Hadrons in Medium via DSE Hadrons in Medium via DSE Yuxin Liu

Department of Physics, Peking Universityyxliu@pku.edu.cn

The 1st Sino-Americas Workshop and School on the Bound-state Problem in Continuum QCD, Oct. 22-26, 2013, Hefei

OutlineOutline I. IntroductionI. Introduction ⅡⅡ. QCD Phase Transitions . QCD Phase Transitions via the DSE Approachvia the DSE Approach ⅢⅢ. Hadrons in Medium via the DSE. Hadrons in Medium via the DSE Ⅳ Ⅳ. Summary . Summary

Fundamental Problems of Early UniverseFundamental Problems of Early Universe

Non-confined Non-confined quarks and gluons quarks and gluons and leptonsand leptons

Quarks and Gluons get Confined

Hadrons

Nuclear Synthesis

Nuclei

Comp.

Atoms

G a l a x y

F o r m e d

Pre s e n t

Uni v e r s e

mq > 0 , Expl. CSB

mq = 0 ， Chiral Sym.

Why & How

Confined ? Mu,d >= 100mu,d ,

DCSB ! How ？

“New Sate of Matter”QGP ? sQGP ?

Composition ？ Mass Spectrum？ EM-Properties ？ PDA--PDF?

FD problems are sorted to QCD FD problems are sorted to QCD PTsPTs QCD Phase Diagram: Phase Boundary, Specific States, e.g., CEP, sQGP, Quakyonic,

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

Density ( 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

？？

？？

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 .

“QCD” Phase Transitions may Happen

Possible ObservablesPossible Observables

General idea ，Phenom. Calc., Sophist. Calc.,

quark may get deconfined(QCD PT) at high T and/or

Signals for QCD Phase Transitions: In Lab. Expt. Jet Q., v2, Viscosity, CC Fluct. & Correl., Hadron

Prop.,···

In Astron. Observ. M-R Rel., Rad. Sp., Inst. R. Oscil., Freq. G-M. Oscil., ···

QCD Phase TransitionQCD Phase Transitions

Slavnov-Taylor Identity

Dyson-Schwinger Equations

axial gauges BBZ

covariant gauges QCD

ⅡⅡ. QCD Phase Transitions via the DSE Approach. QCD Phase Transitions via the DSE Approach

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; .

Slavnov-Taylor Identity

Dyson-Schwinger Equations

axial gauges BBZ

covariant gauges QCD

A comment on the A comment on the DSE approach in DSE approach in QCD QCD

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; .

Practical Algorithm :Overwhelmingly

important !

？？

Practical Algorithm at Present Practical Algorithm at Present Truncation ： Preserving Symm. Quark

Eq.

Decomposition of the Lorentz Structure

Quark Eq. in Vacuum :

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

Models of the effective gluon propagatorModels of the effective 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/ 2 t

Derivation and analysis in arXiv:1209.1974 show that the one in 4-D should be infrared constant.

Models of quark-gluon interaction vertexModels of quark-gluon interaction vertex

(1) Bare Ansatz

(2) Ball-Chiu Ansatz

(3) Curtis-Pennington Ansatz

),( pq (Rainbow-Ladder Approx.)

(4) BC+ACM Ansatz (Chang, Liu, Roberts, PRL 106, 072001 (‘11) )

Satisfying W-T Identity, L-C. restricted

Satisfying Prod. Ren.

Verification of the BC + ACM Vertex

S.X. Qin, L. Chang, Y. X. Liu, C. D. Roberts, & S. M. Schmidt, Phys. Lett. B 722, 384 (2013).

)()()( 222 ppp ACMBC

Combining the Ward-Green-Takahashi Identities of vector & axial-vector vertices,

one can obtain that the minimum form of the vertex is just

Quantity to identify the phase transitionQuantity to identify the phase transition

! condensatequark chiral : O qqparameterrder Traditionally

Criterion in Dynamics: Equating Effective TPs

With fully Nonperturbative approach, one could

not

have the ETPs. New Criterion must be established!

