1. CCAST_Workshop Mar. 2008 Min He @ NJU Chiral Susceptibility in an Effective Interaction Model 南京大学物理系 何 敏 导师 宗红石

2. CCAST_Workshop Mar. 2008 Min He @ NJU Outline Introduction ---- QCD and its phases ---- Chiral suscept. : lattice studies Our approach ---- Analytical derivation ---- DSE-BSE treatment and result Summary

3. CCAST_Workshop Mar. 2008 Min He @ NJU QCD Phase Diagram (m_q\=0) --- from M.Stephanov

4. CCAST_Workshop Mar. 2008 Min He @ NJU QCD Phase Diagram(m_q=0) --- from M.Stephanov

5. CCAST_Workshop Mar. 2008 Min He @ NJU Chiral Suscept.:Lattice Study Nature 443,675(2006) (1) No volume-dependent peak height is observed at physical quark mass (2) This implies an analytic crossover, rather than a true transition

6. CCAST_Workshop Mar. 2008 Min He @ NJU Our Analytical Approach Chiral suscpt. Adopting the identities we arrive at The finite temperature version reads

7. CCAST_Workshop Mar. 2008 Min He @ NJU Identification of Disconnected Part # Quadratic divergence # Dirac operator formulation ---The first two parts constitute the disconnected part, --- Measure the fluctuation of order parameter --- It is this part that is of direct physical relevance and interest # Connected part # Disconnected part : free from quadratic divergence

8. CCAST_Workshop Mar. 2008 Min He @ NJU DSE-BSE Treatment # Rainbow-DSE for quark propagator # Ladder-BSE for dressed scalar vertex # A seperable, ultravioletly finite model gluon propagator

9. CCAST_Workshop Mar. 2008 Min He @ NJU Numerical Result The disconnected chiral susceptibility # A narrow,pronounced divergent peak is observed # This is a characteristic of a phase transition of 2nd order # The transition temperature T_c=150 Mev

10. CCAST_Workshop Mar. 2008 Min He @ NJU Summary # A model independent, closed integral formula for chiral suscept. is derived, which expresses the latter in terms of basic QFT objects: dressed propagator and vertex. # Its physically relevant disconnected part is identified, which suffers from no quadratic divergence and arises from the scalar vertex correction by non-perturbative effects. # This is then illustrated by a model calculation based on rainbow-DSE ladder-BSE with an effective seperable model gluon propagator. # A phase transition of 2nd order driven by chiral symmetry restoration is established for two flavors in the chiral limit.

11. CCAST_Workshop Mar. 2008 Min He @ NJU Thank You !