Ferromagnetism of quark matter in the two-flavor color superconducting phase

1. Ferromagnetism of quark matter in the two-flavor color superconducting phase Graduate School of Science, Osaka City University M.Inui, H.Kohyama A.Niegawa

2. Motivation • Inroduction • Model (Mei’s work) • Set up • Calculus • Result • Summary ＆ Future works

3. Motivation Quark star, Neutron star Signals of such compactstar . . . RXJ185635-375：Candidate Quark StarPicture Credit: M. van Kerkwijk etc Gravitational wave Electromagnetic wave RHIC LHC Study of the magnetic property of quark matter ! QGP is perfect fluid ? New sight of QGP ?

4. Introduction Ｔ QGP coexistence-phase Ferromagnetism? Hadron- phase ２ＳＣ CFL…etc μq Where is the ferromagnetism-phase? evaluate the thermodynamic potential ! Mei Huang Chiral condensate coexistence-phase ＋ Int.J.Mod.Phys.E14 (2005) 675 Diquark condensate

5. Mei Huang Int.J.Mod.Phys.E14 (2005) 675 Extended NJL model two-quark-current-interaction QCD Lagrangian；one-gluon exchange（mass→∞） Fierztransformation Leave the attractive channel ＧＤ：diquark condensate Coupling constant ＧＳ：chiral condensate Mean field approximation diquak：Δ～　　　　、sigma meson：σ～

6. Mei Huang Int.J.Mod.Phys.E14 (2005) 675 Generating functional b Imaginary-time formalism Chemical potential ＜ rg＞

7. Mei Huang Int.J.Mod.Phys.E14 (2005) 675 Nambu-Gorkov formalism

8. Mei Huang Int.J.Mod.Phys.E14 (2005) 675 Thermodynamic potential current quark mass constituent quark mass Each value which satisfies the above equations are the actual Δ、ｍ　

9. Mei Huang Int.J.Mod.Phys.E14 (2005) 675 Ｔ＝０ CutoffΛ＝637 MeV m0=5.5 MeV m=330 MeV coexistence-phase

10. Motivation • Introduction • Model (Mei’s work) • Set up • Calculus • Result • Summary ＆Future works

11. set up –(1) Polarization of the system polarization projector Toshitaka Tatsumi Phys. Lett B 489 (2000) 280 By choosing along the z axis we call spin-up and spin-down

12. set up –(2) Number density Distribution function Polarized number density 0 down-spin up-spin 0 0

13. set up –(3) Decision of chemical potential fix a value Average value of chemical potential use use Difference of chemical potential state has magnetism !

14. set up –(4) Thermodynamic potential Mei’s thermodynamic potential Thermodynamic potential including difference of chemical potential

15. Calculus –(1) External value of thermodynamic potential Respective achieved state is the under condition is got from Solve the above equation Determine Substitute into We get physical thermodynamic potential

16. set up Calculus –(2) Evaluate the thermodynamic potential in T=0 limit internal energy Stable state has lower energy Stable state We can see as a function of order parameter ？ ？ ？ ？ If Suggest a ferromagnetism !

17. Result-(1) respective behaviors of

18. Result-(2) “Ferromagnetism-phase” “normal-phase”

19. Result-(3) State1 =normal-phase State2 =ferromagnetism-phase state1 state2 State2 State1 First order phase transition Realized state !

20. summary normal-phase ferromagnetism- phase Phase structure about magnetism Ｔ QGP Coexistence-phase Extended NJL model Hadron- phase ２ＳＣ CFL…etc 0 There is a transition point of normal-phase to ferromagnetism-phase suppress the generation of

21. Future works normal-phase ferromagnetism- phase • Calculation of including residual interaction • Calculation of extended to finite temperature Ｔ QGP 0 • Calculation of polarized • Color or electric neutrality condition ….