The regularization dependence on the phase diagram in the Nambu-Jona-Lasinio model Hiroaki Kohyama (CYCU) 2012.02.24

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Presentation transcript:

The regularization dependence on the phase diagram in the Nambu-Jona-Lasinio model Hiroaki Kohyama (CYCU)

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

Model parameters

Parameter sets

The condition: Stable vacuum

Chiral condensate current quark constituent quark Constituent picture in NJL

4. Phase diagram

Constituent mass

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 …)