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Ferromagnetic properties of quark matter

Ferromagnetic properties of quark matter. a microscopic origin of magnetic field in compact stars. T. Tatsumi Department of Physics, Kyoto University. 30 th anniversary of March 5, 1979 Gamma-ray burst event. Introduction and motivation

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Ferromagnetic properties of quark matter

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  1. Ferromagnetic properties of quark matter a microscopic origin of magnetic field in compact stars T. Tatsumi Department of Physics, Kyoto University 30th anniversary of March 5, 1979 Gamma-ray burst event • Introduction and motivation • Relativistic Fermi-liquid theory and magnetic susceptibility • Screening effects for gluons • Magnetic properties at T=0 • Finite temperature effects and Non-Fermi-liquid behavior • Summary and concluding remarks T.T., Proc. of EXOCT07 (arXiv:0711.3348) T.T. and K. Sato., Phys. Lett., B663 (2008) 322. K. Sato and T.T. , Prog. Theor. Phys. Suppl. 174 (2008) 177. T.T. and K. Sato, Phys. Lett. B672(2009) 132. K. Sato and T.T., Nucl. Phys. A (2009) in press. （arXiv: 0812.1347）

  2. Phase diagram of QCD Quark-Gluon Plasma ~150MeV CSC Hadron Ferromagnetism ? Compact stars Magnetars I. Introduction and motivation (I) Phase diagram of QCD In density-temperature plane Low temperature and moderate densities (II) Strong magnetic field in compact stars • Origin: • Fossil field • Dynamo scenario (crust) • Microscopic origin (core)

  3. Spontaneous magnetization of quark matter Is there ferromagnetic instability in QCD? It is a long-standing problem since the first discovery of pulsars. There have been done many calculations of nuclear matter. No possibility for nuclear matter For recent references, I.Bombaci et al, PLB 632(2006)638 G.H. Bordbar and M. Bigdeli, PRC76 (2007)035803 （ungapped quark matter） E.Nakano, T. Maruyama, T.T., PRD 68(2003) 105001

  4. q’ q v v OGE v v q q’ Spontaneous spin polarization in quark matter Ferromagnetism in gauge theories T.T. PLB489(2000)280. T.T.,E. Nakano and K. Nawa, Dark matter, p.39 (Nova Sci. Pub., 2005) Fock exchange interaction is responsible to ferromagnetism in quark matter (Bloch mechanism) c.f. Ferromagnetism of itinerant electrons (Bloch,1929) q k k q

  5. (Pauli-Lubanski vector) Weakly first order c.f. A.Niegawa, Prog. Theor. Phys. 113(2005)581, which also concludes ferromagnetism at low density, by the use of the resummation technique. Magnetars as quark stars

  6. No direct int. Fock exchange int. No flavor dep. In the following we are concerned with only one flavor. Color symmetric int.: II. Relativistic Fermi liquid theory: (G.Baym and S.A.Chin, NPA262(1976)527.) Quarks as Quasi-particles:

  7. 0 Magnetic susceptibility :response to the external magnetic field Dirac magneton spin susceptibility Magnetization Change of the distribution function

  8. ０ ０ Magnetic (spin) susceptibility in the Fermi liquid theory which also measures the curvature of the free energy at the origin f: Landau parameters N(T): effective density of states at the Fermi surface Free energy Fermi velocity spontaneous magnetization Infrared (IR) singularities

  9. q k P(p) p=k-q q k HDL resummation III Screening effects Gauge choice (Debye mass) (Landau damping) （i) Debye screening in the longitudinal (electric) gluons improve IR behavior (ii) Transverse (magnetic) gluons only gives the dynamical screening, which leads to IR (Log) divergence Non-Fermi-liquid behavior

  10. q k IV. Magnetic properties at T=0 P(p) Quasiparticle interaction: q k transverse longitudinal log div Susceptibility cancellation Simple OGE Screening effect

  11. Paramagnetic phase without screening s quark only NFdependence Ferromagnetic phase u,d,ssymmetric matter ● ● suppression enhancement

  12. To summarize: Screening effect Some features: （i) Debye screening in the longitudinal (electric) gluons improve IR behavior (ii) Transverse (magnetic) gluons only gives the dynamical screening, which leads to IR (Log) divergence Non-Fermi-liquid behavior (iii) Divergences cancel each other to give a finite c (iv) Results are independent of the gauge choice x

  13. V. Finite temperature effects and Non-Fermi-liquid behavior ○　Density of state: ○ ・We consider the low T case, T/m<<1, but the usual low-T expansion cannot be applied. ・Quasiparticle energy exhibits an anomalous behavior near the Fermi surface

  14. Quark self-energy Schwinger-Dyson One loop result: Anomalous term (C. Manuel, PRD 62(2000) 076009)

  15. Non-Fermi liquid behavior ・Specific heat ・Gap equation How about susceptibility? Peculiar temperature dep. of susceptibility Curie temperature Role of transverse gluons =relevant interactions in RG (A. Ipp et al., PRD 69(2004)011901) (D.T. Son, PRD 59(1999)094019)

  16. Magnetic susceptibility at T>0 T-indep. term T2-term Non Fermi-liquid effect

  17. Magnetic phase diagram of QCD Curie (critical) temperature should be order of several tens of MeV. Paramag. Non-Fermi-liquid effect FM

  18. VI. Summary and concluding remarks ・We have considered magnetic susceptibility of QCD within Fermi-liquid theory Roles of static and dynamic screening are figured out: Static Dynamic Novel non-Fermi liquid effect! ・Non-perturbative effects, Large Nc, Nf etc. other than OGE ・How to distinguish various ideas about the origin Thermal evolution as well as magnetic evolution No decay of B, suggested by statistical analysis of X-ray pulsars Novel mechanism of emissivity or superconductivity Spin wave or magnons （T.T., arxiv:07113349）

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