｢｢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

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

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

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

Y. Nambu, Nobel Lecture (Dec.8, 2008), page 22/25

Y. Nambu, Nobel Lecture (Dec.8, 2008), page 24/25

One-page summary of NJL One-page summary of NJL

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

[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 ?

Y. Nambu, Nobel Lecture (Dec.8, 2008), page 21/25

NJL+KMT vs. Exp. datataken from Hatsuda & Kunihiro,Phys.Rep. 247 (1994).

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

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

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

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

(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

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)

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

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 ?

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

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

　　　 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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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