Nonequilibrium photon production by classical color fields

Transcription

1 Nonequilibrium photon production by classical color fields Naoto Tanji Heidelberg University arxiv: ECT* Workshop Dec. 04 th 2015

2 Photons in heavy-ion collisions 1/30 hadron decays thermal hadron gas pre-equilibrium hadron QGP jet-medium thermal QGP pre-equilibrium production prompt hard scattering

3 Photons in heavy-ion collisions 1/30 hadron decays thermal hadron gas pre-equilibrium hadron QGP jet-medium thermal QGP pre-equilibrium production prompt hard scattering small space-time volume initially almost no quark high energy density non-equilibrium dynamic processes (e.g. coherent acceleration by color fields)

4 Outline Introduction direct photon puzzle geometrical scaling photon production in glasma EM current in uniform color electric fields SU(2) vs. SU(3) color direction dependence Glasma-like color fields thermal-like photon spectrum from nonequilibrium quarks 2/30

5 Direct photon puzzle (I) Large photon yields PHENIX ALICE taken from a slide by K. Reygers taken from a slide by A. Drees The state-of-the-art hydro calculations underestimate the photon yields at low momenta. 3/30

6 Direct photon puzzle (II) 4/30 Large photon v2 taken from a slide by A. Drees taken from a slide by K. Reygers Large anisotropy of the photon spectrum comparable to that of pions are observed. Hydro calculations underestimate the photon v2.

7 Direct photon puzzle 5/30 It is difficult to simultaneously explain the large direct photon excess and the photon flow. (I) large photon yields (II) large photon v2 high temperature early-time emission large flow of QGP, hadrons late-time emission Improvement of current models? Exotic new photon sources? Photon production in pre-equilibrium (Glasma)

8 Geometrical scaling C.K.-Bösing, L.McLerran, Phys.Lett. B734 (2014) The data points of different kinds of collisions and different energies are on the same line. The saturation scale is the only relevant scale. Imply photon production at early times when other scales (system size, particle masses) are not yet important. 6/30

9 Photon production in glasma 7/30 Studied by M. Chiu et al. (2013), L.McLerran, B.Schenke (2014). Based on a simple model for the gluon and quark distribution functions A computation based on a first principle is needed. The glasma is initially a pure gluonic state. Photons do not directly couple to gluons. A real-time description of the quark production in the glasma

10 Quark production in glasma 8/30 Glasma gauge fields produce quarks. Quarks are accelerated or kicked by the gauge fields. Chemical and thermal equilibration? Glasma flux tubes Lappi, McLerran (2006)

11 Quark production in glasma 8/30 Glasma gauge fields produce quarks. Quarks are accelerated or kicked by the gauge fields. Chemical and thermal equilibration? Glasma flux tubes

12 Quark production in glasma 8/30 Glasma gauge fields produce quarks. Quarks are accelerated or kicked by the gauge fields. Chemical and thermal equilibration? Glasma flux tubes

13 Photon production in glasma 9/30 Glasma gauge fields produce quarks. Quarks are accelerated or kicked by the gauge fields. Chemical and thermal equilibration? During these processes, quarks can emit photons. Glasma flux tubes radiation annihilation Can be computed by real-time lattice simulations with the classical(-statistical) approximation for the non-abelian gauge fields.

14 Classical approximation for gauge fields 10/30 In the CGC and glasma, the coupling is weak and the field is strong.

15 Classical approximation for gauge fields 10/30 In the CGC and glasma, the coupling is weak and the field is strong. the same order

16 Classical approximation for gauge fields 10/30 In the CGC and glasma, the coupling is weak and the field is strong. the same order

17 Classical approximation for gauge fields 10/30 In the CGC and glasma, the coupling is weak and the field is strong. the same order The non-abelian gauge field obeys the classical Yang-Mills equation. The quark field does the Dirac equation under the classical gauge field.

18 Photon production formula 11/30 In thermal equilibrium, McLerran and Toimela (85), Weldon (90), Gale and Kapsta(91) Extension to non-equilibrium.

