Magnetic field in heavy-ion collision and anisotropy of photon production

Transcription

1 Magnetic field in heavy-ion collision and anisotropy of photon production Vladimir Skokov Strong Magnetic Field and QCD; 12 November 2012 G. Basar, D. Kharzeev, V.S., arxiv: ; PRL A. Bzdak, V.S., arxiv:

2 Outline motivation: photon puzzle magnetic field in heavy-ion collisions photon production from magnetic field in QCD; scale anomaly and production of γ comparison to experimental data data experimental signatures

3 HIC evolution and γ Kinematical freeze-out Chemical freeze-out Hadron gas Mixed phase Hadronization Expansion & Cooling Thermalization QGP: thermal and jets in QGP Pre-equilibrium: photons from Glasma Collision: prompt photons Hard scatterings Maya Shimomura hadronic probes: from chemical/kinetic freeze-out: late stage of the evolution photons probe entire evolution of fireball

4 HIC evolution and γ no free lunch: rather small emission rate and large background

5 Experimental facts about γ transverse momentum spectrum Tave = 221 MeV Tini = 300 to 600 MeV τ0 = 0.15 to 0.6 fm/c Tave is higher then phase transition temperature: semiqgp: photon emission ~ T 4 or thermalizing Glazma?! (L. McLerran and Co: arxiv: ) or something else?! Tserruya, QM 12

6 QGP source of soft photons Tave = 221 MeV theory: hydro calculations +prompt photons (pqcd) d q 0 d 3 q = 1 Tr[Im r ] (2 ) 3, =1/T 1 exp q 0 Turbide, Gale, Jeon and Moore, PRC 72, (2005) Tserruya, QM 12 hadron gas contribution

7 Intro: Hadronic flow Initial anisotropy in coordinate space translates to final state anisotropy in momentum space: owing to strong interaction transverse plane p y y z p x x

8 Intro: Azimuthal anisotropy p y φ p x Azimuthal anisotropy is quantified by Fourier coefficients " dn p? dp? d = dn X # 1+ 2v k (p? ) cos(k ) 2 p? dp? k In this talk: v2 and v4 : v 2 (p? )= v 4 (p? )= R d R d cos(2 ) dn dp? d dn dp? cos(4 ) dn dp? d dn dp?

9 Azimuthal anisotropy Direct photons: Hadrons: arxiv: PHENIX prelim Hydro model K p v PHENIX Data STAR Data h +h + - K +K K 0 S p+ p p t (GeV/c) Photon v2 ~ hadron v2 Contradiction to expectations High Tave -> early emission High v2 -> late emission Large photon v2 is difficult to explain with dominant QGP source

10 Azimuthal anisotropy:lhc

11 Theory: Hydrodynamics I Turbide, Gale, Jeon and Moore, PRC 72, (2005) hydro model, which describes hadronic observables many ingredients overall good description hadron gas does not contribute significantly

12 Theory: Hydrodynamics II Dion et al, 11 (b) Hydro: 5 times smaller v2 then in experiment v AIC, η/s = 0 AIC, η/s = 1/4π FIC p T (GeV) AIC: averaged initial conditions FIC: fluctuating initial conditions Large photon v2 is difficult to explain with dominant QGP source

13 Theory: Another approach Hadron source is the first candidate photon v2 to constrain evolution of fireball v H. van Hees, C. Gale and R. Rapp, 11 PHENIX dir (BBC) PHENIX dir (RXN) model (a) model (b) evolution contradicts to (1+n)-d hydro large acceleration in fireball expansion hadron gas gives major contribution to v2 and photon spectra q 0 dn/d 3 q (GeV -2 ) interesting, but not satisfactory p T (GeV) 0-20% Au-Au, y <0.35 hadron gas QGP primordial total PHENIX hadron gas p T (GeV)

14 Summing up Experiment: high effective T of photon source Experiment: azimuthal anisotropy of photons ~ that of hadrons Theory: photon production ~ T 4, thus biggest in the initial stage, where the hadronic flow is small.

15 Another source of anisotropy? anisotropy flow! other sources for anisotropy not related to flow?! magnetic field?! Perfect candidate for anisotropic photon production.

