Phase Diagram and Thermal Properties of Strong Interaction

Matter

Yuxin LiuDept. Phys., Peking Univ., China

XQCD 2015, CCNU, Sept. 22, 2015

OutlineOutline I. I. IntroductionIntroduction ⅡⅡ. . The DS Eq. Approach ⅢⅢ. . The Phase DiagramThe Phase Diagram Ⅳ Ⅳ. . Thermal PropertiesThermal Properties V. RemarksV. Remarks

1

I. I. FD problems are sorted to QCD FD problems are sorted to QCD PTsPTs QCD Phase Diagram: Phase Boundary, Thermal Property, Specific States, e.g., CEP,

sQGP, Quakyonic,

Items Influencing the Items Influencing the Phase Transitions:Phase Transitions:Medium ： Temperature T ,

Density ρ ( or )

Size

Intrinsic ： Current mass,

Coupling Strength,

Color-flavor structure,

••• •••

Phase Transitions involved ：Deconfinement–confinement

DCS – DCSB

Flavor Sym. – FSBChiral SymmetricQuark deconfined

SB, Quark confined

sQGP

？？

？

2

Theoretical ApproachesTheoretical Approaches ：： Two kindsTwo kinds--Continuum & Discrete Continuum & Discrete (lattice)(lattice)

Lattice QCD ： Running coupling behavior ， Vacuum Structure ， Temperature effect ， “Small chemical potential” ；

Continuum ： (1)Phenomenological models (p)NJL 、 (p)QMC 、 QMF 、 (2)Field Theoretical Chiral perturbation, Renormalization Group, QCD sum rules, Instanton(liquid) model, DS equations ,DS equations , AdS/CFT, HD(T)LpQCD ,

The approach should manifest simultaneously: (1) DCSB & its Restoration , (2) Confinement & Deconfinement . 3

For the location of the CEP, different For the location of the CEP, different

approaches give quite distinct approaches give quite distinct results.results. (p)NJL model & others give quite large E

q/TE (> 3.0) Sasaki, et al., PRD 77, 034024 (2008); 82, 076003 (2010); 82, 116004 (1010); 0). Costa, et al., PRD 77, 096001 (‘08); EPL 86, 31001 (‘09); PRD 81, 016007(‘10); Fu & Liu, PRD 77, 014006 (2008); Ciminale, et al., PRD 77, 054023 (2008); Fukushima, PRD 77, 114028 (2008); Kashiwa, et al., PLB 662, 26 (2008); Abuki, et al., PRD 78, 034034 (2008); Schaefer, et al., PRD 79, 014018 (2009); Hatta, et al., PRD 67, 014028 (2003); Cavacs, et al., PRD 77, 065016(2008); Bratovic, et al., PLB 719, 131(‘13); Bhattacharyya, et al., PRD 87,054009(‘13); Jiang, et al., PRD 88, 016008 (2013); Ke, et al., PRD 89, 074041 (2014);

Lattice QCD gives smaller Eq/TE ( 0.4 ~ 1.1)

Fodor, et al., JHEP 4, 050 (2004); Gavai, et al., PRD 71, 114014 (2005); Gavai, et al., PRD 78, 114503 (2008); Schmidt et al., JPG 35, 104013 (2008);

Li, et al., PRD 84, 071503 (2011); Gupta, et al., PRD 90, 034001 (2014);

DSE Calculations with different techniques generate different results for the E

q/TE (0.0, 1.1 ~ 1.3, 1.4 ~ 1.6, ) Blaschke, et al, PLB 425, 232 (1998); He, et al., PRD 79, 036001 (2009); Qin, et al., PRL 106, 172301 (2011); Fischer, et al., PLB 702, 438 (‘11); PLB 718, 1036 (‘13); PRD 90, 034022 (‘14); 4

Relation between the chiral PT Relation between the chiral PT and and the deconfinement PT the deconfinement PT

claim that there exists a quarkyonic phase.

and General (large-Nc) Analysis McLerran, et al., NPA 796, 83 (‘07); NPA 808, 117 (‘08); NPA 824, 86 (‘09),

Lattice QCD Calculation de Forcrand, et al., Nucl. Phys. B Proc. Suppl. 153, 62 (2006);

Is there any hierarchy between the two PTs ?

