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1、Chiral symmetry breaking and Chiral Magnetic Effect in QCD with very strong magnetic field,P.V.Buividovich (ITEP, Moscow, Russia and JIPNR “Sosny” Minsk, Belarus), M.N.Chernodub (LMPT, Tours University, France and ITEP, Moscow), E.V.Luschevskaya (ITEP, Moscow, Russia), M.I.Polikarpov (ITEP, Moscow,
2、Russia),Fourth International Sakharov Conference on Physics 18 May, 2009, Moscow,I use a lot of slides made by M.N. Chernodub and P.V. Buividovich and some made by D.E. Kharzeev,Plan,nStrong magnetic (not chromo-magnetic!) fields n Lattice simulations with magnetic fields n The enhancement of the ch
3、iral symmetry: Dirac eigenmodes and their localization n Magnetization of the vacuum: first lattice results n Chiral Magnetic Effect? - a new effect at RHIC? n Conclusions,Magnetic fields in non-central collisions,The medium is filled with electrically charged particles Large orbital momentum, perpe
4、ndicular to the reaction plane Large magnetic field along the direction of the orbital momentum,Another estimation of magnetic fields, now in eV,Enhancement of the chiral condensate Magnetization of the QCD vacuum Chiral Magnetic Effect signatures of “CP violation” at non-zero topological chargeFuku
5、shima, Kharzeev, Warringa, McLerran 07-08(new experimental data from RHIC: Conference “Quark Matter 2009, 30 March - 4 April” in Knoxville, USA, ),What effects can we expect at very strong magnetic fields?,Magnetic fields in our lattice simulations,1) We use the overlap Dirac operator on the lattice
6、2) We perform simulations in the quenched limit,Quenched vacuum, overlap Dirac operator, external magnetic field,1,0,2,3,means confining vacuum fields,Quenched vacuum, overlap Dirac operator, external magnetic field,Free massless fermions in (2+1) dimensions,V.P.Gusynin, V.A.Miransky, I.A.Shovkovy,
7、hep-ph/9405262I Physics: strong magnetic fields reduce the system to D = (0 + 1) ! Physics: magnetic field is the only dimensionful parameter!,Free massless fermions in (3+1) dimensions,V.P.Gusynin, V.A.Miransky, I.A.Shovkovy, hep-ph/9412257 Physics: strong magnetic fields reduce the system to D = (
8、1 + 1) ! Physics: the poles of fermionic propagator are at Landau levels,Chiral condensate in QCD,1997,A. Gorsky, A. Zayakin 2008,How to calculate the chiral condensate?,Evolution of the eigenmodes with increase of the magnetic field,Q=1 Q=0 Features:1) The stronger the field the denser near-zero ei
9、gemodes2) The exact zero eigenmode is insensitive to the field!,Chiral condensate vs. field strength,We get an agreement with the chiral perturbation theory: the chiral condensate is a linear function of the strength of the magnetic field!,Lattice results vs. chiral perturbation theory,Localization
10、of Dirac EigenmodesTypical densities of the chiral eigenmodes vs. the strength of the external magnetic field,Localization of Dirac Eigenmodes,Zero fields, B=0no clear visible localization but in fact the localization exists on 2D surfaces,Non-zero fields, B a few GeV2Localization appears atLowest L
11、andau Level,The magnetic susceptibilityof the Yang-Mills vacuum,Magnetization of the vacuum as a function of the magnetic field,Chiral susceptibility - results,Chiral Magnetic Effect,Fukushima, Kharzeev, Warringa, McLerran 07-08,Electric dipole moment appears at regions 1. with non-zero topological
12、charge density 2. exposed to external magnetic field,Experimentally observed at RHIC : charge asymmetry of produced particles at heavy ion collisions,Chiral Magnetic Effect on the lattice, qualitative picture,Density of the electric charge vs. magnetic field,Chiral Magnetic Effect on the lattice, qu
13、alitative picture,Non-zero field, subsequent time slices,Chiral Magnetic Effect on the lattice, qualitative picture,Effect of field increasing,Chiral Magnetic Effect on the lattice, numerical results,Regularized electric current:,Chiral Magnetic Effect on the lattice, numerical results,Regularized e
14、lectric current:,Chiral Magnetic Effect, EXPERIMENT VS LATTICE DATA (Au+Au),Chiral Magnetic Effect, EXPERIMENT VS LATTICE DATA,experiment,our fit,D. E. Kharzeev, L. D. McLerran, and H. J. Warringa, Nucl. Phys. A 803, 227 (2008),our lattice data at T=350 Mev,Chiral Magnetic Effect on the lattice, RES
15、ULTS and QUESTIONS,yWe see rather weak correlation between topological charge density and fluctuations of the density of the electric currents (What is the origin of CME effect?) 1 K. Fukushima, D. E. Kharzeev, and H. J. Warringa, Phys. Rev. D 78, 074033 (2008), URL http:/arxiv.org/abs/0808.3382. 2
16、D. Kharzeev, R. D. Pisarski, and M. H. G.Tytgat, Phys. Rev. Lett. 81, 512 (1998), URL http:/arxiv.org/abs/hep-ph/9804221. 3 D. Kharzeev, Phys. Lett. B 633, 260 (2006), URL http:/arxiv.org/abs/hep-ph/0406125. 4 D. E. Kharzeev, L. D. McLerran, and H. J. Warringa, Nucl. Phys. A 803, 227 (2008), URL http:/arxiv.org/abs/0711.0950.,Chiral Magnetic Effect on the lattice, RESULTS and QUESTIONS,D. Leinweber Topological charge density after vacuum cooling,S.Morozov, F.Gubarev, M.Polikarpov, V. Zakharov De
