
Slide 17
Slide 18
Slide 19
Slide 20
Slide 21
Slide 22
Slide 23
Slide 24
Slide 25
Slide 26
Slide 27
Slide 28
Slide 29
Slide 30
Slide 31
Slide 32
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
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)
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
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Slide 11
Slide 12
Slide 13
Slide 14
Slide 15
Slide 16
Slide 17
Slide 18
Slide 19
Slide 20
Slide 21
Slide 22
Slide 23
Slide 24
Slide 25
Slide 26
Slide 27
Slide 28
Slide 29
Slide 30
Slide 31
Slide 32
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
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)
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
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Slide 11
Slide 12
Slide 13
Slide 14
Slide 15
Slide 16
Slide 17
Slide 18
Slide 19
Slide 20
Slide 21
Slide 22
Slide 23
Slide 24
Slide 25
Slide 26
Slide 27
Slide 28
Slide 29
Slide 30
Slide 31
Slide 32
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
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)
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
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Slide 11
Slide 12
Slide 13
Slide 14
Slide 15
Slide 16
Slide 17
Slide 18
Slide 19
Slide 20
Slide 21
Slide 22
Slide 23
Slide 24
Slide 25
Slide 26
Slide 27
Slide 28
Slide 29
Slide 30
Slide 31
Slide 32
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
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)
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
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)
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
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Slide 11
Slide 12
Slide 13
Slide 14
Slide 15
Slide 16
Slide 17
Slide 18
Slide 19
Slide 20
Slide 21
Slide 22
Slide 23
Slide 24
Slide 25
Slide 26
Slide 27
Slide 28
Slide 29
Slide 30
Slide 31
Slide 32
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)
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)
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
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Slide 11
Slide 12
Slide 13
Slide 14
Slide 15
Slide 16
Slide 17
Slide 18
Slide 19
Slide 20
Slide 21
Slide 22
Slide 23
Slide 24
Slide 25
Slide 26
Slide 27
Slide 28
Slide 29
Slide 30
Slide 31
Slide 32
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)
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)
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
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Slide 11
Slide 12
Slide 13
Slide 14
Slide 15
Slide 16
Slide 17
Slide 18
Slide 19
Slide 20
Slide 21
Slide 22
Slide 23
Slide 24
Slide 25
Slide 26
Slide 27
Slide 28
Slide 29
Slide 30
Slide 31
Slide 32
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)
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)
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
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)
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
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Slide 11
Slide 12
Slide 13
Slide 14
Slide 15
Slide 16
Slide 17
Slide 18
Slide 19
Slide 20
Slide 21
Slide 22
Slide 23
Slide 24
Slide 25
Slide 26
Slide 27
Slide 28
Slide 29
Slide 30
Slide 31
Slide 32
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)
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
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Slide 11
Slide 12
Slide 13
Slide 14
Slide 15
Slide 16
Slide 17
Slide 18
Slide 19
Slide 20
Slide 21
Slide 22
Slide 23
Slide 24
Slide 25
Slide 26
Slide 27
Slide 28
Slide 29
Slide 30
Slide 31
Slide 32
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)
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
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
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
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
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
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
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
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Slide 11
Slide 12
Slide 13
Slide 14
Slide 15
Slide 16
Slide 17
Slide 18
Slide 19
Slide 20
Slide 21
Slide 22
Slide 23
Slide 24
Slide 25
Slide 26
Slide 27
Slide 28
Slide 29
Slide 30
Slide 31
Slide 32
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
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Slide 11
Slide 12
Slide 13
Slide 14
Slide 15
Slide 16
Slide 17
Slide 18
Slide 19
Slide 20
Slide 21
Slide 22
Slide 23
Slide 24
Slide 25
Slide 26
Slide 27
Slide 28
Slide 29
Slide 30
Slide 31
Slide 32
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
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Slide 11
Slide 12
Slide 13
Slide 14
Slide 15
Slide 16
Slide 17
Slide 18
Slide 19
Slide 20
Slide 21
Slide 22
Slide 23
Slide 24
Slide 25
Slide 26
Slide 27
Slide 28
Slide 29
Slide 30
Slide 31
Slide 32
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
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Slide 11
Slide 12
Slide 13
Slide 14
Slide 15
Slide 16
Slide 17
Slide 18
Slide 19
Slide 20
Slide 21
Slide 22
Slide 23
Slide 24
Slide 25
Slide 26
Slide 27
Slide 28
Slide 29
Slide 30
Slide 31
Slide 32
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
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Slide 11
Slide 12
Slide 13
Slide 14
Slide 15
Slide 16
Slide 17
Slide 18
Slide 19
Slide 20
Slide 21
Slide 22
Slide 23
Slide 24
Slide 25
Slide 26
Slide 27
Slide 28
Slide 29
Slide 30
Slide 31
Slide 32
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
Slide 1
Slide 2
Slide 3
Slide 4
Slide 5
Slide 6
Slide 7
Slide 8
Slide 9
Slide 10
Slide 11
Slide 12
Slide 13
Slide 14
Slide 15
Slide 16
Slide 17
Slide 18
Slide 19
Slide 20
Slide 21
Slide 22
Slide 23
Slide 24
Slide 25
Slide 26
Slide 27
Slide 28
Slide 29
Slide 30
Slide 31
Slide 32
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