Coleman-Witten Conjecture (PRL 45, 100 (‘80)):

Confinement coincides with DCSB !! Inconsistent with each other ?!

quarkyonic

Slavnov-Taylor Identity

Dyson-Schwinger Equations

axial gauges BBZ

covariant gauges QCD

ⅡⅡ. . The Dyson-Schwinger Equation The Dyson-Schwinger Equation ApproachApproach

C. D. Roberts, et al, PPNP 33 (1994), 477; 45-S1, 1 (2000); EPJ-ST 140(2007), 53; R. Alkofer, et. al, Phys. Rep. 353, 281 (2001); LYX, Roberts, et al., CTP 58 (2012), 79; .

6

Algorithms Algorithms of Solving the DSEs of of Solving the DSEs of QCD QCD

？？

(1) Solving the coupled quark, ghost and

gluon (parts of the diagrams) equations,

e.g.,

(2) Solving the truncated quark equation with the symmetries being preserved.

7

Expression of the quark gap Expression of the quark gap

equationequation Truncation ： Preserving Symm. Quark

Eq.

Decomposition of the Lorentz Structure

Quark Eq. in Vacuum :

8

Quark Eq. in MediumQuark Eq. in MediumMatsubara Formalism

Temperature T : Matsubara Frequency

Density ： Chemical Potential

Decomposition of the Lorentz Structure

Tnn )12(

S

S

S

S

9

Models of the eff. gluon propagatorModels of the eff. gluon propagator

(3)

Commonly Used: Maris-Tandy Model (PRC 56, 3369) Cuchieri, et al, PRD, 2008

A.C. Aguilar, et al.,JHEP 1007-002

Recently Proposed: Infrared Constant Model ( Qin, Chang, Liu, Roberts, Wilson, PRC 84, 042202(R), (2011). )

Taking in the coefficient of the above expression

1// 222 kt

Derivation and analysis in PRD 87, 085039 (2013) show that the one in 4-D should be infrared constant. 10

Models of quark-gluon interaction Models of quark-gluon interaction vertexvertex

(1) Bare Ansatz

(2) Ball-Chiu Ansatz

(3) Curtis-Pennington Ansatz

),( pq (Rainbow-Ladder Approx.)

(4) BC+ACM (Chang, etc, PRL 106,072001(‘11), Qin, etc, PLB 722,384(‘13))

Satisfying W-T Identity, L-C. restricted

Satisfying Prod. Ren.

11

A regirous check on the ACM A regirous check on the ACM model formodel for

the quark-gluon interaction vertexthe quark-gluon interaction vertex

12

In DSE approach

)(

)(22

2

)(pA

pBpM

Dynamical chiral symmetry breakingDynamical chiral symmetry breaking

Increasing the interaction

strength induces the

dynamical mass generation

0qq

K.L. Wang, YXL, et al., PRD 86,114001(‘12); K.L. Wang, YXL, et al., PRD 86,114001(‘12);

Numerical results

13

with D = 16 GeV2, 0.4 GeV

DCSB still exists beyond chiral DCSB still exists beyond chiral limit limit

Solutions of the DSE with

With = 0.4 GeV

16 0.4

L. Chang, Y. X. Liu, C. D. Roberts, et al, arXiv: nucl-th/0605058; R. Williams, C.S. Fischer, M.R. Pennington, arXiv: hep-ph/0612061.

14

S.X. Qin, D. Rischke, Phys. Rev. S.X. Qin, D. Rischke, Phys. Rev. D 88, 056007 (2013)D 88, 056007 (2013)

H. Chen, YXL, et al., Phys. Rev. D 78, H. Chen, YXL, et al., Phys. Rev. D 78, 116015 (2008)116015 (2008)

15

T=0.8TcT=0.8Tc

K.L. Wang, Y.X. Liu, C.D. Roberts, Phys. Rev. D 87, 074038 (2013)

Screening masses of hadrons can identify the phase transitions

, when , the color gets deconfined.

GT Relation

M M

can be a signal of the DCS.

SS Mr /1 mdS rr

Hadron properties provide signals for not only the chiral phase transt. but also the confinement-deconfnmt. phase transition.

