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H. Ohno for WHOT-QCD Collaboration

Scaling study of the chiral phase transition in two-flavor QCD for the improved Wilson quarks at finite density. H. Ohno for WHOT-QCD Collaboration. The 3rd A01 group workshop CCS, University of Tsukuba, July 7, 2010. Plan of this talk. Introduction QCD phase diagram

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H. Ohno for WHOT-QCD Collaboration

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  1. Scaling study of the chiral phase transitionin two-flavor QCD for the improved Wilson quarks at finite density H. Ohno for WHOT-QCD Collaboration The 3rd A01 group workshop CCS, University of Tsukuba, July 7, 2010

  2. Plan of this talk • Introduction • QCD phase diagram • Scaling behavior of QCD • Scaling study with Wilson quarks • Scaling behavior at finite μ • Derivative of chiral order parameter with respect to μ/T • Numerical results • Conclusion and future plan Scaling study of the chiral phase transitionin two-flavor QCD for the improved Wilson quarks at finite density

  3. QCD phase diagram Quark-gluon-plasma critical end point Important to understand Crossover T • Early universe • Heavy ion collisions • Neutron star Hadron gas χSB m Scaling study of the chiral phase transitionin two-flavor QCD for the improved Wilson quarks at finite density

  4. Critical behavior of QCD at zero chemical potential Nf=2 Quenched  1storder O(4) 2ndorder Tri-critical point mtc Physical point Z(2) ms Nf=3 Interesting subject: Crossover • O(4) scaling at ms >> mtc • Tri-critical point • 1st order phase transition • at ms << mtc 1storder Z(2) 0  mud 0 Scaling study of the chiral phase transitionin two-flavor QCD for the improved Wilson quarks at finite density

  5. Scaling behavior of chiral order parameter in 2-flavor QCD Chiral symmetry of 2-flavor QCD [Wilczek, Intn.J.Mod.Phys. A7('92)3911; Rajagopal, Wilczek, NP B399('93)395] 3-d O(4) Heisenberg model Recent lattice studies Wilson quarks KS quarks • Local for any Nf • Conserved flavor symmetry • Explicit chiral symmetry breaking • Higher computational cost • Non-local except for Nf = 4 • Explicit flavor symmetry breaking • Partly conserved chiral symmetry • Lower computational cost O(2) Subtraction and renormalization Simulation at physical point Consistent with O(4) scaling O(N) scaling? [CP-PACS, PRD63, 034502(2000)] [BNL-Bielefeld-GSI, arXiv:0909.5122] Scaling study of the chiral phase transitionin two-flavor QCD for the improved Wilson quarks at finite density

  6. Recent study with Wilson quarks [CP-PACS, PRD63, 034502(2000)] • Iwasaki improved gauge • Clover improved Wilson quark • Nf = 2 • 163×4 lattice O(4) scaling function Scaling study of the chiral phase transitionin two-flavor QCD for the improved Wilson quarks at finite density

  7. Critical behavior of 2-flavor QCD at finite density mud0 Nf = 2 Quenched  T 1storder Interesting subject: mud m Crossover • O(4) scaling at small μ • Curvature of critical or • crossover line • Tri-critical point at finite μ mud mud=0 T 1storder 2ndorder 0  m 0 O(4) m Scaling study of the chiral phase transitionin two-flavor QCD for the improved Wilson quarks at finite density

  8. Our study We investigate scaling behavior • of 2-flavor QCD • at finite chemical potential • with Wilson quarks • using derivative of chiral order parameter • calculating curvature of 2nd order critical line in β-μ plane Scaling study of the chiral phase transitionin two-flavor QCD for the improved Wilson quarks at finite density

  9. Comparison with 3-d O(4) spin model chiral order parameter: 3-d O(4) spin model ud-quark mass: mq 2-flavor QCD critical value of β: βct magnetization: M external field: h reduced temperature: t Scaling function: Scaling study of the chiral phase transitionin two-flavor QCD for the improved Wilson quarks at finite density

  10. Chiral order parameter with Ward-Takahashi identity Wilson quarks : explicit chiral symmetry breaking A proper subtraction and renormalization are required. Ward-Takahashi identities [Bochichio et al., NPB262, 331 (1985)] Ward-Takahashi identities in the continuum limit : Tree level renormalization factor Scaling study of the chiral phase transitionin two-flavor QCD for the improved Wilson quarks at finite density

  11. Scaling behavior for finite density The critical line runs on mq = 0 axis in (mq,μ) plane mq=0 t=0 β c is the curvature of the critical ine in the (β, μq/T) plane. μq/T To confirm this scaling property, we calculate the second derivative of with respect to μq/T. Scaling study of the chiral phase transitionin two-flavor QCD for the improved Wilson quarks at finite density

  12. Derivative of chiral order parameter These operators can be calculated by random noise method Scaling study of the chiral phase transitionin two-flavor QCD for the improved Wilson quarks at finite density

  13. Simulation setup • Action • Iwasaki improved gauge action • Clover improved Wilson fermion action • Nf =2 • Lattice size • 163×4 • # conf. • 500-600 • # noise vectors • 50 for each color and spin indices mps/mv = 0.65 mps/mv = 0.80 Scaling study of the chiral phase transitionin two-flavor QCD for the improved Wilson quarks at finite density

  14. Numerical result at zero μ (1) as a function of Filled symbols: CP-PACS, PRD63, 034502(2000) Open symbols: New data in this study mq: measured in T=0 simulations. Scaling study of the chiral phase transitionin two-flavor QCD for the improved Wilson quarks at finite density

  15. Numerical result at zero μ (2) Comparison with O(4) scaling function Filled symbols: CP-PACS, PRD63, 034502(2000) Open symbols: New data in this study Dashed line: O(4) scaling function [Toussaint,’97] β,δ: critical exponents of O(4) spin model. Scaling behavior is consistent with 3-d O(4) spin model. Scaling study of the chiral phase transitionin two-flavor QCD for the improved Wilson quarks at finite density

  16. Numerical result at finite density (1) Second derivative of Solid line: O(4) scaling function with c =0.05 c =0.04 c =0.03 c =0.02 Scaling behavior is roughly consistent with our expectation. Scaling study of the chiral phase transitionin two-flavor QCD for the improved Wilson quarks at finite density

  17. Numerical result at finite density (2) Curvature of βc(μq) b m To calculate the curvature of Tc(μq), we need a(dβ/da)in the chiral limit. Scaling study of the chiral phase transitionin two-flavor QCD for the improved Wilson quarks at finite density

  18. Conclusion • Scaling behavior of chiral order parameter is investigated in two-flavor QCD. • At zero chemical potential, • it is consistent with 3-d O(4) spin model. • At finite density, • chemical potential dependence for scaling variables is almost consistent with our expectation • and the curvature of second order critical line in β-μ plane is roughly calculated. Scaling study of the chiral phase transitionin two-flavor QCD for the improved Wilson quarks at finite density

  19. Future plan • More precise scaling study • increasing the statistics and the number of noise vectors • Lighter mud • 2+1-flavor simulation Scaling study of the chiral phase transitionin two-flavor QCD for the improved Wilson quarks at finite density

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