Bottomonium and transport in the QGP

Transcription

1 Bottomonium and transport in the QGP Gert Aarts (FASTSUM collaboration) Kyoto, December 201 p. 1

2 Introduction QCD thermodynamics euclidean formulation lattice QCD pressure, entropy, fluctuations,... this talk: QCD real-time dynamics in or close to thermal equilibrium (linear response) lattice QCD analytical continuation to real time Green functions, in particular spectral functions quarkonium spectral functions transport coefficients from the lattice Kyoto, December 201 p. 2

3 Outline quarkonia bottomonium spectral functions in the QGP S waves: Υ at rest, moving P waves: melting light quarks transport: electrical conductivity conclusion Kyoto, December 201 p.

4 FASTSUM collaboration GA (Swansea) Chris Allton (Swansea) Seyong Kim (Sejong University) Maria-Paola Lombardo (Frascati) Sinead Ryan (Trinity College Dublin) Jonivar Skullerud (Maynooth) Simon Hands (Swansea) Don Sinclair (Argonne) Alessandro Amato (Swansea) Wynne Evans (Swansea) Pietro Giudice (Münster) Tim Harris (Trinity College Dublin) Aoife Kelly (Maynooth) Bugra Oktay (Utah) bottomonium: PRL (2011) [hep-lat] JHEP (2011) [hep-lat] JHEP (201) [hep-lat] JHEP (2014) [hep-lat] conductivity: PRL (201) [hep-lat] Kyoto, December 201 p. 4

5 Quarkonia and the QGP quarkonia as a thermometer for the quark-gluon plasma Matsui & Satz 86 tightly bound states of charm quarks (J/ψ,...) or bottom quarks (Υ,...) survive to higher temperatures broader states melt at lower temperatures melting pattern informs about temperature of the QGP figure by A. Mocsy relevant for heavy-ion collisions quantitative predictions required Kyoto, December 201 p. 5

6 Quarkonia and the QGP CMS results at the LHC: Υ spectrum compare PbPb collisions (left) and pp collisions (right) Υ(1S) survives Υ(2S,S) suppressed sequential melting Kyoto, December 201 p. 6

7 Quarkonia and the QGP how to find the response of quarkonia to the QGP? potential models lattice QCD... at T > 0: plethora of potential models: (seemingly) conflicting results interpretation of lattice correlators hindered by thermal (periodic) boundary conditions re-addressed recently using first-principle approach: effective field theories (EFTs) and separation of scales Kyoto, December 201 p. 7

8 Quarkonia and EFTs M T >... hierarchy of scales: heavy quark mass M temperature T inverse size Mv Debye mass gt binding energy Mv 2 weak coupling corresponding EFTs: NRQCD NRQCD + HTL pnrqcd pnrqcd + HTL... Laine, Philipsen, Romatschke & Tassler 07 Laine Burnier, Laine & Vepsäläinen Beraudo, Blaizot & Ratti 08 Escobedo & Soto 08 Brambilla, Ghiglieri, Vairo & Petreczky 08 Brambilla, Escobedo, Ghiglieri, Soto & Vairo 10 Escobedo, Soto & Mannarelli Kyoto, December 201 p. 8

9 Non-relativistic QCD this talk: use NRQCD, one of the EFTs, nonperturbatively no potential model / no weak coupling lattice QCD: heavy quarks with NRQCD requirement M T bottomonium: M b 4.5 GeV T MeV use of NRQCD very well motivated Kyoto, December 201 p. 9

10 Lattice QCD QGP with two light flavours (Wilson-like) many time slices: highly anisotropic lattices (a s /a τ = 6) lattice spacing: a 1 τ 7.5 GeV, a s fm lattice size: 12 N τ N τ N cfg bottom quark: NRQCD mean-field improved action with tree-level coefficients, including up to O(v 4 ) terms Davies et al 94 in progress: extension to N f = [hep-lat] Kyoto, December 201 p. 10

11 Spectrum at zero temperature exponential decay G(τ) exp( m eff τ) no periodicity in euclidean time: initial-value problem 0.25 S1 (Upsilon) = P1 (χ b1 ) = a τ m eff a τ m eff τ/a τ Υ (S wave) τ/a τ χ b1 (P wave) effective mass plot m eff = log[g(τ)/g(τ a τ )] Kyoto, December 201 p. 11