19 Photon production formula 11/30 In thermal equilibrium, McLerran and Toimela (85), Weldon (90), Gale and Kapsta(91) Extension to non-equilibrium. One of characteristic features of a non-equilibrium state is nonzero current expectation. Gives the same order contribution in as the connected one-loop

20 Photon production formula 11/30 In thermal equilibrium, McLerran and Toimela (85), Weldon (90), Gale and Kapsta(91) Extension to non-equilibrium. One of characteristic features of a non-equilibrium state is nonzero current expectation. Gives the same order contribution in as the connected one-loop

21 EM currents in uniform color electric fields 12/30

22 Abelianization of uniform color fields 13/30 Consider a uniform color field at first. Diagonalize constant vector in color space U(1) theory with effective coupling

23 Abelianization of uniform color fields Consider a uniform color field at first. Diagonalize constant vector in color space U(1) theory with effective coupling An important difference between SU(2) and SU(3) SU(2) is rank 1: SU(3) is rank 2: color direction parameter 13/30

24 Abelianization of SU(3) fields Relation between and gauge invariant quantity (Casimir invariant) characterizing the color direction rotated weight diagram The color direction can be parametrized in a gauge-invariant way. Physical observables can depend on it. 14/30

25 Quark production in SU(2) uniform electric fields 15/30 The diagonalized effective couplings are always 1/2 and -1/2. Uniform and constant electric field color 1 color 2 The distribution functions of produced quarks The distributions of anti-quarks are given by

26 Quark production in SU(2) uniform electric fields 15/30 The diagonalized effective couplings are always 1/2 and -1/2. Uniform and constant electric field color 1 color 2 The distribution functions of produced quarks The distributions of anti-quarks are given by

27 Cancellation of EM current in SU(2) fields 16/30 The contributions from color 1 and 2 are cancelled out. In the case of the Schwinger mechanism,

28 Quark production in SU(3) uniform electric fields 17/30 Uniform and constant electric field color 1 color 2 color 3 0 The distribution functions of produced quarks

29 Non-cancellation of EM current in SU(3) fields 18/30 Depending on the color direction, nonzero EM current is induced.

30 Glasma-like color fields 19/30

31 Glasma-like color fields Uniform in the z-direction Fluxtube-like configuration in the transverse plane Non-expanding fixed box Initially there are only electric fields SU(2) SU(3) Glasma random numbers The transverse profile of the initial energy density 20/30

32 Glasma-like color fields Uniform in the z-direction Fluxtube-like configuration in the transverse plane Non-expanding fixed box Initially there are only electric fields Glasma SU(2) SU(3) The time dependence of the gauge field energy density 20/30

33 Induction of the EM current: SU(2) 21/30 Plots of x-component y-component z-component Even in SU(2), nonzero EM current is induced.

34 Induction of the EM current: SU(3) 22/30 Plots of x-component y-component z-component

35 Comparison between SU(2) and SU(3) 23/30 z-component SU(2) SU(3) Several orders different! For the induction of the EM current (and the subsequent photon production), it is important to use SU(3).

36 Photon spectrum 24/30 Compute the spectrum of photons produced by classical processes Solve the Maxwell equation Photon energy spectrum Photon number spectrum

37 Photon energy spectrum 25/30 SU(3) px-distribution with py=0, and py-distribution with px=0 are plotted. The width of the spectrum is characterized by. The low momentum region fluctuates largely depending on the random background.

38 Photon number spectrum SU(3) At At with, the spectrum fluctuates largely run by run., the spectrum can be fitted by, although the system is far away from thermal equilibrium. 26/30

39 Time evolution of the photon number spectrum 27/30

40 Spectra of gluons, quarks and photons 28/30 gluons quarks photons

41 Summary 29/30 Investigated the induction of EM currents and the subsequent photon production by classical color fields as a first step to understand photon production in glasma. For SU(3) color fields, the induced EM current can depend on the color direction of the fields. In the glasma-like color fields, the photon spectrum shows an exponential behavior in pt.

42 Outlook 30/30 Is the exponential spectrum universal? Are there signatures specific to pre-equilibrium photons? More realistic setup polarization? correlations? expanding system, initial condition consistent with CGC Effects of gauge field fluctuations and backreaction Genuine quantum process (ongoing in collaboration with people in Heidelberg)