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The regularization dependence on the phase diagram in the Nambu-Jona-Lasinio model Hiroaki Kohyama (CYCU) 2012.02.24 Fri @AS
1.Introduction 2.NJL model 3.Regularization 4.Phase diagram Contents
QCD phase diagram Density Temperature Hadron Quark Gluon Plasma Color Super CP? (Exp.) (Lattice) ? Model studies
current quark constituent quark Observed quark mass
gluon Shifman, Vainshtein, Zacharov, Nucl. Phys. B147 (1979) 385. Energy of Gluons? current quark constituent quark
2. NJL model
Lagrangian of NJL
Replace just a number! E. Farhi, L. Susskind, Phys. Rep. 74 (1981) 277. Contact interaction
Chiral condensate Constituent quark mass Mean Field Approximation
After a bit of algebra, Effective Potential
Regularizations Regularization Dimensional: Cutoff: Finite Potential! Divergent contribution
The condition: Stable vacuum
Chiral condensate current quark constituent quark Constituent picture in NJL
4. Phase diagram
Drawing phase diagram
Resulting phase diagram
Numerical results Diagrams with various parameter sets
Comparison with Cutoff Striking qualitative difference!
Consideration (1) Strong first order seen in the dimensional Dimensional Cutoff Due to the different shape of the potential
Consideration (2) Strong first order seen in the dimensional Because the KMT term drives first order
Summary - Drew ph. diagram - Compared results with Cutoff ones - Gave numerical considerations Further studies obviously needed (Neutron star, Color superconductivities …)
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