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Magnetic aspects of QCD and compact stars

Magnetic aspects of QCD and compact stars. T. Tatsumi Department of Physics, Kyoto University. Introduction and motivation Chiral symmetry and spin density wave (SDW) Ferromagnetism (FM) and magnetic susceptibility Screening effects for gluons Magnetic properties at T=0

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Magnetic aspects of QCD and compact stars

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  1. Magnetic aspects of QCD and compact stars T. Tatsumi Department of Physics, Kyoto University • Introduction and motivation • Chiral symmetry and spin density wave (SDW) • Ferromagnetism (FM) 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. A826 (2009) 74. T.T., Proc. of CSQCDII (2010) in press.

  2. Magnetic phase diagram of QCD Critical end-point CSC I. Introduction and motivation (I) Phase diagram of QCD Spin degrees of freedom Meson (Pion) condensation (PIC) Antiferromagnetism(AFM) Deconfinement Ferromagnetism (FM) Chiral restoration Spin density wave (SDW) Color superconductivity . . Deconfinement ? Chiral restoration

  3. Magnetars (II) Strong magnetic field in compact stars Its origin is a long-standing problem since the first discovery of pulsars. Recent discovery of magnetars seems to revive this issue • Origin: • Fossil field • Dynamo scenario (crust) • Microscopic origin (core)

  4. It would be rather natural to attribute its origin to strong interaction Ferromagnetism or spin polarization Nuclear matter calculations have shown negative results For recent references, I.Bombaci et al, PLB 632(2006)638 G.H. Bordbar and M. Bigdeli, PRC76 (2007)035803 Spontaneous magnetization of quark matter or ferromagnetism in quark matter

  5. Some ideas in QCD Bloch mechanism Cf. Other mechanism in CSC: ・Gluon condensate E.J. Ferrer, de la Incera, PRL 97(2006) 122301; PRD 76(2007) 045011; PRD 76(2007)114012. arXiv:0810.3886 B ・Axial anomaly in CFL D.T. Son, M.A. Stephanov, PRD 77(2008)014021. X B

  6. II. Chiral symmetry and Spin density wave (SDW) A typical example of the condensed phase: Liquid crystal with antiferromagnetic order T.Takatsuka et al., Prog.Theor.Phys. 59(1978) 1933. T.Suzuki et al., arXiv:nucl-th/9901097

  7. Chiral symmetry restoration and SDW ref. T.T. and E. Nakano, hep-ph/0408294 PRD71(2005)114006. A magnetic phase in the intermediate densities A density-wave instability before/around chiral-symmetry restoration or another restoration path due to pseudo-scalar density SDW Chiral-restoration path

  8. Remarks: • Nesting (Overhauser, Peiels) is the key mechanism • for generating SDW Level crossing of the energy spectrum near the Fermi surface kF q Model indep. SDW,CDW A.W. Overhauser, PRL 4(1960) 462. R.E. Peierls, Quntum Theory of Solids (1955)

  9. (ii) Similar idea (iii) Similarity to LOFF in superconductor

  10. DCDW Spin density wave　（SDW） DCDW (c.f. Overhauser)

  11. (iii) Phason and spin-wave as NG modes in SDW G.Gruener, Rev.Mod.Phys. 66(1994) 1. It would be interesting to see that both modes have the linear dispersion relation: Cf. Spin waves in FM and AFM Counting rule of NG bosons

  12. q’ q v v OGE v v q q’ III. Ferromagnetism (FM) and magnetic susceptibility T.T. PLB489(2000)280. T.T.,E. Nakano and K. Nawa, Dark matter, p.39 (Nova Sci. Pub., 2005) Isthere ferromagnetic instability in QCD? Fock exchange interaction is responsible to ferromagnetism in quark matter (Bloch mechanism) c.f. Ferromagnetism of itinerant electrons (Bloch,1929) q k k q

  13. 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

  14. No direct int. Fock exchange int. No flavor dep. In the following we are concerned with only one flavor. Color symmetric int.: Ferromagnetism in gauge theories Relativistic Fermi liquid theory (G.Baym and S.A.Chin, NPA262(1976)527.)

  15. 0 Magnetic susceptibility :response to the external magnetic field Dirac magneton spin susceptibility Magnetization Change of the distribution function

  16. 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

  17. q k P(p) p=k-q q k HDL resummation IV 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

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

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

  20. Paramagnetism Ferromagnetism SDW? Large fluctuations (or paramagnon) cf.n emissivity (talk by S. Reddy) cf in electron gas FM(Bloch) SDW(Overhauser) low densityhigh-density Note that this SDW has nothing to do with chiral symmetry, but nesting is also important

  21. 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

  22. VI. 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

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

  24. 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 Effective coupling is Infrared free (Schaefer, K. Schwenzer, PRD 70(2004) 054007) (A. Ipp et al., PRD 69(2004)011901) (D.T. Son, PRD 59(1999)094019)

  25. Magnetic susceptibility at T>0 T-indep. term Non Fermi-liquid effect T2-term Cf. paramagnon effect

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

  27. VII. Summary and concluding remarks ・Possibilities and properties of SDW and FM have been discussed ・We have considered magnetic susceptibility c(q=0) of QCD within Fermi-liquid theory Roles of static and dynamic screening are figured out: Static Dynamic Novel non-Fermi liquid effect! ・Since the order parameter is color singlet, FM and SDW survive even in the large Nc limit. ・Observational signatures of magnetic phases Thermal evolution as well as magnetic evolution Novel mechanism of neutrino emissivity!? Specific heat and thermal conductivity? ・Spin wave or magnons in FM ・SDW and phasons （T.T., arxiv:07113349）

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