16 <eb> <eb> Magnetic field in HIC z=0 y transverse plane y z O b/2 x spectators form two currents x resulting average magnetic field at the center x=y=z=0 <eby> ~ mπ 2 (out-plane) <ebx> ~ 0 (in-plane) magnetic field <eb>=(0, mπ 2,0) can be a source of anisotropy in HIC

17 D. Kharzeev, L. McLerran, H. Warringa, V.S. et al, Time-dependence maximal eb ~ s (energy of collision)~υ maximum at tm ~ 1/ s eb y /m π b = 4 fm s NN 1/2 =130 GeV s NN 1/2 =200 GeV life time tlt ~ 1/ s trhic 0.1 fm/c 0.5 thus tlhc ( srhic / slhc) trhic = 0.01 fm/c V.S. et al t, fm/c integrated eb is approximately the same for different energies Z ebdt = const

18 Time-dependence: plasma response Large magnetic field may induce current in charged plasma; currents lead to induced magnetic field Characteristic life time for induced magnetic field ~ electric conductivity Potentially important for top RHIC and LHC energies Relativistic magneto hydrodynamics; initial quark density at tlt ~ 1/ s: quark productions from classical gluon field (glasma)? K. Tuchin,

19 Impact parameter dependence <eb> ~ b (impact parameter) for b < 2R (similar to initial eccentricity <ε2>) eb from spectators is defined by centrality eby/m 2 π Au-Au Pb-Pb s=200 GeV s=2760 GeV b, fm

20 Fluctuations of eb Fluctuating proton positions in colliding nuclei lead to fluctuations of eb in each event: A. Bzdak and V.S.,

21 Fluctuations of eb for observables <eb> is not as significant as as < eby - ebx > A. Bzdak and V.S., azimuthal fluctuations of eb relative to orientation of participant plane: J. Bloczynski et al

22 Magnetic field in HIC III eb in HIC compared to Hybrid magnet at National High Magnetic field Lab 45 Tesla ~ mπ2 Pulsed magnets: 100 Tesla ~10-12 mπ2 Radio pulsars: mπ2 Magnetars: mπ2

23 Observables related to eb Effects, that can be potentially observed: modification of QCD phase diagram chiral magnetic effect chiral magnetic wave vacuum superconductivity many other effect which will be discussed this week photon production! G. Basar, D. Kharzeev, V.S., arxiv: ; PRL

24 Photon production from eb Several mechanisms: synchrotron radiation of quarks in eb (K. Tuchin) unknown: density and distribution function of quarks in early stage R. Venugopalan and V.S. Quark production in Glasma axial anomaly (K. Fukushima) ~ unknown: µ5 (and spectral function of GG) B G. Basar and D. Kharzeev LPV conformal anomaly θμ μ eb γ

25 Conformal anomaly divergence of dilatation µ S µ = µ µ = (g) 2g Gµ a G µ a + X q m q [1 + m (g)] qq color singlet states σ~θμ μ Migdal, Shifman h0 S µ i = iq µ f ; µ S µ i = m 2 f γ effective Lagrangian L = g F µ F µ θμ μ γ gσγγ 0.02 GeV -1 Ellis and Lanik; Crewther; Chanowitz

26 Photon production rate one of the photons: classical field eb θμ μ eb production rate, as usual (β=1/t): γ g 2 (B2 y q 0 d B d 3 q =2 f m 2 B 2 x)q 2 x + q 2? B2 x exp( q 0 ) 1 (q 0 = ~q ).

27 Spectral function of θμ μ hydrodynamic approximation (q 0, ~q) = 1 Im[Gµµ, R (q 0, ~q)] = 9q ( + p) 1 3 c 2 s 2 q 0 s ~q 4 (q 2 0 c 2 s ~q 2 ) 2 +(q 0 s ~q 2 ) 2 real photons, sound peak does not contribute: (q 0, ~q) 9q 0 anisotropy: q 0 d B d 3 q =2 g f m 2 2 (B2 y B 2 x)q 2 x + q 2? B2 x exp( q 0 ) 1 (q 0 = ~q ).

28 or...

