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「「第5回 第5回 J-PARCJ-PARC における高エネルギーハドロン物理における高エネルギーハドロン物理」」
J-PARCJ-PARC に活きる南部先生のアイデアに活きる南部先生のアイデア
1. Introdution2. Stability of hadronic matter3. Chiral symmetry in vacuum & in medium
4. No summary
T. Hatsuda (Univ. of Tokyo) KEK, Jan. 8, 2009
plan
○ Y. Nambu, “Broken Symmetry”, Selected Papers of Y. Nambu, World Scientific (1995).
○ Y. Nambu, “Spontaneus symmetry breaking in particle physics: a case of cross fertilization”,
Nobel Lecture (Dec. 8, 2008) pp.1-25.
○ T. Hatsuda & T. Kunihiro, “QCD phenomenology based on a chiral effective lagrangian”,
Phys. Rep. Vol. 247 (1994) pp.221-367.
○ R. Hayano & T. Hatsuda, “Hadron properties in the nuclear medium”, Rev. Mod. Phys. (2009) [arXiv:0812.1702 [nucl-ex] ]
references
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String ?
r << 10-4 [fm]
Nuclei
r ~ 10 [fm] r ~ 1 [fm]
Hadron
Y. Nambu at INPC2007
1. Repulsive core in nuclear force: “ Possible existence of a heavy neutral meson”, Phys. Rev. 106
(1957) 1366.
2. Dynamical breaking of chiral symmetry (with G. Jona-Lasinio):
“Dynamical model of elementary particles based on an analogy with superconductivity I, II”, Phys. Rev. 122 (1961) 345, ibid. 124 (1961) 246.
3. Quantum chromodynamics: “A systematics of hadrons in subnuclear physics”, in Preludes in Theoretical Physics (North-Holland, Amsterdam, 1966)
.
4. String theory: “Duality and hadrodynamics”, note prepared for the Copenhagen High Energy Symposium, Aug.
1970.
Subatomic structure of matterSubatomic structure of matter
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Phys. Rev. 106 (1957) 1366 ω-meson
NN,YN and YY interactions in lattice QCD (Aoki, Ishii, Nemura & Hatsuda, 2008)
YN and YY interactions at J-PARCStructure of neutron stars
after 50 years powered by QCD
Repulsive core in nuclear forceRepulsive core in nuclear force
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Origin of the fermion massOrigin of the fermion mass
These ideas are relevant in QCD and are dual
relevant Nambu’s fermion/boson = quark/pion Skyrme’s fermion/boson = nucleon/pion
dual bosonized Nambu = Skyrme
Y. Nambu and G. Jona-Lasinio, Phys. Rev. 122 (’61) 345
1. massless fermion ⇒ massive fermion + massless composite boson
2. massless boson ⇒ massive topological fermion + massless boson
T.H.R. Skyrme, Proc. Roy. Soc. Lond. A260 (’61) 127
Two revolutionary ideas proposed in 1961
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Y. Nambu, Nobel Lecture (Dec.8, 2008), page 22/25
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Y. Nambu, Nobel Lecture (Dec.8, 2008), page 24/25
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One-page summary of NJL One-page summary of NJL
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One-page summary of NJL One-page summary of NJL
massless Dirac seamassive Dirac sea
-M
“Cooper” instability
・ Dynamical mass
・ Vacuum energy
M
g<gc g=gc g> gc
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[QCD] ・ most attractive channels : scalar & pseudo-scalar ・ running coupling : large at low energies ⇒ NJL mechanism is expected to take place
Superconductivity Strong interaction
Microscopic theory(relevant symmetry)
electron + phonon
(global gauge symmetry) quark + gluon
(global chiral symmetry)
Effective theory for fermions
BCS model for electrons e↑(x) & e↓(x)
NJL model for quarks qL(x) & qR(x)
Effective theory for soft modes
Ginzburg-Landau theory for Cooper pair Δ(x)
Chiral perturbation theory for pion π(x)
What about QCD ?What about QCD ?
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Y. Nambu, Nobel Lecture (Dec.8, 2008), page 21/25
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NJL+KMT vs. Exp. datataken from Hatsuda & Kunihiro,Phys.Rep. 247 (1994).
