Quark-Gluon Plasma in Proton-Proton Scattering at the LHC?

Transcription

1 Quark-Gluon Plama in Proton-Proton Scattering at the LHC? K. Werner (a), Iu. Karpenko (b), T. Pierog (c) (a) SUBATECH, Univerity of Nante INP/CNRS EMN, Nante, France (b) Bogolyubov Intitute for Theoretical Phyic, Kiev,, Ukraine (c) Karlruhe Intitute of Technology (KIT) - Campu North, Int. f. Kernphyik, Germany Abtract We dicu recent experimental reult from proton-proton cattering at 7 TeV and their interpretation in term of a cenario of a hydrodynamical expanion initiated by flux tube initial condition. EPOS i a multiple cattering model in the pirit of the Gribov-Regge approach[]. Here, one doe not mean imply multiple hard cattering, the elementary procee correpond to complete parton ladder, which mean hard cattering plu initial tate radiation. In thi cae, thi elementary proce carrie an important fraction of the available energy, and therefore we treat very carefully the quetion of energy haring in the multiple cattering proce. Open and cloed ladder have to be conidered in order to have a conitent quantum mechanical treatment. The correponding graph are quared, and we employ cutting rule technique and Markov chain to obtain finally partial cro ection. The cut parton ladder are identified with longitudinal color field or flux tube, treated via relativitic tring theory. In cae of very high energy pp colliion (at the LHC) or heavy ion cattering already at RHIC, many flux tube overlap and produce high energy denitie. Let u conider the energy denity at an early time in a Au-Au cattering at RHIC, a obtained from an EPOS imulation []. In fig., we plot the energy denity at different value of pace-time rapidity η, a a function of the tranvere coordinate x and y. We oberve a very bumpy tructure concerning the x y dependence, wherea the variation with η i mall. There are in particular peak in the x y plane, which how up at the ame poition at different value of η. So we have ub-flux-tube which exhibit a long range tructure in the longitudinal variable η. In fig., we clearly identify everal ub-flux-tube, with a typical width of the order of a fermi. Thi i exactly the width we obtain if we compute the initial energy denity in protonproton cattering at the LHC. Thi mean, if a hydrodynamic treatment i jutified for Au-Au colliion at RHIC, it i equally jutified for pp cattering at the LHC, provided the energy denitie are high enough, which eem to be the cae. We therefore employ a ophiticated hydrodynamical cenario (for detail ee []), for both heavy ion and proton-proton cattering at the LHC, with initial condition

2 energy denity [GeV/fm =., τ =. fm/c) C 5 energy denity [GeV/fm =.5, τ =. fm/c) C Figure : Energy denity in central Au-Au cattering at GeV. rad velocity [% of c =., τ =. fm/c) C 5 rad velocity [% of c =.5, τ =. fm/c) C Figure : Radial flow velocity at a proper time τ =. fm/c, at a pace-time rapiditie η = and η =.5. obtained from a flux tube approach (EPOS), compatible with the tring model, ued ince many year for elementary colliion (electron-poitron, proton proton), and the color gla condenate picture []. The equation-of-tate i compatible with lattice gauge reult of ref. []. We ue a hadronic cacade procedure after hadronization from the thermal ytem at an early tage [, 5]. In ref. [], we tet the approach by invetigating all oft obervable of heavy ion phyic, in cae of AuAu cattering at GeV. Here, we are going to dicu ome elected (and intereting) topic. In fig., we ee a complicated tructure of the initial energy denity in the tranvere plane, but thi tructure i longitudinally tranlational invariant (ame tructure at different value of η ). The equation of hydrodynamic preerve thi tranlational invariance, and tranport it to different quantitie, a the radial flow, ee fig.. A a conequence, particle emitted from different longitudinal poition get the ame tranvere boot, when their emiion

3 φ η Figure : Dihadron η φ correlation in a central Au-Au colliion at GeV. point correpond to the azimuthal angle of a common flow peak poition. And ince longitudinal coordinate and (peudo)rapidity are correlated, one obtain finally a trong η φ correlation, a een in fig., where we plot the dihadron correlation dn/d η d φ, with η and φ being repectively the difference in peudorapidity and azimuthal angle of a pair of particle. Here, we conider trigger particle with tranvere momenta between and GeV/c, and aociated particle with tranvere momenta between GeV/c and the p t of the trigger, in central Au-Au colliion at GeV. Our ridge i very imilar to the tructure oberved by the STAR collaboration []. The CMS collaboration publihed recently reult [7] on two particle correlation in η and φ, in pp cattering at 7 TeV. Mot remarkable i the dicovery of a ridge-like tructure around φ =, extended over many unit in η, referred to a the ridge, in high multiplicity pp event. A imilar tructure ha been oberved in heavy ion colliion at RHIC, a dicued earlier, and there i little doubt that the phenomenon i related to the hydrodynamical evolution of matter. Thi fluid dynamical behavior i actually conidered to be the major dicovery at RHIC. So doe pp cattering provide a well a liquid, jut ten time maller than a heavy ion colliion? It eem o! We howed recently [] that if we take exactly the ame hydrodynamic approach which ha been o ucceful for heavy ion colliion at RHIC [], and apply it to pp cattering, we obtain already very encouraging reult compared to pp data at.9 TeV. In thi paper, we apply thi fluid approach, alway the ame procedure, to undertand the 7 TeV reult. In fig., we how that our hydrodynamic picture indeed lead to a near-ide ridge, around φ =, extended over many unit in η. One hould note that the correlation function are defined and normalized a in the CMS publication, o we can ay that our ridge i quite cloe in hape and