12 Spectrum zero temperature: ground and first excited states state a τ E Mass (MeV) Exp. (MeV) 1 1 S 0 (η b ) 0.118(1) 948(8) 990.9(2.8) 2 1 S 0 (η b (2S)) 0.197(2) 10019(15) - 1 S 1 (Υ) 0.121(1) (26) 2 S 1 (Υ ) 0.198(2) 10026(15) (1) 1 1 P 1 (h b ) 0.178(2) 9879(15) 9898.(1.1)(1.1) 1 P 0 (χ b0 ) 0.175(4) 9857(29) (42)(1) 1 P 1 (χ b1 ) 0.176() 9864(22) (26)(1) 1 P 2 (χ b2 ) 0.182() 9908(22) (26)(1) Υ(1S) used to set the scale Kyoto, December 201 p. 12

13 Increasing the temperature Υ S wave χ b1 P wave 0.25 S1 (Upsilon) = P1 (χ b1 ) = a τ m eff a τ m eff τ/a τ τ/a τ = 0.42 Kyoto, December 201 p. 1

14 Increasing the temperature Υ S wave χ b1 P wave S1 (Upsilon) =0.42 P1 (χ b1 ) =0.42 =1.05 = a τ m eff a τ m eff τ/a τ τ/a τ = 1.05 Kyoto, December 201 p. 1

15 Increasing the temperature Υ S wave χ b1 P wave S1 (Upsilon) =0.42 P1 (χ b1 ) =0.42 =1.05 =1.20 =1.05 = a τ m eff a τ m eff τ/a τ τ/a τ = 1.20 Kyoto, December 201 p. 1

16 Increasing the temperature Υ S wave χ b1 P wave S1 (Upsilon) =0.42 P1 (χ b1 ) = =1.05 =1.20 = =1.05 =1.20 =1.40 a τ m eff a τ m eff τ/a τ τ/a τ = 1.40 Kyoto, December 201 p. 1

17 Increasing the temperature Υ S wave χ b1 P wave S1 (Upsilon) =0.42 P1 (χ b1 ) =0.42 a τ m eff 0.2 =1.05 =1.20 =1.40 =1.68 a τ m eff 0.5 =1.05 =1.20 =1.40 = τ/a τ τ/a τ = 1.68 Kyoto, December 201 p. 1

18 Increasing the temperature Υ S wave χ b1 P wave S1 (Upsilon) =0.42 P1 (χ b1 ) =0.42 a τ m eff 0.2 =1.05 =1.20 =1.40 =1.68 =1.86 a τ m eff 0.5 =1.05 =1.20 =1.40 =1.68 = τ/a τ τ/a τ = 1.86 Kyoto, December 201 p. 1

19 Increasing the temperature Υ S wave χ b1 P wave a τ m eff S1 (Upsilon) =0.42 =1.05 =1.20 =1.40 =1.68 =1.86 =2.09 a τ m eff P1 (χ b1 ) =0.42 =1.05 =1.20 =1.40 =1.68 =1.86 = τ/a τ τ/a τ = 2.09 little T dependence substantial T dependence no exponential decay melting? clear difference in S and P wave correlators Kyoto, December 201 p. 1

20 Spectral functions from euclidean correlators to spectral functions G(τ,p) = dωk(τ,ω)ρ(ω,p) K(τ,ω) = cosh[ω(τ 1/2T)] sinh(ω/2t) inversion: use Maximal Entropy Method (MEM) first discussed quite some time ago but full of pitfalls and obstacles Asakawa & Hatsuda 1999, 2001 Karsch, Petreczky et al GA & Martinez Resco 02 Umeda 07 Petreczky et al Kyoto, December 201 p. 14

21 Spectral functions most problems absent in NRQCD: effective theory around two-quark threshold no transport contribution as ω 0 no thermal boundary conditions simple spectral relation G(τ,p) = dωe ωτ ρ(ω,p) why? factor out heavy quark mass scale: ω = 2M +ω M T : thermal effects exponentially suppressed Laine et al 08, GA et al 10 Kyoto, December 201 p. 15

22 Spectral functions no thermal boundary conditions simple spectral relation G(τ) = dωe ωτ ρ(ω) example at p = 0: correlators for free quarks with kinetic energy E k = k2 2M G S (τ) G P (τ) d k exp( 2E k τ) d kk 2 exp( 2E k τ) ρ S (ω) ρ P (ω) d kδ(ω 2E k ) d kk 2 δ(ω 2E k ) Burnier, Laine & Vepsäläinen 08 temperature dependence only enters via medium! Kyoto, December 201 p. 16

