1• Main purpose was:
− Probing of an existence of Quark Gluon
Plasma− QGP signatures were observed at RHIC& LHC
ü J/y, U suppressions
ü Thermal photons from the mediumü Jet quenchingü Collective flow

1

• Main purpose was:
− Probing of an existence of Quark Gluon
Plasma− QGP signatures were observed at RHIC& LHC
ü J/y, U suppressions
ü Thermal photons from the mediumü Jet quenchingü Collective flow
− But some of important signatures are still
missing…

2

From GSI HP• Large playground in low T & more
dense region to be explored− NOT just back to AGS energy
region• Interesting topics addressed tofuture experiments at FAIR, JPARC-HIü Critical point searchü Thermal dileptons
ü Chiral symmetry restoration
ü Hyper nuclei
ü Hadron correlations
ü Exotic QCD state
ü…

2

From GSI HP• Large playground in low T & more
dense region to be explored− NOT just back to AGS energy
region• Interesting topics addressed tofuture experiments at FAIR, JPARC-HIü Critical point searchü Thermal dileptons
ü Chiral symmetry restoration
ü Hyper nuclei
ü Hadron correlations
ü Exotic QCD state
ü…

3

Direct photon v2 puzzle
PRC94, 064901 (2016)

Each theory curve has
multiple contributing
direct photon sources

vn is the weighted
average of source vn’s

• Thermal
dileptons for QGP
Difficult forphotons
theory to&reproduce
temperature
measurements
and large vn
large low pT yields− 1-3 GeV/c photons or 1-3 GeV/c2
Yields/Theory
dileptons• What we’ve learnt from “direct photon
Fireballpuzzle”− Possibly late stage photons are
Semi-QGP
dominant due to bule shift by radial
w.o viscousflow− Hard to extract initial temperature of
PHSD the medium from photon spectrum→ Only solution = thermal dileptons

the data are compared with the expected contributions from known hadronic sources, i.e. the RAA modified HF cocktail shown with dashed lines and the Ncoll -scaled HF cocktail displayed as full lines,
both explained in Section 4.1.2. In the p 0 (mee < 0.135 GeV/c2 ) and J/y (2.7 < mee < 3.3 GeV/c2 )mass regions, where dielectrons from p 0 -Dalitz and J/y decays are expected to dominate the yield ofe+ e pairs, respectively, the data are well reproduced by the hadronic cocktails.

T,eeDataCocktail (〈N〉-scaled HF)

collc,b → e±Cocktail (R AA-modified HF)+ −+ −

Light Flavor w/ ρ → e e , e e X
J/ψ → e+e−, e+e−γ
cc → e+e− (〈N1〉-scaled)coll

bb → e+e− (〈N coll〉-scaled)c,b → ecc → e+e− (R AA10− 1+ −bb → e e±-modified)c,b → e±(R AA-modified)10− 2• Only missing EM probe so far
10− Open heavy flavors as dominant
10background in RHIC & LHC energies
1 − Almost free from them at FAIRenergy
10→ Can be measured if thermalized
10medium is created

1 dN [(GeV/c 2)−1]
N ev dm ee

10ALICE
0−10% Pb−Pb s NN = 5.02 TeV
0.2 < p < 10 GeV/ c , |η e| < 0.8T,e
0.0 < p< 8.0 GeV/c2

ALICE

Cocktail1 + QGP + in-medium ρ (R.Rapp)
Cocktail1 + QGP + in-medium ρ (PHSD)
Cocktail2 + QGP + in-medium ρ (R.Rapp)
Cocktail2 + QGP + in-medium ρ (PHSD)

0−10% Pb−Pb s NN = 5.02 TeV
0.2 < p < 10 GeV/c , |η e| < 0.8T,e

0.0 < pT,ee< 8.0 GeV/cData

Cocktail1 (LF w/o ρ + J/ψ + 〈N〉-scaled HF)

collc,b → e±

Cocktail2 (LF w/o ρ + J/ψ + R AA

-modified HF)−1−2−3−3Data
Cocktail

102.50
2
1.5
1
0.5

0.5

1

1.5

2

2.5

Data
Cocktail

102.50
2
1.5
1
0.5

0.5

11.5

22.5

3.5mee (GeV/c 2)

00.5

11.5

22.5

33.5m ee (GeV/c 2)

33.5m ee (GeV/c 2)

