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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

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

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

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current quark constituent quark Observed quark mass

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

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2. NJL model

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Lagrangian of NJL

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

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Chiral condensate Constituent quark mass Mean Field Approximation

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After a bit of algebra, Effective Potential

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Regularizations Regularization Dimensional: Cutoff: Finite Potential! Divergent contribution

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Model parameters

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Parameter sets

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The condition: Stable vacuum

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Chiral condensate current quark constituent quark Constituent picture in NJL

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4. Phase diagram

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Constituent mass

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Drawing phase diagram

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Resulting phase diagram

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Numerical results Diagrams with various parameter sets

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Comparison with Cutoff Striking qualitative difference!

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

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

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

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