4 R( η, φ) φ η Figure : (Color online) Two particle correlation function R veru η and φ for high multiplicity event in pp colliion at 7 TeV. in magnitude compared the experimental reult. The experimental high multiplicity bin correpond to about 7 time average, wherea in our calculation (extremely demanding concerning CPU power) high multiplicity refer to 5. time average (we actually trigger on event with elementary cattering). We cannot go beyond at the moment. It i eay to undertand the origin of the ridge, in a hydrodynamical approach baed on flux tube initial condition. Imagine many (ay ) flux tube of mall tranvere ize (radiu. fm), but very long (many unit of pace-time rapidity η ). For a given event, their tranvere poition are randomly ditributed within the overlap area of the two proton. Even for zero impact parameter (which dominated for high multiplicity event), thi randomne produce azimuthal aymmetrie, a hown in fig. 5, upper panel. The energy denity obtained from the overlapping flux tube (detail will be dicued later) how an elliptical hape. And ince the flux tube are long, and only the tranvere poition are random, we oberve the ame aymmetry at different longitudinal poition (η = and η =.5 in the figure). So we oberve a tranlational invariant azimuthal aymmetry! If one take thi aymmetric but tranlational invariant energy denity a initial condition for a hydrodynamical evolution, the tranlational invariance i conerved, and in particular tranlated into other quantitie, like the flow. In fig. 5, lower panel, we how the radial flow velocity at a later time again at the two pace-time rapiditie η = (left) and η =.5 (right). In both cae, the flow i more developed along the direction perpendicular to the principal axi of the initial energy denity ellipe. Thi i a very typical fluid dynamical phenomenon, referred to a elliptical flow.

5 energy denity [GeV/fm =., τ =. fm/c) J energy denity [GeV/fm =.5, τ =. fm/c) J rad velocity [% of c =., τ =.7 fm/c) J 7.5 rad velocity [% of c =.5, τ =.7 fm/c) J Figure 5: (Color online) Initial energy denity (upper panel) and radial flow velocity at a later time (lower panel) for a high multiplicity pp colliion at 7 TeV at a pacetime rapidity η = (left) and η =.5 (right). Finally, particle are produced from the flowing liquid, with a preference in the direction of large flow. Thi preferred direction i therefore the ame at different value of η. And ince η and peudorapidity η are highly correlated, one oberve a η φ correlation, around η =, extended over many unit in η: a particle emitted a ome peudorapidity η ha a large chance to ee a econd particle at any peudorapidity to be emitted in the ame azimuthal direction. Acknowledgment Thi reearch ha been carried out within the cope of the ERG (GDRE) Heavy ion at ultra-relativitic energie. Iu.K. acknowledge partial upport by the State Fund for Fundamental Reearche of Ukraine (Agreement of ) and National Academy of Science of Ukraine (Agreement of ). T.P. and K.W. acknowledge partial upport by a PICS (CNRS) with KIT (Karlruhe). Reference [] K. Werner, Iu. Karpenko, T. Pierog, M. Bleicher, K. Mikhailov, arxiv:.5, Phy. Rev. C, 9 () 5

6 [] L.D. McLerran, R. Venugopalan, Phy. Rev. D 9, (99). ibid. D9, 5 (99); D 5, 5 (99) [] S. Boranyi et al., arxiv:7.5 [] M. Bleicher et al., J. Phy. G5 (999) 59 [5] H. Peteren, J. Steinheimer, G. Burau, M. Bleicher and H. Stocker, Phy. Rev. C7 () 9 [] STAR Collaboration, B. Abelev et al., Phy. Rev. C (9) 9 [7] CMS Collaboration, JHEP 9:9, [] K. Werner, Iu. Karpenko, T. Pierog, M. Bleicher, K. Mikhailov, arxiv:., Phy. Rev. C, 95 ()