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100G
100P
10P
1P
100T
10T
1T
10G
1990 1995 2000 2005 2010 2015
Keisoku
Growth in Supercomputer peak performance Growth in Supercomputer peak performance
(year)
(Flo
ps)
Doubling time = 1.2 years
Adapted from Wikimedia Commons
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Gell-Mann-Oakes-Renner (GOR) formula (1968)
0
Lattice QCD calculation byJLQCD+TWQCD Collaborations, arXiv:0810.0085 [hep-lat]
Di Vecchia-Veneziano formula (1980)
Dim.3 chiral condensate (Nambu condensate) in the QCD vacuumDim.3 chiral condensate (Nambu condensate) in the QCD vacuum
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Dynamical quark-mass in the QCD vacuumDynamical quark-mass in the QCD vacuum
Lattice QCD calculation in Landau gauge, 203x64, a=0.125fm, MILC config.P. O. Bowman et al., Phys. Rev. D71 (2005) 054507
M (0) ~ 300-400 MeV
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σ (600)
Spectral evidence of DBCS in QCDSpectral evidence of DBCS in QCD
3
GeV2)MeV250(
qq
Nambu condensate
“Higgs” in QCD
Nambu-Goldstone boson
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(Theoretical) Nambu condensate in the QCD medium (Theoretical) Nambu condensate in the QCD medium
Lattice QCD, (2+1)-flavorCheng et al., PRD 77 (2008)
Finite Temperature
Nuclear chiral perturbation Kaiser et al., PRC 77 (2008)
Finite Baryon Density
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Experimental determination of in-medium Nambu condensatefrom deeply bound pionic atom
Experimental determination of in-medium Nambu condensatefrom deeply bound pionic atom
Toki, Hirenzaki, Yamazaki & Hayano, NP A501 (1989) 653
Suzuki et al., PRL 92 (2004) 72302
Jido, Hatsuda & Kunihiro, PL B670 (2008) 109Hayano & Hatsuda, Rev. Mod. Phys. (2009)
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What about other mesons (ρ, ω, φ, σ, η, η’ …) ?What about other mesons (ρ, ω, φ, σ, η, η’ …) ?
・ Many models proposed (BR scaling, HLS, Bag, ….)・ None of them are exact except for spectral sum rules from OPE
e.g. Weinberg-type sum rules
Hatsuda, Koike & Lee. Nucl. Phys. B394 (1993) 221Kapusta & Shuryak, Phys. Rev. D49 (1994) 4694
Dim.6 chiral condensate
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ALEPH Collaboration, Phys. Rep. 421 (2005) 191
V & A spectral functions in the QCD vacuum fromτ-decay at LEP-1 V & A spectral functions in the QCD vacuum fromτ-decay at LEP-1 ρ
V(s
)/s
ρA(s
)/s
[ρV(s
)-ρ
A(s
)] /
s
Precision measurement at KEKB ?
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Dim.6 chiral condensate
Messages
1.DBCS is best seen in the spectral difference: <VV>-<AA>, <SS>-<PP>, etc
2.Spectral difference in different channels ⇔ different chiral condensates
3.“Origin of hadron mass = Nambu condensate” : true for the pion (GOR)
BUT , ρ, ω, N, … could be massive even if chiral restoration takes place
“Origin of hadron mass = Nambu condensate” ?“Origin of hadron mass = Nambu condensate” ?
Theretically, we need further logical step Experimentally, precision measurement of SPF at J-PARC
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Spectral sum at finite T on the lattice (π, σ, δ) Spectral sum at finite T on the lattice (π, σ, δ)
π
σ
δ
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Color Superfluid
Chiral Superfluid
~ 1 GeV
~0.2
G
eV
Quark-Gluon Plasma
“Phase” diagram of QCD “Phase” diagram of QCD
Q
~1 G
eV
RHIC/LHC
Neutron star
J-PARC
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J-PARCJ-PARC に活きる南部先生のアイデア に活きる南部先生のアイデア
nucleon
quark
「「物質安定性の起源と質量の起源」 物質安定性の起源と質量の起源」
J-PARCJ-PARC as a QCD machineas a QCD machine