23 S wave at finite temperature Υ spectral function: zero temperature = ρ(ω)/m S1 (vector) Upsilon ω [GeV] dotted lines: ground and first excited state Υ(1S, 2S) from exponential fits Kyoto, December 201 p. 17

24 S wave at finite temperature temperature dependence in Υ channel =0.42 =1.05 =1.05 =1.20 =1.20 = ρ(ω)/m =1.40 =1.68 =1.68 =1.86 =1.86 =2.09 S1 (vector) Upsilon ω [GeV] Υ ground state survives excited states suppressed Kyoto, December 201 p. 17

25 S wave at finite temperature temperature dependence in η b channel =0.42 =1.05 =1.05 =1.20 =1.20 = ρ(ω)/m =1.40 =1.68 =1.68 =1.86 =1.86 = S0 (pseudoscalar) 200 η b ω [GeV] η b ground state survives excited states suppressed Kyoto, December 201 p. 17

26 movingυat finite temperature non-zero momentum: moving through the QGP predictions from EFT, AdS/CFT, potential models,... no clear picture: e.g. dissociates at lower/higher temperatures on the lattice in our case: a s p i = 2πn i N s n i N s 4 maximal momentum: p max 1.7 GeV maximal velocity of ground state: v = p/m S 0.2 non-relativistic Kyoto, December 201 p. 18

27 movingυat finite temperature non-relativistic speeds: v/c S1 (vector) Upsilon =0.42 G(τ,p)/G(τ,0) p (GeV) ratio G(τ, p)/g(τ, 0): τ/a τ clear momentum dependence in correlators expected from dispersion relation M(p) = M +p 2 /(2M) Kyoto, December 201 p. 19

28 movingυat finite temperature non-relativistic speeds: v/c 0.2 [G(τ,p:T)/G(τ,0;T)] / [G(τ,p:T 0 )/G(τ,0;T 0 )] S1 (vector) Upsilon =1.40 p (GeV) τ/a τ double ratio [G(τ,p;T)/G(τ,0;T)]/[G(τ,p;T 0 )/G(τ,0;T 0 )] very little temperature dependence in the momentum dependence Kyoto, December 201 p. 19

29 movingυat finite temperature non-relativistic speeds: v/c 0.2 ρ(ω)/m 2 2 S1 (vector) Upsilon =1.05 p (GeV) ρ(ω)/m 2 2 S1 (vector) Upsilon =1.40 p (GeV) ω [GeV] ω [GeV] spectral functions: survival of moving groundstate Kyoto, December 201 p. 19

30 P waves at finite temperature Kyoto, December 201 p. 20

31 P waves at finite temperature P wave correlators show drastically different behaviour a τ m eff P1 (χ b1 ) =0.42 =1.05 =1.20 =1.40 =1.68 =1.86 = τ/a τ no exponential decay what to expect: no isolated states? melting? spectral analysis Kyoto, December 201 p. 21

32 P waves at finite temperature χ b1 axial-vector channel 0.12 P1 (χ b1 ) = ρ(ω)/m ω [GeV] groundstate below T c, agreement with exp. fit Kyoto, December 201 p. 22

33 P waves at finite temperature χ b1 axial-vector channel ρ(ω)/m P1 (χ b1 ) =0.42 =1.05 =1.20 =1.40 =1.68 =1.86 = ω [GeV] melting immediately above T c consistent with correlator decay Kyoto, December 201 p. 22

34 P waves at finite temperature χ b1 axial-vector channel ρ(ω)/m P1 (χ b1 ) =1.05 =1.20 =1.40 =1.68 =1.86 = ω [GeV] no sign of ground state immediate melting above T c Kyoto, December 201 p. 22

35 Systematics systematic checks for MEM: default model dependence ω range: ω min < ω < ω max sensitive to ω min, additive constant in NRQCD! number of configurations high-precision data important, rel. error 10 4 τ range: τ = τ min...τ max a τ (N τ 1) see papers for details, in particular , Kyoto, December 201 p. 2

36 Transport coefficients dynamics on long length and timescales: effective theory: hydrodynamics ideal hydrodynamics: equation of state viscous hydro: transport coefficients shear/bulk viscosity, conductivity,... depend on underlying microscopic theory typically: large in weakly interacting theory small in strongly coupled systems perfect-fluid paradigm: η/s = 1/4π (holography) Kyoto, December 201 p. 24

