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

Non-Peturb QCD, IAP Paris, Klaus WERNER, Subatech, Nantes - Quark-Gluon Plasma in Proton-Proton Scattering at the LHC? Klaus Werner <werner@subatech.inp3.fr> in collaboration with Iu. Karpenko, T. Pierog, M. Bleicher, K. Mikhailov

Non-Peturb QCD, IAP Paris, Klaus WERNER, Subatech, Nantes - UR heavy ion collisions seem to produce matter which expands as an almost ideal fluid (of quark matter) Houvinen et al, Many nontrivial observations can be explained on the basis of hydrodynamics like azimuthal anisotropies expressed via v =< cos φ > in hydro, space asymmetry translates into momentum asymmetry via flow

Non-Peturb QCD, IAP Paris, Klaus WERNER, Subatech, Nantes - Also known (from RHIC): No drastic change when considering smaller systems smaller nuclei and/or semi-peripheral collisions What about proton-proton scatterings? First LHC results: signs for collective fluid-like behavior in high multiplicty pp events as well...

Non-Peturb QCD, IAP Paris, Klaus WERNER, Subatech, Nantes -3 We employ a hydrodynamical scenario for pp@lhc (same procedure as for heavy ion collisions): Multiple scattering approach EPOS (marriage of pqcd and Gribov-Regge) used as initial condition for a hydrodynamic evolution, if the energy density is high enough; event-by-event procedure, taking into account the irregular space structure of single events, leading to so-called ridge structures in two-particle correlations; core-corona separation, considering the fact that only a part of the matter thermalizes; 3+ D ideal hydro evolution, including the conservation of baryon number, strangeness, and electric charge;

Non-Peturb QCD, IAP Paris, Klaus WERNER, Subatech, Nantes -4 parton-hadron transition * realistic equation-of-state with a cross-over transition for μ B =, compatible with latest lattice gauge results hadronization, (S. Borsanyi et al, arxiv:7.58 or M. Chenget al., arxiv:9.5) * here: Cooper-Frye, using complete hadron table, * at an early stage (66 MeV, in the transition region), * with subsequent hadronic cascade procedure (UrQMD) details see: arxiv:4.85 (Ridges + many other things at RHIC), PRC 8,4494 arxiv:.4 (Hydrodyn. evolution in pp@lhc), PRC 83, 4495 arxiv:.375 (Ridges in pp@7tev), PRL 6:4, arxiv:4.45 (BoseEinstein correlations in pp@7tev)

Non-Peturb QCD, IAP Paris, Klaus WERNER, Subatech, Nantes -5 Elementary scatterings - flux tubes AA - even pp: many elementary collisions happening in parallel. Not just rescattering of hard partons! Elementary scattering = parton ladder Parton evolutions from the projectile and the target side towards the center (small x) low x partons nonlinear effects flux tube Evolution is governed by an evolution equation, in the simplest case according to DGLAP. Parton ladder may be considered as a quasilongitudinal color field, a so-called flux tube, conveniently treated as a relativistic string. The intermediate gluons are treated as kink singularities in the language of relativistic strings, providing a transversely moving portion of the object. This flux tube decays via the production of quark-antiquark pairs, creating in this way fragments which are identified with hadrons

Non-Peturb QCD, IAP Paris, Klaus WERNER, Subatech, Nantes -6 Quantum mechanical treatment of multiple scattering is quite involved... in particular when the energy sharing between the parallel scatterings is taken into account Details: Parton-based Gribov-Regge Theory, H. J. Drescher, M. Hladik, S. Ostapchenko, T.Pierog, and K. Werner, Phys. Rept. 35 () 93-89 Based on cutting rule techniques, one obtains partial cross sections for exclusive event classes, which are then simulated with the help of Markov chain techniques.

Non-Peturb QCD, IAP Paris, Klaus WERNER, Subatech, Nantes -7 Parton ladder -> flux tube -> kinky string: At LHC, almost all scatterings are hard, nevertheless flux tubes are mainly longitudinal objects (here parallel to the z-axis) but due to the kinks there are string pieces moving transversely (in y-direction in the picture). x y z But despite these kinks, most of the string carries only little transverse momentum!

Non-Peturb QCD, IAP Paris, Klaus WERNER, Subatech, Nantes -8 Heavy ion collisions or very high energy proton-proton scattering: the usual procedure has to be modified, since the density of strings will be so high that they cannot possibly decay independently We split each string into a sequence of string segments, corresponding to widths δα and δβ in the string parameter space x X(α+δα,β+δβ) z X( α, β) y

Non-Peturb QCD, IAP Paris, Klaus WERNER, Subatech, Nantes -9 For core part, T μν and the flavor flow at initial proper time τ = τ : T μν (x) = δp μ { } i δpν i X(α, β) X(α, β) δp g(x x i ), δp = δα + δβ i i β α N μ q (x) = i δp μ i δp i q i g(x x i ), q {u, d, s} Evolution according to the equations of ideal hydrodynamics: μ T μν =, using T μν =(ɛ + p) u μ u ν pg μν N μ k =, Nμ k = n ku μ, with k = B, S, Q referring to respectively baryon number, strangeness, and electric charge.