16

222 4 qMMM

Dyson-Schwinger Equations

QCD

A comment on the DSE approach of A comment on the DSE approach of QCDQCD

C. D. Roberts, et al, PPNP 33 (1994), 477; 45-S1, 1 (2000); EPJ-ST 140(2007), 53; R. Alkofer, et. al, Phys. Rep. 353, 281 (2001); C.S. Fischer, JPG 32(2006), R253; .

17

III. TIII. The Phase Diagramhe Phase Diagram

! condensatequark chiral : O qqparameterrder

Quantity to identify the phase transition Traditionally

Criterion in Dynamics: Equating Effective TPs

With fully Nonperturbative approach, one could not one could not have the ETPs.have the ETPs. New Criterion must be established!

18

Chiral Susceptibility as a Chiral Susceptibility as a CriterionCriterion

S.X. Qin, L. Chang, H. Chen, Y.X. Liu, C.D. Roberts, PRL 106, 172301(‘11)

19

In the chiral limit

Beyond the chiral limitFor 2nd order PT & Crossover, s of the two phases diverge at the same state.For 1st order PT, the s diverge at different states. the criterion can not only give the phase

boundary, but also determine the position of the CEP.

Phase diagram is given, CEP is Phase diagram is given, CEP is proposedproposed

S.X. Qin, L. Chang, H. Chen, Y.X. Liu, & C.D. Roberts, Phys. Rev. Lett. 106, 172301 (2011)

Phase diagram in bare vertex Phase diagram in BC vertex

},{},{

DeconfinedCSConfinedDCSB

regionexistenceCo

20

In Chiral Limit

Phase diagram is given, CEP is Phase diagram is given, CEP is proposedproposed

Fei Gao, Y.X. Liu, et al., to be published

Beyond Chiral Limit

21

IV.IV. Thermal PropertiesThermal Properties

Pressure

Sound Speed

Basic Formulae:

22

Heat capability & latent heat

IV.IV. Thermal Properties Thermal Properties Trace Anomaly at Zero Chemical Potential

23TM = 140 MeV

IV.IV. Thermal Properties Thermal Properties Pressure & Trace Anomaly at Non-Zero Chemical Potential

24TM = 140 MeV

IV. IV. Thermal Properties Thermal Properties Sound Speed squared

25TM = 140 MeV

IV. IV. Thermal Properties Thermal Properties Specific heat capability & Latent heat

26TM = 140 MeV

The 2nd, 3rd, 4th order fluctuations

where

Quark Number Fluctuations

. XXX NNN

Quark number:

27

Quark Number Density Fluctuations vs T in the DSE

X.Y. Xin, S.X. Qin, YXL, PRD 90, 076006 (2014)28

Quark Number Density Fluctuations vs μ in the DSE

X.Y. Xin, S.X. Qin, YXL, PRD 90, 076006 (2014)29

Quark Number Density Fluctuations vs μ in the DSE

X.Y. Xin, S.X. Qin, YXL, Phys. Rev. D 90, 076006 (2014)30

In crossover region, the fluctuations oscillate obviously;In 1st transt., overlaps exist. At CEP, they diverge!

Relating with Experiment Directly

Jing Chen, Fei Gao, Yu-xin Liu, et al., to be published31

Key issue:Taking the Finite size effect into account !

Chemical Freeze out Conditions

Critical Behavior

Fei Gao, Yu-xin Liu, et al., to be published32

Critical Behavior

Fei Gao, Yu-xin Liu, et al., to be published33

Small ωω long range in coordinate space

Different methods give distinct Different methods give distinct locations locations of the CEP arises from diff. Conf. of the CEP arises from diff. Conf. Length Length

MN model infinite range in r-spaceNJL model “ zero” range in r-space Longer range Int. Smaller E/TE

S.X. Qin, YXL, et al, PRL106,172301(‘11); X. Xin, S. Qin, YXL, PRD90,076006

34

Dynamical Mass is generated by DCSB; Confinement can be described with the positivity violation of the spectral function. The phase diagram and CEP are given.

Far from well established promising !

VV.. Summary & Remarks

QCD phase transitions are investigated via DSE

DSE, a npQCD approach, is described

Some thermal properties are discussed Trace anomaly, sound speed, etc; quark number fluctuations; critical exponents of the & the Cv , etc .

35Thanks !! Thanks !!

