Chiral symmetry breaking andChiral Magnetic Effect in QCD ：手征对称性破缺和手性磁效应在量子色动力学

1、chiral symmetry breaking and chiral magnetic effect in qcd with very strong magnetic fieldp.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, mosco

2、w, 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. kharzeevplannstrong magnetic (not chromo-magnetic!) fieldsn lattice simulations with magnetic fieldsn the enhancement of the chi

3、ral symmetry: dirac eigenmodes and their localizationn magnetization of the vacuum: first lattice resultsn chiral magnetic effect? - a new effect at rhic?n conclusionsmagnetic fields in non-central collisionsthe medium is filled with electrically charged particleslarge orbital momentum, perpendicula

4、r to the reaction planelarge magnetic field along the direction of the orbital momentumanother estimation of magnetic fields, now in evenhancement of the chiral condensatemagnetization of the qcd vacuumchiral magnetic effect signatures of “cp violation” at non-zero topological chargefukushima, kharz

5、eev, 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 simulations1) we use the overlap dirac operator on the lattice2) we perform

6、simulations in the quenched limitquenched vacuum, overlap dirac operator, external magnetic field, 1i1023fieldmagneticexternalhmeans confining vacuum fields quenched vacuum, overlap dirac operator, external magnetic fieldmeveblqkeb250;22free massless fermions in (2+1) dimensionsv.p.gusynin, v.a.mira

7、nsky, i.a.shovkovy,hep-ph/9405262iphysics: strong magnetic fields reduce the system to d = (0 + 1) !physics: magnetic field is the only dimensionfulparameter!2ebfree massless fermions in (3+1) dimensionsv.p.gusynin, v.a.miransky, i.a.shovkovy,hep-ph/9412257physics: strong magnetic fields reduce the

8、system to d = (1 + 1) !physics: the poles of fermionic propagator are at landau levels222ln4mmebuvchiral condensate in qcd1997a. gorsky, a. zayakin 2008 how to calculate the chiral condensate?evolution of the eigenmodes with increase of the magnetic field q=1 q=0features:1) the stronger the field th

9、e denser near-zero eigemodes2) the exact zero eigenmode is insensitive to the field!chiral condensate vs. field strengthwe 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 th

10、eorylocalization of dirac eigenmodestypical densities of the chiral eigenmodes vs. the strength of the external magnetic fieldlocalization of dirac eigenmodeszero fields, b=0no clear visible localization but in fact the localization exists on 2d surfacesnon-zero fields, b a few gev2localization appe

11、ars atlowest landau levelthe magnetic susceptibilityof the yang-mills vacuummagnetization of the vacuum as a function of the magnetic fieldchiral susceptibility - resultschiral magnetic effectfukushima, kharzeev, warringa, mclerran 07-08electric dipole moment appears at regions 1. with non-zero topo

12、logical charge density 2. exposed to external magnetic fieldexperimentally observed at rhic : charge asymmetry of produced particles at heavy ion collisions chiral magnetic effect on the lattice, qualitative picturedensity of the electric charge vs. magnetic fieldchiral magnetic effect on the lattic

13、e, qualitative picturenon-zero field, subsequent time slices chiral magnetic effect on the lattice, qualitative pictureeffect of field increasingchiral magnetic effect on the lattice, numerical results33232323,)0 , 0(),(jjthjjirregularized electric current:chiral magnetic effect on the lattice, nume

14、rical resultsiiiiirijjthjj,)0 , 0(),(222202322211200jjjjftregularized electric current:202322211200jjjjftchiral magnetic effect, experiment vs lattice data (au+au)chiral magnetic effect, experiment vs lattice datafmfmfmr12.05experimentour fitd.?e.?kharzeev,l.?d.?mclerran,?and?h.?j.?warringa,?nucl.?p

15、hys.?a?803,?227?(2008),?our lattice data at t=350 mevchiral magnetic effect on the lattice, results and questionsyywe see rather weak correlation between topological charge density andfluctuations of the density of the electric currents (what is the origin of cme effect?)1?k.?fukushima,?d.?e.?kharze

16、ev,?and?h.?j.?warringa,?phys.?rev.?d?78,?074033?(2008),?url?/abs/0808.3382.2?d.?kharzeev,?r.?d.?pisarski,?and?m.?h.?g.tytgat,?phys.?rev.?lett.?81,?512?(1998),?url?/abs/hep-ph/9804221.3?d.?kharzeev,?phys.?lett.?b?633,?260?(2006),?url?/abs/hep-ph/0406125.4?

17、d.?e.?kharzeev,?l.?d.?mclerran,?and?h.?j.?warringa,?nucl.?phys.?a?803,?227?(2008),?url?/abs/0711.0950.chiral magnetic effect on the lattice, results and questionsd. leinwebertopological charge density after vacuum coolings.morozov, f.gubarev, m.polikarpov,v. zakharovdensity of eigenfu

18、nctions of the diracequation in not cooled vacuumchiral magnetic effect on the lattice, results and questions55yylarge correlation between square of the electric dipole moment and chirality ,00iii1. we observe that the chiral condensate is proportional to the strength of the magnetic field, the coefficient of the proportionality agrees with chiral perturbation theory2. microscopic mechanism for the chiral enhancement: localization of fermions in the vacuum3. the calculated vacuum magnetization is in a qualitative agreement with model calculation