Extracting ˆq from single inclusive data at RHIC and at the LHC for different centralities: a new puzzle? Carlota Andrés Universidade de Santiago de Compostela Hard Probes 2016, Wuhan, China N. Armesto, Carlos A. Salgado, Matthew Luzum and Pia Zurita arxiv:1606.04837 [hep-ph] 1 / 17
Outlilne 1 Introduction 2 Energy loss implementation 3 Hydrodynamic modelling of the medium 4 Results 5 Limitations and conclusions 6 Next steps 2 / 17
Introduction Study of suppression of high-p T particles in PbPb collisions at the LHC and AuAu collisions at RHIC. Analysis based on the quenching weights (QW) for medium-induced gluon radiation. QW computed in multiple soft scattering approximation. Embedded in different hydrodynamical descriptions of the medium. Study done for different centrality classes. First study of centrality and energy dependence of R AA. 3 / 17
Single inclusive cross section The single inclusive cross section is described by dσ AA h+x dx2 dz = x 1 f dp T dy x 2 z i/a (x 1, Q 2 )x 2 f j/a (x 2, Q 2 ) i,j d ˆσij k D k h (z, µ 2 F dˆt ) Factorization scale Q 2 = (p T /z) 2. Fragmentation scale as µ F = p T. CTEQ6M + EPS09 (NLO). We absorb energy loss in a redefinition of the fragmentation functions: D (med) k h (z, µ2 F ) = 1 0 1 dɛp E (ɛ) 1 ɛ D(vac) k h P E (ɛ) is the Quenching Weight and D (vac) fragmentation functions. k h (z, µ2 F ( ) z 1 ɛ, µ2 F ), DSS 4 / 17
Quenching Weights The ASW Quenching Weights are given by P( E) = [ n ] 1 di (med) (ω i ) dω i n! dω i=1 ( ) n δ E ω i exp n=0 i=1 Independent gluon emission assumed. QW are Poisson distributions. 0 dω di (med) Support in recent works of coherence and resummation by J. Casalderrey-Solana, Y. Mehtar-Tani, C. A. Salgado, K. Tywoniuk... dω 5 / 17
In di (med) dω the medium properties appear in: σ(r)n(ξ). In the multiple soft scattering approximation we use Perturbative tails neglected. σ(r)n(ξ) 1 2 ˆq(ξ)r2 We specify the relation between ˆq(ξ) and the medium properties given by our hydrodynamic model as K is our fitting parameter. ˆq(ξ) = K ˆq QGP (ξ) K 2ɛ 3/4 (ξ) Energy density obtained by solving the relativistic hydrodynamic equations. 6 / 17
Hydrodinamic medium modelling We use several hydrodynamic simulations: Hirano : no viscous, optical Glauber model, τ 0 = 0.6 fm. Glauber : viscous η/s=0.08, energy density proportinal to ρ bin as initial condition, τ 0 = 1 fm. fkln : viscous η/s=0.16, factorised Kharzeev-Levin-Nardi model, τ 0 = 1 fm. Uncertainty coming from the hydrodynamic background is negligible with respect to our conclusions. Ambiguity before thermalization. 3 extrapolations: Case i): ˆq(ξ) = 0 for ξ < τ 0. Case ii): ˆq(ξ) = ˆq(τ 0 ) for ξ < τ 0. Case iii): ˆq(ξ) = ˆq(τ 0 )/ξ 3/4 for ξ < τ 0. 7 / 17
Nuclear modification factor We use R AA experimental data: R AA = dn AA/d 2 p T dy N coll dn pp /dp 2 T dy From Pb-Pb collisions at s NN = 2.76 TeV and Au-Au at snn = 200 GeV. ALICE data on R AA for charged particles with p T > 5 GeV in different centrality classes and for η < 0.8, arxiv:1208.2711 [hep-ex]. PHENIX data on π 0 R AA p T > 5 GeV, arxiv:0801.4020 [nucl-ex]. 8 / 17
R AA at s NN =200 GeV for different centralities 0.8 Au-Au 200 GeV 0-5% PHENIX 0.8 Au-Au 200 GeV 0-10% PHENIX 0.8 Au-Au 200 GeV 10-20% PHENIX R AA 0.6 0.4 0.6 R AA 0.4 0.6 R AA 0.4 0.2 0.2 0.2 0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8 10 12 14 16 18 20 Au-Au 200 GeV 20-30% PHENIX Au-Au 200 GeV 30-40% PHENIX 0.8 0.8 0 2 4 6 8 10 12 14 16 18 20 R AA 0.6 0.4 0.2 0.6 R AA 0.4 0.2 0 2 4 6 8 10 12 14 16 18 20 0 2 4 6 8 10 12 14 16 18 20 9 / 17