3

QGP + in-medium ρ (R.Rapp)
QGP + in-medium ρ (PHSD)

Data
Cocktail

102

2.50
2
1.5
10.5

0.5

11.5

2

2.5

Data
Cocktail

1 dN [(GeV/c 2)−1]
N ev dm ee

arXiv: 2308.16704 (ALICE)

2.50
2
1.5
10.5

0.5

11.5

2

2.5

3.5mee (GeV/c 2)

00.5

1

1.5

2

2.5

33.5
m ee (GeV/c 2)

33.5
m ee (GeV/c 2)

345NA60実験
Phys.Rev.lett
162302(2006)
PRL96,96162302• Hadron mass generation by chiralsymmetry breaking− Partial restoration in hot and/or highdensity environment• Observed positive indications
カイラル対称性回復の効果は無い、− Lower mass tail of f peak for low b at
あるいは、E325 (KEK-PS)
重イオンのレプトン対では見えない、− Broader r peak in In-In at NA60 (SPS)と言っているわけでは無い。
Ø Better description by broadening
due to hadronic effects(個人的には、ピーク近傍を見る→ No conclusive result so far
限りp+Aの物理だと思うが、、)では、レプトン対の何を見ればいいのかは、

6
PRD78, 114003 (2008), arXiv: 2308.03305• What can be conclusive signatures of CSR− Degeneracy of mass for chiral partners− V-A mixing (r-a1/w-f1 mixing)→ Additional contribution in dilepton spectrum
due to Modification of LVM spectral function

Results: Invariant mass spectrum• First hydrodynamic calculation w/ CSR− Assuming high T & µB = 0→ Moderate enhancement in M>1.1GeV/c2
High T & µB=0Fig. Spectral function

6

成物質

PRD78, 114003 (2008), arXiv: 2308.03305

JAM2 Min.bias• What can be conclusive signatures of CSR− Degeneracy of mass for chiral partners− V-A mixing (r-a1/w-f1 mixing)→ Additional contribution in dilepton spectrum
due to Modification of LVM spectral function

Results: Invariant mass spectrum

High T & µB=0、生成物質は高密度側に行くPARC)は原子核内部はおろか• First hydrodynamic calculation w/ CSR− Assuming high T & µB = 0→ Moderate enhancement in M>1.1GeV/c2• V-A mixing strength linearly increases with µB− ref: PRD 106, 054034 (2022)→ Expect stronger signal at FAIR energy
Fig. Spectral function

7Byz• Emergence of spatial modulation infinite density region predicted by theory− Fragile against fluctuations• External field/fast rotation can assist to
realize such inhomogeneity− Strong magnetic field with peripheral
collision
ü Chiral Spiral: PRL 104, 232301
x(2010)ü Chiral Soliton Lattice: JHEP 02, 069(2018)• Hot subject in material science as well
− With same form of Hamiltonian

8• Remnant of “primordial inhomogeneity”
may survive until freeze-out− 1-dimensional inhomogeneity along
Quasi Long
magnetic field
Range Order− Periodic cluster substructure"ü Wave number !~2$! = $$ from
#Chiral Spiral• Proposal of HBT measurement to detectPrimordial
the cluster substructure
Inhomogeneity
Chiral Soliton LatticeØ arXiv: 2306.17619 (Fukushima, Inoue,Hidaka, Shigaki, Yamaguchi)

9!! = !" = #• Demonstration of simple Gaussian
source with modulation− Gaussian source size &% = 6fm− Wave number ! = 80MeV for *&& =30GeV− Maximum effect for -⃗ ∥ / = 0'→ Peak around ! = 80MeV• Strong dependence on 1(− 1( = discrepancy of measured /from true /10,! = 20°• Feasibility study done with AMPT
− Impact parameter 2 = 3 − 4fm− *&& = 39GeV− Modulation by hand, base on AMPT
particle distribution− 6 ± − 6 ± correlation• Wash-out of signal with large ∆− ∆- = -*" + -+"− Can serve as baseline→ Ratio of C2(small ∆-)/C2(inclusive ∆-)helps for signal detection− Cancel out systematic errors

11• Exploration of low T & high density region in QCD phase
diagramü Based on our current knowledge from RHIC & LHC• Important/unique topics can be studied at FAIRü Thermal dileptons for initial temperatureü V-A mixing signal for chiral symmetry restoration
ü Search for exotic QCD state by HBT measurement