1. The regularization dependence on the phase diagram in the Nambu-Jona-Lasinio model Hiroaki Kohyama (CYCU) 2012.02.24 Fri @AS

2. 1.Introduction 2.NJL model 3.Regularization 4.Phase diagram Contents

3. QCD phase diagram Density Temperature Hadron Quark Gluon Plasma Color Super CP? (Exp.) (Lattice) ? Model studies

4. current quark constituent quark Observed quark mass

5. gluon Shifman, Vainshtein, Zacharov, Nucl. Phys. B147 (1979) 385. Energy of Gluons? current quark constituent quark

6. 2. NJL model

7. Lagrangian of NJL

8. Replace just a number! E. Farhi, L. Susskind, Phys. Rep. 74 (1981) 277. Contact interaction

9. Chiral condensate Constituent quark mass Mean Field Approximation

10. After a bit of algebra, Effective Potential

11. Regularizations Regularization Dimensional: Cutoff: Finite Potential! Divergent contribution

12. Model parameters

13. Parameter sets

14. The condition: Stable vacuum

15. Chiral condensate current quark constituent quark Constituent picture in NJL

16. 4. Phase diagram

17. Constituent mass

18. Drawing phase diagram

19. Resulting phase diagram

20. Numerical results Diagrams with various parameter sets

21. Comparison with Cutoff Striking qualitative difference!

22. Consideration (1) Strong first order seen in the dimensional Dimensional Cutoff Due to the different shape of the potential

23. Consideration (2) Strong first order seen in the dimensional Because the KMT term drives first order

24. Summary - Drew ph. diagram - Compared results with Cutoff ones - Gave numerical considerations Further studies obviously needed (Neutron star, Color superconductivities …)