New Criterion: Chiral New Criterion: Chiral SusceptibilitySusceptibility

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

Phase diagram in bare vertex Phase diagram in BC vertex

For 2nd order PT & Crossover, s diverge at same states.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.

parameters are taken from Phys. Rev. D 65, 094026 (1997), with fitted as

Effect of the Running Coupling Effect of the Running Coupling Strength Strength on the Chiral Phase Transition on the Chiral Phase Transition

f MeVf 93

(W. Yuan, H. Chen, Y.X. Liu, Phys. Lett. B 637, 69 (2006))(W. Yuan, H. Chen, Y.X. Liu, Phys. Lett. B 637, 69 (2006))

Lattice QCD result Lattice QCD result PRD 72, 014507 (2005)PRD 72, 014507 (2005)

((BC Vertex: L. Chang, Y.X. Liu, R.D. Roberts, et al., Phys. Rev. C 79, 035209 BC Vertex: L. Chang, Y.X. Liu, R.D. Roberts, et al., Phys. Rev. C 79, 035209 (2009)(2009)))

Bare vertexBare vertexCS phaseCS phase

CSB CSB phasephase

with D = 16 GeV2, 0.4 GeV

DCSB exists beyond the chiral DCSB exists beyond the chiral limit limit

Solutions of the DSE with

Mass function

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.

Dynamical massDynamical mass

Effective Thermal Potential

Checking the stability

Phase diagram

Intuitive picture of Mass Intuitive picture of Mass GenerationGeneration

(K.L. Wang, S.X. Qin, L. Chang, Y.X. Liu, C. D. Roberts, & (K.L. Wang, S.X. Qin, L. Chang, Y.X. Liu, C. D. Roberts, & S.M. Schmidt, Phys. Rev. D 86, 114001 (2012) S.M. Schmidt, Phys. Rev. D 86, 114001 (2012)

Chiral Symmetry Breaking Chiral Symmetry Breaking Generates also Generates also the Anomalous Magnetic Moment of the Anomalous Magnetic Moment of QuarkQuark

L. Chang, Y.X. Liu, & C.D. Roberts, PRL 106, 072001 (‘11)

Violation of the positivity of spectral function

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

With the propagator obtained in DSE, one can have the quark SF with MEM

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, C.D. Roberts, PRD 84, 014017(‘11);S.X. Qin, L. Chang, Y.X. Liu, C.D. Roberts, PRD 84, 014017(‘11); F. Gao, S.X. Qin, Y.X. Liu, C.D. Roberts, to be published. F. Gao, S.X. Qin, Y.X. Liu, C.D. Roberts, to be published.

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: GCM bag modelⅢⅢ. . Hadrons via DSEHadrons via DSE

RZ

jqB BRNTE 0334),(

,),(0

1

),(/

j

e

Tj Tj

jgT

,),(),(

TRj T

ⅢⅢ. . Hadrons via DSEHadrons via DSEApproach 2: BSE + DSE Mesons BSE with DSE solutions being the input

Baryons Fadeev Equation or Diquark model

(BSE+BSE)

L. Chang,

C.D. Roberts,

PRL 103,

081601

(2009);

G. Eichmann,

et al., PRL 104,

201601 (2010);

,c PTR ,c PTR

Collective Quantization: Nucl. Phys. A790, 593 (2007).

DSE Soliton Description of Nucleon

B. Wang, H. Chen, L. Chang, & Y. X. Liu, Phys. Rev. C 76, 025201 (2007)

Density & Temperature Dependence of some Properties of Nucleon in DSE Soliton Model

0/ BB 0/ RR0/MM (Y. X. Liu, et al.,

NP A 695, 353 (2001);

NPA 725, 127 (2003);

NPA 750, 324 (2005) )

( Y. Mo, S.X. Qin, and Y.X. Liu, Phys. Rev. C 82, 025206 (2010) )

( 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

Effect of F.-S.-B. Effect of F.-S.-B. ((m0) ) on Meson’s on Meson’s MassMass 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) )

( Kun-lun Wang, Yu-xin Liu, Lei Chang, C.D. Roberts, & S.M. Schmidt, Phys. Rev. D 87, 074038 (2013) )

T-dependence of some hadrons’ properties in DSE

A point of view on confinement: Self-organization

( Kun-lun Wang, Yu-xin Liu, & C.D. Roberts, to be published. )

rho-meson in Magnetic Field via DSE BSE + DSE in magnetic field

Fluctuation & Correlation of Baryon Numberss

Xian-yin Xin, Yu-xin Liu, et al., to be published

Dynamical Mass is generated by DCSB; Phase Diagram is given; CEP is fixed & Coexisting Phase is discussed; sQGP above but near the Tc is discussed.

Thanks !! Thanks !!

Powerful for studying hadron physics & proper time for developing !

ⅣⅣ. Summary & Remarks. Summary & Remarks

QCD phase transitions are investigated via DSE

DSE, a npQCD approach, is described

Some properties of hadrons are discussed in DSE

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.

Hadron StructureHadron Structure

Some Numerical ResultsSome Numerical Results