P.V.Buividovich, M.N.Chernodub,T.K. Kalaydzhyan, D.E. Kharzeev, E.V.Luschevskaya, O.V. Teryaev, M.I. Polikarpov

Transcription

1 Strong magnetic fields in lattice gluodynamics P.V.Buividovich, M.N.Chernodub,T.K. Kalaydzhyan, D.E. Kharzeev, E.V.Luschevskaya, O.V. Teryaev, M.I. Polikarpov arxiv: , arxiv: , arxiv: , arxiv: , arxiv: , arxiv: , arxiv: , arxiv: , arxiv: Quarks, Gluons, and Hadronic Matter under Extreme Conditions 15th of March th of March 011 Schlosshotel Rheinfels, St. Goar, Germany

2 Strong magnetic fields in lattice gluodynamics P.V.Buividovich, M.N.Chernodub,T.K. Kalaydzhyan, D.E. Kharzeev, E.V.Luschevskaya, O.V. Teryaev, M.I. Polikarpov arxiv: , arxiv: , arxiv: , arxiv: , arxiv: , arxiv: , arxiv: , arxiv: , arxiv: Quarks, Gluons, and Hadronic Matter under Extreme Conditions 15th of March th of March 011 Schlosshotel Rheinfels, St. Goar, Germany

3 Lattice simulations with magnetic fields, status 1. Chiral Magnetic Effect 1.1 CME on the lattice 1. Vacuum conductivity induced by magnetic field 1.3 Quark mass dependence of CME (+ talk of P. Buividovich) 1.4 Dilepton emission rate (+ talk of P. Buividovich). Other effects induced by magnetic field.1 Chiral symmetry breaking. Magnetization of the vacuum.3 Electric dipole moment of quark along the direction of the magnetic field

4 Lattice simulations with magnetic fields, future 1. Calculations of OLD quantities in SU(3), SU() with dynamical quarks, QCD. Decreasing systematic errors in SU() calculations. Calculation of NEW physical quantities

5 Magnetic fields in non-central collisions [Fukushima, Kharzeev, Warringa, McLerran 07-08] Heavy ion Heavy ion Quarks and gluons

6 Magnetic fields in non-central collisions [Fukushima, Kharzeev, Warringa, McLerran 07-08] [1] K. Fukushima, D. E. Kharzeev, and H. J. Warringa, Phys. Rev. D 78, (008), URL [] D. Kharzeev, R. D. Pisarski, and M. H. G.Tytgat, Phys. Rev. Lett. 81, 51 (1998), URL [3] D. Kharzeev, Phys. Lett. B 633, 60 (006), URL [4] D. E. Kharzeev, L. D. McLerran, and H. J. Warringa, Nucl. Phys. A 803, 7 (008), URL

7 Magnetic fields in non-central collisions Charge is large Velosity is high Thus we have two very big currents The medium is filled by electrically charged particles Large orbital momentum, perpendicular to the reaction plane Large magnetic field along the direction of the orbital momentum

8 McLerran,Kharzeev,Fukushima B Magnetic fields in non-central collisions Instanton Two very big currents produce a very big magnetic field The medium is filled by electrically charged particles Large orbital momentum, perpendicular to the reaction plane Large magnetic field along the direction of the orbital momentum

9 In heavy ion collisions magnetic forces are of the order of strong interaction forces eb Λ QCD

10 Magnetic forces are of the order of strong interaction forces eb Λ QCD We expect the influence of magnetic field on strong interaction physics

11 Chiral Magnetic Effect by Fukushima, Kharzeev, Warringa, McLerran 1. Massless quarks in external magnetic field. Red: momentum Blue: spin

12 Chiral Magnetic Effect by Fukushima, Kharzeev, Warringa, McLerran 1. Massless quarks in external magnetic field. Red: momentum Blue: spin

13 Chiral Magnetic Effect by Fukushima, Kharzeev, Warringa, McLerran. Quarks in the instatnton field. Red: momentum Blue: spin Effect of topology: u L u R d L d R

14 Chiral Magnetic Effect by Fukushima, Kharzeev, Warringa, McLerran 3. Electric current along magnetic field Red: momentum Blue: spin Effect of topology: u L u R d L d R u-quark: q=+/3 d-quark: q= - 1/3

15 Chiral Magnetic Effect by Fukushima, Kharzeev, Warringa, McLerran 3. Electric current is along magnetic field In the instanton field Red: momentum Blue: spin Effect of topology: u L u R d L d R u-quark: q=+/3 d-quark: q= - 1/3

16 3D time slices of topological charge density, lattice calculations D. Leinweber Topological charge density after vacuum cooling P.V.Buividovich, T.K. Kalaydzhyan, M.I. Polikarpov Fractal topological charge density without vacuum cooling