29 Bulk viscosity first principle Lattice QCD: H. Meyer SU(3) Yang Mills (YM) However, this is very preliminary... approximations: ζ = Cζ η (1/3-cs 2 ) 2 (vs ADS/QCD ζ 2 η (1/3-cs 2 )) Cζ = 15 in relaxation time appr. (S. Weinberg 71) Cζ = 45 in NLO SU(3) YM (K. Dusling and T. Schafer 11) Cζ = phenomenological constraints in this talk: conservative Cζ = also conservative η/s=1/(4π). Entropy, s, from matrix model fitted to YM SU(3) (R. Pisarski)

30 Anisotropy of production rate d B g q 0 d 3 q =2 f m 2 2 (B2 y qy B 2 x)q 2 x + q 2? B2 x exp( q 0 ) 1 (q 0 = ~q ). in this mechanism: dn/dφ=c1+c2 cos(2φ) consequently: non-zero v2 small vn, n=4,... in contrast to hadronic v4 PHENIX: v4/v2 2 ~1 our prediction for photons: v4/v2 2 1 qx number of photons in out-plane (qy) is smaller then in in-plane (qx) direction in-plane polarization of photons

31 Other parameters Bjorken expansion for thermodynamic variables initial temperature T = MeV initial time τ=0.1 fm/c (no need for complete equilibrium) EoS: matrix model by R. Pisarski et al magnetic field from spectators only (with fluctuations taken into account)

32 Numerical calculations: v2 ingredients: thermal photons and photons from conformal anomaly+eb significant contribution to v2 higher p : prompt v 2 photons suppress v Cζ = PHENIX preliminary p, GeV G. Basar, D. Kharzeev, V.S., arxiv:

33 Transverse momentum spectra conformal anomaly: dn/dp ~ p 2 / [exp(p0/t)-1] similar to effect of direct flow higher than thermal photons for p >1 GeV higher p : prompt photons p 0 dn / d 3 p dz, GeV Conformal Anomaly Conventional Sum p, GeV G. Basar, D. Kharzeev, V.S., arxiv:

34 Experimental tests I 1) magnetic field is generated mostly by spectators 2) hadronic flow: initial eccentricity so switch off either 1) or 2) central U+U collisions: negligible eb but non-zero eccentricity non-central collisions: fluctuations of eccentricity in given centrality class (e.g % defined by ZDC), eb = const; while hadronic v2 fluctuates because of initial eccentricity fluctuations. Limiting case: non-central collisions ( eb 0) with zero v2. v γ thus in such events anisotropy of photon production is due to eb. A. Bzdak and V.S., B only ϵ 2 only ϵ 2 and B v π 2

35 Experimental tests II small v4; violation of scaling v4~v2 2 number of photons Nin-plane > Nout-plane (Nin-plane - Nout-plane)~eB 2 and thus is quadratic function of impact parameter in-plane polarization of photons (presumably difficult to measure)

36 Outlook:LHC energies Higher initial temperatures lower bulk viscosity Tave = 304 MeV Large γ short time scales for non-zero magnetic field tlhc = trhic ΥRHIC / ΥLHC tlhc 0.01 fm/c vs trhic 0.1 fm/c Stay tuned! MAGNETO-HYDRO

37 Outlook:RHIC low energy scan lower energies -> lower eb, but longer time scales in equilibrium: bulk viscosity, ζ, is divergent at critical point (CP) in reality (HIC): at CP ζ~ξ 2.8, ξ is correlation length on O(4) line: ζ~ξ 2 (while shear viscosity is finite) see E. Nakano, V.S. and B. Friman, arxiv: rather speculative: small eb can compensate large ζ MAGNETO-HYDRO

38 Outlook:Glasma and v2 this work: production from thermal YM in principle: this mechanism works also for photon production in Glasma could be a nice combination of results For each of three color bands, the Η or varies as Η ± at Λ 0.29 AuAu Min. Bias 10 4 AuAu AuAu Ed 3 N dp k T + = M. Chiu,...,L. McLerran,..., arxiv: v p, GeV

39 Summary photon v2 puzzle: - hadronic physics?! - or QEDxQCD conformal anomaly in non-zero magnetic field?! there are ways to discriminate between hadronic and anomaly related mechanisms of v2! axial anomaly: similar effect, but unknown µ5 (similar to CME) Synchrotron radiation: similar effect: but unknown quark distribution in initial state

40 Backup Drescher Dumitru Hayashigaki Nara, nucl-th/