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Hadrons in Medium via DSE Yuxin Liu Department of Physics, Peking University yxliu@pku.edu.cn The 1st Sino-Americas Workshop and School on the Bound- state Problem in Continuum QCD, Oct. 22-26, 2013, Hefei Outline I. Introduction Ⅱ. QCD Phase Transitions Ⅱ. QCD Phase Transitions via the DSE Approach via the DSE Approach Ⅲ. Hadrons in Medium via the DSE Ⅲ. Hadrons in Medium via the DSE Ⅳ. Summary Ⅳ. Summary

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Fundamental Problems of Early Universe Non-confined Non-confined quarks and gluons quarks and gluons and leptons and 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 m q > 0, Expl. CSB m q = 0 ， Chiral Sym. Why & How Confined ? M u,d >= 100m u,d, DCSB ! How ？ “New Sate of Matter” QGP ? sQGP ? Composition ？ Mass Spectrum ？ EM- Properties ？ PDA--PDF?

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FD problems are sorted to QCD PTs QCD Phase Diagram: Phase Boundary, Specific States, e.g., CEP, sQGP, Quakyonic, Items Influencing the 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. – FSB Chiral Symmetric Quark deconfined SB SB, Quark confined sQGP ？ ？ ？ ？

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Theoretical Approaches ： Two kinds - Continuum & Discrete (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, AdS/CFT, HD(T)LpQCD, The approach should manifest simultaneously: (1) DCSB & its Restoration, (2) Confinement & Deconfinement.

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“QCD” Phase Transitions may Happen Possible 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., v 2, Viscosity, CC Fluct. & Correl., Hadron Prop.,··· In Astron. Observ.. M-R Rel., Rad. Sp., Inst. R. Oscil., Freq. G-M. Oscil., ··· QCD Phase Transitions s

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Slavnov-Taylor Identity Dyson-Schwinger Equations axial gauges BBZ covariant gauges QCDQCD Ⅱ. 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; .

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Slavnov-Taylor Identity Dyson-Schwinger Equations axial gauges BBZ covariant gauges QCDQCD A comment on the DSE approach in 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 ! ？ ？

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Practical Algorithm at Present Truncation ： Preserving Symm. Quark Eq. Decomposition of the Lorentz Structure Quark Eq. in Vacuum :

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Quark Eq. in Medium Matsubara Formalism Temperature T : Matsubara Frequency Density ： Chemical Potential Decomposition of the Lorentz Structure S S S S

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

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Models of quark-gluon interaction vertex (1) Bare Ansatz (2) Ball-Chiu Ansatz (3) Curtis-Pennington Ansatz (Rainbow-Ladder Approx.) (4) BC+ACM Ansatz (Chang, Liu, Roberts, PRL 106, 072001 (‘11) ) Satisfying W-T Identity, L-C. restricted Satisfying Prod. Ren.

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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). Combining the Ward-Green-Takahashi Identities of vector & axial-vector vertices, one can obtain that the minimum form of the vertex is just

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Quantity to identify the phase transition Traditionally Criterion in Dynamics: Equating Effective TPs With fully Nonperturbative approach, one could not have the ETPs. New Criterion must be established!

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New Criterion: Chiral Susceptibility S.X. Qin, L. Chang, H. Chen, Y.X. Liu, C.D. Roberts, PRL 106, 172301(‘11) S.X. Qin, L. Chang, H. Chen, Y.X. Liu, C.D. Roberts, PRL 106, 172301(‘11) Phase diagram in bare vertexPhase diagram in BC vertex For 2 nd 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.

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parameters are taken from Phys. Rev. D 65, 094026 (1997), with fitted as Effect of the Running Coupling Strength on the Chiral Phase Transition (W. Yuan, H. Chen, Y.X. Liu, Phys. Lett. B 637, 69 (2006)) Lattice QCD result PRD 72, 014507 (2005) (BC Vertex: L. Chang, Y.X. Liu, R.D. Roberts, et al., Phys. Rev. C 79, 035209 (2009)) Bare vertex CS phase CSB phase

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with D = 16 GeV 2, 0.4 GeV DCSB exists beyond the chiral limit Solutions of the DSE with Mass function With = 0.4 GeV 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.

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Dynamical mass Effective Thermal Potential Checking the stability Phase diagram

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

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Chiral Symmetry Breaking Generates also the Anomalous Magnetic Moment of Quark L. Chang, Y.X. Liu, & C.D. Roberts, PRL 106, 072001 (‘11)

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DSE description of the confinement- deconfinement phase transition 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

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T = 3.0T c Disperse Relation and Momentum Dependence of the Residues of the Quasi-particles’ poles T = 1.1T c 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 (<7.0T c ), 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.

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Approach 1: GCM bag model Ⅲ. Hadrons via DSE

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Approach 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);

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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)

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

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( S.X. Qin, L. Chang, Y.X. Liu, C.D. Roberts, et al., Phys. Rev. C 84, 042202(R) (2011) ) S ome properties of mesons in DSE-BSE ( L. Chang, & C.D. Roberts, Phys. Rev. C 85, 052201(R) (2012) ) Present work

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Effect of F.-S.-B. () on Meson’s Mass Effect of F.-S.-B. (m 0 ) on Meson’s 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) )

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( 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

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( Kun-lun Wang, Yu-xin Liu, & C.D. Roberts, to be published. ) rho-meson in Magnetic Field via DSE BSE + DSE in magnetic field

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Fluctuation & Correlation of Baryon Numberss Xian-yin Xin, Yu-xin Liu, et al., to be published

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Dynamical Mass is generated by DCSB; Phase Diagram is given; CEP is fixed & Coexisting Phase is discussed; sQGP above but near the T c is discussed. Thanks !! Powerful for studying hadron physics & proper time for developing ! Ⅳ. Summary & Remarks QCD phase transitions are investigated via DSE DSE, a npQCD approach, is described Some properties of hadrons are discussed in DSE

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Analytic Continuation from Euclidean Space to Minkowskian Space ( W. Yuan, S.X. Qin, H. Chen, & YXL, PRD 81, 114022 (2010) ) = 0, e i =1, ==> E.S. = , e i = 1, ==> M.S.

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Hadron Structure

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Some Numerical Results

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