17 Magnetic forces are of the order of strong interaction forces eb Λ QCD We expect the influence of magnetic field on strong interaction physics The effects are nonperturbative, and we use Lattice Calculations

18 < ψ Γψ > ; Γ= 1, γ µ, σ We calculate µν in the external magnetic field and in the presence of the vacuum gluon fields We consider SU() gauge fields and quenched approximation H external magnetic field T

19 Quenched vacuum, overlap Dirac operator, external magnetic field eb qk = π L π ; eb (50Mev)

20 Density of the electric charge vs. magnetic field, 3D time slices

21 1. Chiral Magnetic Effect on the lattice, numerical results T=0 Regularized electric current: < j ψγψ 3 > IR=< j3 ( H, T ) > < j3 (0,0) >, j 3 = 3

22 Chiral Magnetic Effect on the lattice, numerical comparison of results neartc and nearzero T= 0 F1 0 < j < 1 >=< j j 3 >=< j0 > > T> 0 F1 0 < j1 >=< j < j 3 > < j 0 > > < j > =< j ( H, T ) > < j (0,0) >, j = i Regularized electric current: IR i i i ψ i γψ

23 Chiral Magnetic Effect, EXPERIMENT VS LATTICE DATA (Au+Au)

24 Chiral Magnetic Effect, EXPERIMENT VS LATTICE DATA D. E. Kharzeev, L. D. McLerran, and H. J. Warringa, Nucl. Phys. A 803, 7 (008), experiment our fit R 5 ρ τ 1 0. fm fm fm our lattice data at T=350 Mev

25 1. Magnetic Field Induced Conductivity of the Vacuum Qualitative definition of conductivity, s y x m } exp{ C x q x q x j r y x m A C y j x j = + >= < σ γ µ µ α ν µ ) ( ) ( ) ( } exp{ ) ( ) (

26 Magnetic Field Induced Conductivity of the Vacuum - Conductivity (Kubo formula) Maximal entropy method

27 Magnetic Field Induced Conductivity of the Vacuum - Conductivity (Kubo formula) For weak constant electric field < j >= σ i ik E k

28 Magnetic Field Induced Conductivity of the Vacuum Calculations in SU() gluodynamics We use overlap operator + Shifted Unitary Minimal Residue Method (Borici and Allcoci (006)) to obtain fermion propagator

29 Magnetic Field Induced Conductivity of the Vacuum Calculations in SU() gluodynamics T/Tc = 0.45 T/Tc = 1.1

30 Calculations in SU() gluodynamics, conductivity along magnetic field at T/Tc=0.45 B is parallel to 0 Z axis

31 Calculations in SU() gluodynamics, conductivity along magnetic field at T/Tc=0.45 At T=0, B=0 vacuum is insulator Critical value of magnetic field?

32 Calculations in SU() gluodynamics, conductivity along magnetic field at T<Tc, T>Tc T<Tc H is parallel to 0 Z axis

33 Calculations in SU() gluodynamics, conductivity at T/Tc=0.45, variation of the quark mass α 1 β 1

34 Calculations in SU() gluodynamics, conductivity at T/Tc=0.45, variation of the quark mass and magnetic field σ ij BB BB i j i j Bm Bm π q Why?

35 1.3 Dilepton emission rate L. D. McLerran and T. Toimela, Phys. Rev. D 31, 545 (1985), E. L. Bratkovskaya, O. V. Teryaev, and V. D.Toneev, Phys. Lett. B 348, 83 (1995)

36 There should be more soft dileptons in the direction perpendicular to magnetic field d B σ sin θ dpdp m 1 π θ is the angle between the spatial momentum of the leptons and the magnetic field, in the center of mass of dilepton pair

37 . Other effects induced by magnetic field.1 Chiral symmetry breaking. Magnetization of the vacuum.3 Electric dipole moment of quark along the direction of the magnetic field

38 3. Chiral condensate in QCD Σ = < ψψ > m f π π = m < ψψ q >

39 Chiral condensate vs. field strength, SU() gluodynamics We are in agreement with the chiral perturbation theory: the chiral condensate is a linear function of the strength of the magnetic field!

40 Chiral condensate vs. field strength, SU(3) gluodynamics (+ talk of Kalaydzhyan)

41 Localization of Dirac Eigenmodes Typical densities of the nearzero eigenmodes vs. the strength of the external magnetic field B=0 B=(780Mev)

42 Chiral condensate Simulations with dynamical quarks Massimo D Elia, Francesco Negro, Swagato Mukherjee, Francesco Sanfilippo, arxiv: , PoS LATTICE010:179,010. Michael Abramczyk, Tom Blum, and Gregory Petropoulos, R. Zhou, arxiv:

43 4. Magnetization of the vacuum as a function of the magnetic field Spins of virtual quarks turn parallel to the magnetic field < ψψ > χ = 46(3) Mev our result < ψψ > χ 50Mev QCD sum rules (I. I. Balitsky,1985, P. Ball, 003.) < ψσ σ αβ = αβ ψ >= χ < ψψ > 1 [ γ i α, γ β ] F αβ < ψψ > χ = 46(3) Mev < ψψ > χ 50Mev our result QCD sum rules (I. I. Balitsky,1985, P. Ball, 003.)

