｢第５回 J-PARCにおける高エネルギーハドロン物理｣
J-PARCに活きる南部先生のアイデア
1.
2.
3.
4.
plan
Introdution
Stability of hadronic matter
Chiral symmetry in vacuum & in medium
No summary
references
○ 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] ]
T. Hatsuda (Univ. of Tokyo) KEK, Jan. 8, 2009
Subatomic structure of matter
Nuclei
Hadron
r ～10 [fm]
r ～1 [fm]
String？
r << 10-4 [fm]
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) .
Y. Nambu at INPC2007
4. String theory:
“Duality and hadrodynamics”,
note prepared for the Copenhagen High Energy Symposium, Aug. 1970.
Repulsive core in nuclear force
ω-meson
Phys. Rev. 106 (1957) 1366
NN,YN and YY interactions in lattice QCD
(Aoki, Ishii, Nemura & Hatsuda, 2008)
after 50 years
powered by QCD
YN and YY interactions at J-PARC
Structure of neutron stars
Origin of the fermion mass
Two revolutionary ideas proposed in 1961
1.
massless fermion ⇒ massive fermion + massless composite boson
Y. Nambu and G. Jona-Lasinio, Phys. Rev. 122 (’61) 345
2.
massless boson
⇒ massive topological fermion + massless boson
T.H.R. Skyrme, Proc. Roy. Soc. Lond. A260 (’61) 127
These ideas are relevant in QCD and are dual
relevant
dual
Nambu’s fermion/boson
Skyrme’s fermion/boson
=
=
quark/pion
nucleon/pion
bosonized Nambu
=
Skyrme
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
-M
massive Dirac sea
・ Dynamical mass
“Cooper”
instability
massless Dirac sea
g<gc g=gc g> gc
・ Vacuum energy
M
What about QCD ?
[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)
Y. Nambu, Nobel Lecture (Dec.8, 2008), page 21/25
NJL+KMT vs. Exp. data
taken from
Hatsuda & Kunihiro,
Phys.Rep. 247 (1994).
Growth in Supercomputer peak performance
100P
Doubling time = 1.2 years
Keisoku
10P
(Flops)
1P
100T
10T
1T
100G
10G
1990
1995
2000
2005
2010
2015
(year)
Adapted from Wikimedia Commons
Dim.3 chiral condensate (Nambu condensate) in the QCD vacuum
Gell-Mann-Oakes-Renner (GOR) formula (1968)
Di Vecchia-Veneziano formula (1980)
0
Lattice QCD calculation by
JLQCD+TWQCD Collaborations, arXiv:0810.0085 [hep-lat]
Dynamical quark-mass in the QCD vacuum
M (0) ~ 300-400 MeV
Lattice QCD calculation in Landau gauge,
203x64, a=0.125fm, MILC config.
P. O. Bowman et al., Phys. Rev. D71 (2005) 054507
Spectral evidence of DBCS in QCD
Nambu condensate
qq
3


(
250
MeV
)
 2GeV
“Higgs” in QCD
Nambu-Goldstone boson
σ（６００）
(Theoretical) Nambu condensate in the QCD medium
Finite Temperature
Lattice QCD, (2+1)-flavor
Cheng et al., PRD 77 (2008)
Finite Baryon Density
Nuclear chiral perturbation
Kaiser et al., PRC 77 (2008)
Experimental determination of in-medium Nambu condensate
from deeply bound pionic atom
Toki, Hirenzaki, Yamazaki & Hayano,
NP A501 (1989) 653
p
Jido, Hatsuda & Kunihiro, PL B670 (2008) 109
Hayano & Hatsuda, Rev. Mod. Phys. (2009)
Suzuki et al., PRL 92 (2004) 72302
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
Dim.6 chiral condensate
Hatsuda, Koike & Lee. Nucl. Phys. B394 (1993) 221
Kapusta & Shuryak, Phys. Rev. D49 (1994) 4694
V & A spectral functions in the QCD vacuum fromτ-decay at LEP-1
ρA(s)/s
[ρV(s)-ρA(s)] /s
ρV(s)/s
ALEPH Collaboration,
Phys. Rep. 421 (2005) 191
Precision measurement at KEKB ?
“Origin of hadron mass = Nambu condensate” ?
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
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)
δ
σ
π
“Phase” diagram of QCD
～0.2 GeV
Quark-Gluon Plasma
RHIC/LHC
Chiral Superfluid
Color Superfluid
～1 GeV
Q
Neutron star
J-PARCに活きる南部先生のアイデア ｢物質安定性の起源と質量の起源」
quark
nucleon
J-PARC as a QCD machine