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Chiral Magnetic Effect on the Lattice

Chiral Magnetic Effect on the Lattice. Arata Yamamoto (RIKEN). AY, Phys. Rev. Lett . 107, 031601 (2011) AY, Phys. Rev. D 84, 114504 (2011 ) AY, Lect. Notes of Phys., in press. Seminar @ Komaba , June 13, 2012. Chiral Magnetic Effect.

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Chiral Magnetic Effect on the Lattice

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  1. Chiral Magnetic Effect on the Lattice Arata Yamamoto (RIKEN) AY, Phys. Rev. Lett. 107, 031601 (2011) AY, Phys. Rev. D 84, 114504 (2011) AY, Lect. Notes of Phys., in press Seminar @ Komaba, June 13, 2012

  2. Chiral Magnetic Effect [D.E.Kharzeev, L.D.McLerran, H.J.Warringa (2007)] chiral magnetic effect: charge separationinduced by a strong magnetic field via the axial anomaly, i.e., nontrivial topology Early Universe heavy-ion collision (RHIC&LHC) [from KEK’s web page] [from NASA’s web page] [from BNL’s web page]

  3. non-central collision of heavy ions beam beam magnetic field ~ 104 MeV2 cf.)permanent magnet ~ 102 eV2magnetar ~ 10 MeV2

  4. electric current electric current magnetic field If L = R, the net current is zero. If L R, the net current is nonzero.

  5. the index theorem: topological fluctuation in lattice QCD [from D.Leinweber’s web page] Globally, Locally,

  6. electric current magnetic field beam beam topological fluctuation “event-by-event” charge separation

  7. Experiments charged-particle correlationin RHIC & LHC [STAR Collaboration(2009)(2010)] emission magnetic field reaction plane Some asymmetry was observed, but what is it?

  8. Chiral Chemical Potential [K.Fukushima, D.E.Kharzeev, H.J.Warringa (2008)] right-handed Fermi sea left-handed Fermi sea Chiral chemical potential produces a chirally imbalanced matter.

  9. positive helicity negative helicity magnetic field electric current

  10. Induced current [K.Fukushima, D.E.Kharzeev, H.J.Warringa (2008)] the Dirac equation coupled with a background magnetic field magnetic field electric current induced electric current

  11. Sign problem In lattice QCD at finite density, “sign problem” For small chemical potential, reweighting, Taylor expansion, canonical ensemble, imaginary chemical potential, density of states, … For large chemical potential, two-color QCD, isospin chemical potential, chiral chemical potential

  12. Wilson-Dirac operator NO sign problem !!

  13. Lattice QCD Simulation continuum QCD: lattice QCD: countable infinite (finite) multiple integral uncountable infinite functional integral discretization Lattice simulation is powerful in nonperturbative QCD !!

  14. Chiral magnetic effect in lattice QCD topological charge: chiral chemical potential: + Q 0 L R - magnetic field vector current magnetic field by Connecticut and ITEP by A.Y.

  15. Lattice QCD with a fixed-topology 2+1 flavor QCD+QED with the domain-wall fermion [M. Abramczyk, T. Blum, G. Petropoulos, R. Zhou(2009)]

  16. Lattice QCD with a background topology SU(2) quenched QCD with the overlap fermion [P.V.Buividovich, M.N.Chernodub, E.V.Luschevskaya, M.I.Polikarpov (2009)]

  17. Why can we obtain nonzero current? Lattice QCD at : Q=2 gauge configuration [M.Garcia Perez, A.Gonzalez Arroyo, A.Montero, P.van Baal (1999)] Lattice QCD at :

  18. Lattice QCD with a chiral chemical potential • the Wilson gauge action + the Wilson fermion action • flavor: • lattice size: • lattice spacing: fm • pion/rho-meson mass: • deconfinement phase

  19. Chiral charge density

  20. Induced current

  21. Induced current

  22. Induced current by fitting the lattice data from the Dirac equation [K.Fukushima, D.E.Kharzeev, H.J.Warringa (2008)] lattice artifacts e.g. renormalization physical effects e.g. dielectric correction [K.Fukushima, M.Ruggieri (2010)]

  23. Systematic Analysis quenched QCD simulation lattice spacing dependence volume dependence quark mass dependence of

  24. Renormalization The local vector current is renormalization-group variant on the lattice. In the continuum limit , renormalization factor: discretization artifact: cf.) nonperturbative renormalization [L.Maiani, G.Martinelli (1986)]

  25. Lattice spacing The induced current depends on the lattice spacing.

  26. Spatial volume Quark mass chiral limit Independent of volume, quark mass, and temperature

  27. Phase Diagram confinement deconfinement P and its susceptibility is independent of the spatial volume. crossover

  28. isospin chemical potential [J.B.Kogut, D.K.Sinclair (2004)] deconfinement ? crossover confinement 1.0 For a first-order transition,

  29. Summary • We have performed a lattice QCD simulation with the chiral chemical potential. • By applying an external magnetic field, we have obtained the induced current by the chiral magnetic effect. • The continuum extrapolation is quantitatively important. • chiral symmetry ?

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