R AA at s NN =2.76 TeV for different centralities PbPb 2.76 TeV 0-5% ALICE PbPb 2.76 TeV 5-10% ALICE PbPb 2.76 TeV 10-20% ALICE R AA R AA R AA 10 1 0 10 20 30 40 50 10 1 0 10 20 30 40 50 10 1 0 10 20 30 40 50 R AA R AA R AA 10 1 PbPb 2.76 TeV 20-30% ALICE 0 10 20 30 40 50 10 1 PbPb 2.76 TeV 30-40% ALICE 0 10 20 30 40 50 10 1 PbPb 2.76 TeV 40-50% ALICE 0 10 20 30 40 50 χ 2 to the best value of K. χ 2 = 1. 10 / 17
K-factor vs. impact parameter 3.0 RHIC 200 GeV ˆq(τ) =ˆq(τ 0 ), τ <τ 0 Hirano fkln Glauber 3.0 Hirano fkln Glauber LHC 2.76 TeV ˆq(τ) =ˆq(τ 0 ), τ <τ 0 2.5 2.5 K =ˆq/2ɛ 3/4 2.0 K =ˆq/2ɛ 3/4 2.0 1.5 2 4 6 8 10 12 b (fm) Energy density constant before thermalization. 2.5 2.0 RHIC 200 GeV Hirano fkln Glauber 1.5 2.5 2.0 2 4 6 8 10 12 b (fm) LHC 2.76 TeV free streaming, τ <τ 0 Hirano fkln Glauber K =ˆq/2ɛ 3/4 18 RHIC 200 GeV Hirano ˆq(τ) =0, τ <τ 0 16 fkln Glauber 14 12 10 8 6 4 2 2 4 6 8 10 12 b (fm) ˆq(ξ) = 0 before thermalization. K =ˆq/2ɛ 3/4 18 LHC 2.76 TeV Hirano ˆq(τ) =0, τ <τ 16 fkln 0 Glauber 14 12 10 8 6 4 2 2 4 6 8 10 12 b (fm) K =ˆq/2ɛ 3/4 1.5 K =ˆq/2ɛ 3/4 1.5 free streaming, τ <τ 0 2 4 6 8 10 12 b (fm) Free-streaming case. 2 4 6 8 10 12 b (fm) K depends mainly on the energy and it is almost independent of the centrality of the collision!! 11 / 17
K-factor vs. ɛτ 0 for ˆq constant before thermalization K =ˆq/2ɛ 3/4 3.0 2.5 2.0 1.5 ˆq(τ) =ˆq(τ 0 ), τ <τ 0 Hirano RHIC fkln RHIC Glauber RHIC Hirano LHC fkln LHC Glauber LHC 2 4 6 8 10 12 ɛτ 0 (GeV/fm 2 /c) Estimates taken from: arxiv:1509.06727 [nucl.ex] PHENIX Collaboration and arxiv:1603.04775 [nucl.ex] ALICE collaboration. Difficult to reconcile the energy and centrality dependence!! A new puzzle?? 12 / 17
R AA predictions for s NN = 5.02 TeV Using K 5.02 = K 2.76 If RAA 2.76 = R5.02 AA K 5.02 0.85K 2.76 Glauber, K=1.133 ± 0.028 fkln, K=88 ± 0.028 R AA R 5.02 AA /R2.76 AA 5.02 TeV 10 1 2.76 TeV PbPb 2.76 TeV 0-5% ALICE 0 10 20 30 40 50 0 0.95 0.90 0.85 0.80 0.75 Same K values as s NN = 2.76 TeV 0.70 0 10 20 30 40 50 R AA R 5.02 AA /R2.76 AA 5.02 TeV 10 1 2.76 TeV PbPb 2.76 TeV 0-5% ALICE 0 10 20 30 40 50 0 0.95 0.90 0.85 0.80 0.75 Same K values as s NN = 2.76 TeV 0.70 0 10 20 30 40 50 13 / 17
Limitations The definition of ˆq neglects the perturbative tails of the distributions. The QW find support in the coherence analysis of the medium: if coherence is broken they could fail. Finite energy corrections. ˆq energy or length independent. Collisional energy loss is neglected. 14 / 17
Conclusions We fit the single-inclusive experimental data at RHIC and LHC for different centralities. The fitted value at RHIC confirms large corrections to the ideal case. For the case of the LHC, the extracted value of K is close to unity. K-factor is 2 3 times larger for RHIC than at the LHC. Centrality dependences at RHIC and the LHC are rather flat. The change in the value of K does not look to be simply due to the different local medium parameters. Unexpected result!! 15 / 17
Next steps... Using EKRT event-by-event hydro (τ 0 = 0.197) R AA 0.1 Preliminary. ONLY 10 events!! PbPb 2.76 TeV 20-30% ALICE 0 10 20 30 40 50 K = 71 ± 0.046 for 20-30% Pb-Pb collisions. Same result as for the other hydro simulations. 16 / 17