♠ ♠ Positivity Violation of the Spectral FunctionPositivity Violation of the Spectral Function

Criterion for Confinement

S.X. Qin, and D.H. Rischke, Phys. Rev. D 88, 056007 (2013)S.X. Qin, and D.H. Rischke, Phys. Rev. D 88, 056007 (2013)

Maximum Entropy Method Maximum Entropy Method

Result in DSEResult in DSEcTT 8.0

( Asakawa, et al., PPNP 46,459 (2001); Nickel, Ann. Phys. 322, 1949 (2007) )

36

Solving quark’s DSE Quark’s Propagator

Property of the matter above Property of the matter above but but near the T near the Tcc

Maximum Entropy

Method (Asakawa, et al., PPNP 46,459

(2001); Nickel, Ann. Phys.

322,

1949 (2007))

Spectral Function

In M-Space, only Yuan, Liu, etc, PRD 81, 114022 (2010).

Usually in E-Space, Analytical continuation is required.

Qin, Chang, Liu, et al., PRD Qin, Chang, Liu, et al., PRD 84, 014017(2011)84, 014017(2011)

T = 3.0Tc

Disperse Relation and Momentum Dependence of the Residues of the Quasi-particles’ poles

T = 1.1Tc

S.X. Qin, L. Chang, Y.X. Liu, et al., Phys. Rev. D 84, 014017(2011); S.X. Qin, L. Chang, Y.X. Liu, et al., Phys. Rev. D 84, 014017(2011); F. Gao, S.X. Qin, Y.X. Liu, et al., Phys. Rev. D 89, 076009 (2014). F. Gao, S.X. Qin, Y.X. Liu, et al., Phys. Rev. D 89, 076009 (2014).

Normal T. Mode

Plasmino M.

Zero Mode

The zero mode exists at low momentum

(<7.0Tc), and is long-range correlation ( ~ 1 >FP) . The quark at the T where S is restored involves still rich phases. And the matter is sQGP.

Approach 1: Soliton bag modelⅣⅣ. . Hadrons via DSEHadrons via DSE

Approach 2: BSE + DSE Mesons BSE with DSE solutions being the input

Baryons Fadeev Equation or Diquark model

(BSE+BSE)

Pressure difference provides the bag constant.

L. Chang, et al.,PRL 103, 081601 (2009) 。

39

Effect of the F.-S.-B. (Effect of the F.-S.-B. (m0) on Meson) on Meson’’s Masss Mass

Solving the 4-dimenssional covariant B-S equation with the kernel being fixed by the solution of DS equation and flavor symmetry breaking, we obtain

( L. Chang, Y. X. Liu, C. D. Roberts, et al., Phys. Rev. C 76, 045203 (2007) ) 40

( S.X. Qin, L. Chang, Y.X. Liu, C.D. Roberts, et al., Phys. Rev. C 84, 042202(R) (2011) )

Some properties of mesons in DSE-BSE

( L. Chang, & C.D. Roberts, Phys. Rev. C 85, 052201(R) (2012) )

Present work

Electromagnetic Property & PDF of Electromagnetic Property & PDF of hadronshadrons

Proton electromagnetic forma factor

L. Chang et al., AIP CP 1354, 110 (‘11)P. Maris & PCT, PRC 61, 045202 (‘00)

PDF in pion PDF in kaon

R.J. Holt & C.D. Roberts, RMP 82, 2991(2010); T. Nguyan, CDR, et al., PRC 83, 062201 (R) (2011)42

Gravitational Mode Pulsation Frequency Gravitational Mode Pulsation Frequency can be an Excellent Astronomical Signal can be an Excellent Astronomical Signal

W.J. Fu, H.Q. Wei, and Y.X. Liu, arXiv: 0810.1084, Phys. Rev. Lett. 101 ， 181102 (2008)

Neutron Star: RMF, Quark Star: Bag Model Frequency of Frequency of g-mode oscillationg-mode oscillation

Taking into account the DCSB effectTaking into account the DCSB effect

44

Analytic Continuation from Euclidean Space Analytic Continuation from Euclidean Space

to Minkowskian Space to Minkowskian Space

( W. Yuan, S.X. Qin, H. Chen, & YXL, PRD 81, 114022 (2010) )

= 0, ei=1, ==> E.S. = , ei=1, ==> M.S.

45