44 5. Generation of the anomalous quark electric dipole moment along the axis of magnetic field ylarge correlation between square of the electric dipole moment σ = ψ [ γ 0, γ ] ψ and chirality ρ5 = ψγ 5ψ 0i i i

45 Summary CME a) Visualization b) Large fluctuations of the electric current in the direction of the magnetic field c) Conductivity of the vacuum in the direction of the magnetic field Chiral condensate Magnetization of the vacuum < j 3 > IR < j ( x) j ( y) > µ ν < ψψ > < ψσ ψ αβ > Quark local electric dipole moment SU(), variation of T,H,Mq,a, SU(3) for < iψ [ γ, γ ] ψ ψγψ > < ψψ > 0 i 5

46 Systematic errors SU() gluodynamics instead of QCD Moderate lattice volumes Not large number of gauge field configurations In some cases we calculate the overlap propagator using summation over eigenfunctions:

47 It is interesting to study SU(3), SU(3) variation gluodynamics of T,H,Mq,a SU() with dynamical quarks Lattice QCD variation of T,H,mq,a < ψσ ψ > < ψψ > < iψ [ γ 0, γ i ] ψ ψγψ 5 > αβ < j ( x) j ( y) > µ ν CME, vacuum conductivity Chiral condensate Magnetization of the vacuum Quark local electric dipole moment Dilepton pair angular distribution Shift of the phase transition < j 3 > IR

48 New proposals for calculations D. Kharzeev µ µ L = iµψγ ψ + µ ψγψ 5 µ σ σ σ < j ( x) j ( y) > σ < j ( x) j ( y) > 5 µ ν 5 5µ 5ν SU(), SU(3) gluodynamics, SU() with dynamical quarks Chiral Magnetic Effect (CME) + Chiral Separation Effect (CSE) = = Chiral Magnetic Wave Dmitri E. Kharzeev, Ho-Ung Yee, arxiv:

49 New proposals for calculations D. Kharzeev µ = 0, µ 5 0 L µ = µ 5ψγ 5γ 0ψ σ ( µ, BT, ) 5ij 5 SU(), SU(3) gluodynamics, SU() with dynamical quarks, QCD (imaginary unity is absent)

50 New proposals for calculations D.T. Son, N.Yamamoto Holography and Anomaly Matching for Resonances. e-print: arxiv: q < j q j q >= + 4π Nc ωl ( q ) = no quantum corrections q ω 5 α β β= µ ( ) ν ( ) P [ P ( ) ( )] µ ν ωt q Pν ωl q Fαβ N c T ( q ) = there are nonperturbative corrections q SU(), SU(3) gluodynamics, SU() with dynamical quarks, QCD

51 New proposals for calculations D.T. Son, N.Yamamoto Holography and Anomaly Matching for Resonances. e-print: arxiv: N ω = q ω c L ( q ) no quantum corrections c T ( ) = there are nonperturbative corrections N N ω ( q ) = [ < j j > < j j > ] T q N q c c 5 5 µ µ µ µ q fπ SU(), SU(3) gluodynamics, SU() with dynamical quarks, QCD

52 New proposals for calculations D.T. Son, N.Yamamoto Holography and Anomaly Matching for Resonances. e-print: arxiv: q N N < ( ) ( ) >= [ ( [ < > < > ]) + P P 5 α β c c 5 5 jµ q j ν q P P j j j j µ ν µ µ µ µ 4π q fπ N β= c ν ] F αβ q q q q q α α α α µ α= µ µ = ηµ, P µ = q q SU(), SU(3) gluodynamics, SU() with dynamical quarks, QCD

53 New proposals for calculations D.T. Son, N.Yamamoto < ψγ ψ ( x) ψγ γψ ( y) > µ µ 5 D. Kharzeev < ψψ ( x) ψγψ ( y) > 5 SU(), SU(3) gluodynamics, SU() with dynamical quarks, QCD

54 New proposals for calculations L. McLerran Nonsymmetric condensate < ψψ ( x) ψψ ( y) > Calculate parallel and perpendicular to the field. Chiral condensate may depend on the direction! SU(), SU(3) gluodynamics, SU() with dynamical quarks, QCD