Other observables v 2 0.20 0.18 0.16 0.14 0.12 0.10 0.08 0.06 0.04 Using the fitted value of K. v n defined as in Jacquelyn Noronha-Hostler et al., arxiv:1602.03788 Preliminary. ONLY 10 events!! v 2 2.76 TeV 20-30% CMS 0.02 5 10 15 20 25 30 35 40 45 50 55 v 3 0.10 0.08 0.06 0.04 0.02 0.00 0.02 v 3 2.76 TeV 20-30% ALICE Preliminary. ONLY 10 events!! 5 10 15 20 25 30 35 40 45 50 Carlota Andrés, Néstor Armesto, Harri Niemi, Risto Paatelainen, Carlos A. Salgado and Pia Zurita. 17 / 17
Backup 17 / 17
Multiple soft scattering approximation for a static medium The inclusive energy distribution of gluon radiation off an in-medium produced parton is given by di (med) ω dω = α sc R (2π) 2 ω 2 2Re e ik u 1 2 e ξ 0 dy l y l dȳ l ȳ l dξn(ξ)σ(u) y exp i ȳ l y l u du χω 0 u=r(ȳ l ) y=0 dk Dr ( ω dξ ṙ 2 n(ξ)σ(r) ) 2 iω n(ξ), density of scattering centers. σ(r), strength of a single elastic scattering. 17 / 17
The production weight is given by ω(x 0, y 0 ) = T Pb (x 0, y 0 )T Pb ( b (x 0, y 0 )) The average values of an observable and in particular of our fragmentations functions is computed as O = 1 dφdx 0 dy 0 ω(x 0, y 0 )O(x 0, y 0, φ) N k h (z, µ2 F ) = 1 dφdx 0 dy 0 ω(x 0, y 0 ) N 1 dζp(x 0, y 0, φ, ζ) 1 ζ D(vac) k h D (med) where N = 2π dx 0 dy 0 ω(x 0, y 0 ). ( ) z 1 ζ, µ2 F 17 / 17
RHIC results Nuclear modification factors R AA for single-inclusive and I AA for hadron-triggered fragmentation functions for different values of 2K = K /0.73, with K = 0.5, 1, 2, 3,..., 20. The green line in the curve corresponding to the minimum of the common fit to R17 AA / 17
Left: χ 2 -values for different values of K for light hadrons and for the three different extrapolations for ξ < τ 0. Red lines correspond to single-inclusive π 0 data from PHENIX (R AA ) and black ones to the double-inclusive measurements by STAR (I AA ). Right: the corresponding central values (minima of the χ 2 ) and the uncertainties computed by considering χ 2 = 1. 17 / 17
Scaled transverse momentum distributions Tetsufumi Hirano, arxiv: nucl-th/0108004 17 / 17
v 2 for charged pions Tetsufumi Hirano and Keiichi Tsuda, arxiv:nucl-th/0205043 17 / 17
Multiplicity at RHIC Matthew Luzum and Paul Romatschke, arxiv:0804.4015 [nucl-th] 17 / 17
v 2 at RHIC Matthew Luzum and Paul Romatschke, arxiv:0804.4015 [nucl-th] 17 / 17
v 2 at LHC Matthew Luzum and Paul Romatschke, arxiv:0901.4588 [nucl-th] 17 / 17
Initial temperatures for Hirano s hydro In the case of Hirano s ideal hydro, the values of the temperature at tau=0.6 fm and x=y=eta=0 for RHIC and LHC are: LHC RHIC 00-05%: 484.3 MeV 00-05%: 373.2 MeV 05-10%: 476.6 MeV 00-10%: 369.6 MeV 10-20%: 463.6 MeV 10-20%: 356.8 MeV 20-30%: 444.6 MeV 20-30%: 341.1 MeV 30-40%: 421.5 MeV 30-40%: 323.7 MeV 40-50%; 393.6 MeV 50-60%: 359.6 MeV 17 / 17
Initial temperatures for Matt s hydros Matt s viscous hydro for two different initial conditions and η/s.initial temperatures at x=y=0, tau=1 fm: Glauber: fkln: b=2 fm LHC: 418 MeV b=2 fm LHC: 389 MeV b=12 fm LHC: 272 MeV b=12 fm LHC: 296 MeV b=2 fm RHIC: 331 MeV b=2 fm RHIC: 299 MeV 17 / 17
ˆq T 3 ɛ 3/4 both for hadronic and partonic phase arxiv:hep-ph/0209038, R. Baier. 17 / 17
K versus intial temperature K =ˆq/2ɛ 3/4 3.0 2.5 2.0 1.5 ˆq(τ) =ˆq(τ 0 ), τ <τ 0 Hirano RHIC fkln RHIC Glauber RHIC Hirano LHC fkln LHC Glauber LHC 260 280 300 320 340 360 380 400 420 440 460 480 500 T (MeV) 17 / 17
K versus intial energy K =ˆq/2ɛ 3/4 3.0 2.5 2.0 1.5 ˆq(τ) =ˆq(τ 0 ), τ <τ 0 Hirano RHIC fkln RHIC Glauber RHIC Hirano LHC fkln LHC Glauber LHC 10 20 30 40 50 60 70 80 90 100 110 ɛ 0 (GeV/fm 3 ) 17 / 17