37 linear response: Kubo relation Transport coefficients proportional to slope of current-current spectral function at ω = 0 example: conductivity 1 σ = lim ω 0 6ω ρ ii(ω,0) where ρ µν (x) = [j µ (x),j ν (0)] eq is current-current spectral function, j µ is EM current real-time correlator in equilibrium routinely computed with holography Kyoto, December 201 p. 25

38 Transport coefficients from the lattice on the lattice: euclidean correlator related to spectral function G(τ) = dωk(τ,ω)ρ(ω) inversion/analytical continuation much harder than previous problem: K(τ,ω) = cosh[ω(τ 1/2T)] sinh(ω/2t) need reliable estimate of ρ(ω)/ω ω=0 not just ρ(ω) in weakly-coupled theories, correlator is remarkably insensitive to details of ρ(ω) at small ω GA & Martinez Resco 02 Kyoto, December 201 p. 26

39 Transport coefficients from the lattice previous attempts: shear and bulk viscosity Nakamura & Sakai 05, Meyer 07 electrical conductivity quenched (TIFR) S. Gupta 04 (Swansea) GA, Allton, Foley, Hands & Kim 07 (Bielefeld) Ding, Francis, Karsch, Kaczmarek, Laermann & Söldner 11 dynamical (Mainz) Brandt, Francis, Meyer & Wittig 1 (Swansea) GA, Amato, Allton, Giudice, Hands & Skullerud 1 Kyoto, December 201 p. 27

40 several results above T c : Conductivity from the lattice C 1 emσ/t TIFR 1.5, 2, 7 0 staggered Swansea 1.5, (1) 0 staggered Bielefeld (1), Wilson, cont. extrapolated N f Mainz (12) 2 Wilson note: divide out common EM factor C em = e 2 f q 2 f q f = 2, 1 all studies used local current j µ = ψγ µ ψ not the exactly conserved lattice current Kyoto, December 201 p. 28

41 Conductivity from the lattice recent work: Amato, GA et al, [hep-lat] improvements: N f = 2+1 dynamical quark flavours conserved lattice current (no renormalisation required) many temperatures, below and above T c anisotropic lattice, a s /a τ =.5, many time slices N s N τ N cfg Kyoto, December 201 p. 29

42 spectral function ρ(ω)/ω 2 Conductivity from the lattice rho-particle peak around 800 MeV below T c nonzero conductivity: ρ(ω) σω +... inset ρ(ω)/ω: intercept conductivity Kyoto, December 201 p. 0

43 Conductivity from the lattice σ/t across the deconfinement transition N f = 0 (Aarts et al ) N f = 0 (Ding et al ) N f = 2 (Brandt et al ) -1 C em σ/τ T [MeV] previous results Kyoto, December 201 p. 1

44 Conductivity from the lattice σ/t across the deconfinement transition -1 C em σ/τ N f = 0 (Aarts et al ) N f = 0 (Ding et al ) N f = 2 (Brandt et al ) 24 N f = 2+1 } 2 (this work) T [MeV] consistent with previous (quenched) results in QGP first observation of T dependence Kyoto, December 201 p. 1

45 Summary bottomonium: NRQCD on QGP background S wave ground states survive, at rest and moving excited states appear suppressed P wave states melt immediately above T c transport from the lattice: electrical conductivity first large-scale computation with dynamical quarks number of results available above T c mostly consistent, σ/t C em in QGP temperature dependence of σ/t found across T c Kyoto, December 201 p. 2

46 Back-up: melted P waves ρ(ω)/m P1 (χ b1 ) =1.05 =1.20 =1.40 =1.68 =1.86 =2.09 ρ(ω)/m P1 (χ b1 ) =1.05 =1.20 =1.40 =1.68 =1.86 =2.09 free ω [GeV] a τ ω melting above T c : a featureless blob? shape is similar to free lattice spectral function ρ P (ω) p 2 δ(ω 2E p ) Brillouin zone Kyoto, December 201 p.

47 Back-up: conductivity systematics: default model dependence -1 C em σ/τ x16 24 x20 2 x24 2 x28 2 x2 2 x6 24 x40 2 x48 input: no structure b ρ default (ω)/ω = b+cω b needed to allow for a nonzero conductivity stable results provided b is not too small (no bias) Kyoto, December 201 p. 4