Chiral Susceptibility in an Effective Interaction Model

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

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

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

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

5. 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 CCAST_Workshop Mar. 2008 Min He @ NJU

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

7. 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 CCAST_Workshop Mar. 2008 Min He @ NJU

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

9. 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 CCAST_Workshop Mar. 2008 Min He @ NJU

10. 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. CCAST_Workshop Mar. 2008 Min He @ NJU

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