Non-Peturb QCD, IAP Paris, Klaus WERNER, Subatech, Nantes - Interesting observable: dihadron correlation function R(Δη,Δφ) (triggered or untriggered) First PbPb@.76 TeV then pp@7tev

Non-Peturb QCD, IAP Paris, Klaus WERNER, Subatech, Nantes - PbPb@.76TeV (from A. Timmins, ALICE, QM) From peripheral to central jets elliptical flow Ridge

Non-Peturb QCD, IAP Paris, Klaus WERNER, Subatech, Nantes - Our results (untriggered corr functions): 8-9% 6-8% 4-6%.4...8.6.4. -..4.3.. -..5.5 -.5 4 3 Δφ - - -.5 4 3.5 Δφ Δη - - -.5 4 3.5 Δφ Δη - - -.5.5 Δη -%.5.5.5 -.5 ridge 4 3 Δφ - - -.5.5 Δη

Non-Peturb QCD, IAP Paris, Klaus WERNER, Subatech, Nantes -3 translational invariance of initial energy density x y z

Non-Peturb QCD, IAP Paris, Klaus WERNER, Subatech, Nantes -4 leads to translational invariance of transverse flows later give the same collective push x y z to particles produced at different values of η s at the same azimuthal angle

Non-Peturb QCD, IAP Paris, Klaus WERNER, Subatech, Nantes -5 In pp@7tev: spectacular ridge discovery from CMS: using particles with <p t < 3GeV/c, for high multiplicity events

Non-Peturb QCD, IAP Paris, Klaus WERNER, Subatech, Nantes -6 Our calculation provides a similar ridge structure using also particles with <p t < 3GeV/c, for high multiplicity events R(Δη,Δφ).5.5 -.5 Δφ 4 3 - close in form and magnitude compared to the CMS result (5.3 times mean multipl., compared to 7 in CMS) -3 - - 3 Δη

Non-Peturb QCD, IAP Paris, Klaus WERNER, Subatech, Nantes -7 R(Δη,Δφ) Calculation without hydro => NO RIDGE.5.5 -.5 Δφ 4 3 3-3 - - - hydrodynamical evolution makes the effect! HOW? Δη

Non-Peturb QCD, IAP Paris, Klaus WERNER, Subatech, Nantes -8 Random azimuthal asymmetries of initial energy density but translationally invariant y [fm].5.5 -.5 - -.5-3 energy density [GeV/fm ] (η =., τ s =.3 fm/c) J - -.5 - -.5.5.5 x [fm] 8 6 4 8 6 4 y [fm].5.5 -.5 - -.5-3 energy density [GeV/fm ] (η =.5, τ s =.3 fm/c) J - -.5 - -.5.5.5 x [fm] 8 6 4 8 6 4 Initial energy density in the transverse plane for two different η s

Non-Peturb QCD, IAP Paris, Klaus WERNER, Subatech, Nantes -9 Elliptical initial shapes leads to asymmetric flows as well translationally invariant (in η s ) y [fm].5 rad velocity [% of c] (η =., τ s =.7 fm/c) J 7 y [fm].5 rad velocity [% of c] (η =.5, τ s =.7 fm/c) J 7 6 6.5 5.5 5 4 4 -.5 3 -.5 3 - - -.5 -.5 - - -.5 - -.5.5.5 x [fm] give the same collective push to particles produced at different values of η s at the same azimuthal angle - - -.5 - -.5.5.5 x [fm]

Non-Peturb QCD, IAP Paris, Klaus WERNER, Subatech, Nantes - Other observables

Non-Peturb QCD, IAP Paris, Klaus WERNER, Subatech, Nantes - Particle spectra: Little effect of hydro in MB dn/deta dn/dη 8 chrg ALICE INEL> 7 6 5 4 3 full model (solid) no hydro (dotted) -4-3 - - 3 4 pseudorapidity η

Non-Peturb QCD, IAP Paris, Klaus WERNER, Subatech, Nantes - But: big effect for intermediate pt (even for MB) dn/dyd p t (c /GeV ) - - -3-4 -5 chrg CMS full model (solid) no hydro (dotted) - EPOS.9 7TeV η <.4 p t (GeV/c) <= flow!!!

Non-Peturb QCD, IAP Paris, Klaus WERNER, Subatech, Nantes -3 Space-time structure strongly affected (here 9 GeV) dn/d r - dn/dη()=.9 - no casc no hydro full.5.5.5 3 radial distance r (fm)

Non-Peturb QCD, IAP Paris, Klaus WERNER, Subatech, Nantes -4 Consequences for Bose-Einstein correlations Experiments measure: Two-particle correlation functions C(P, q), with P = total momentum vector, q = relative momentum vector. In case of identical mesons (like π + π + ): BoseEinstein correlations, related to the space-time structure of particle production

Non-Peturb QCD, IAP Paris, Klaus WERNER, Subatech, Nantes -5 Under certain assumptions the two-particle correlation function C(P, q) is given as C(P, q) = d 3 r S(P, r ) Ψ(q, r ) S(P, r ) = source function = probability of emitting a pair of hadrons with total momentum P and relative distance r Ψ outgoing two-particle wave function, q, r relative momentum and distance in the pair center-of-mass system. Here: source function S obtained from our simulations parameters entirely determined from yields, spectra.. Pair wave function: we follow R. Lednicky, Physics of Particles and Nuclei 4 (9) 37

Non-Peturb QCD, IAP Paris, Klaus WERNER, Subatech, Nantes -6 Results for high multipl pp@9 GeV (here q = q,).8.7 π + π + BE correlations real / mixed.6 no hydro (dotted): R =.69.5 no casc (dashed): R =.39.4 full model (solid): R =.83.3. KT EPOS.5..9...3.4.5.6.7.8.9 q ALICE data. Radii R from exponential fit. CF(q) KT= [, 5], KT3= [4, 55], KT5= [7, ] (KT=P /)

Non-Peturb QCD, IAP Paris, Klaus WERNER, Subatech, Nantes -7 pp@7tev Consider several multiplicity classes, mult,..., mult 8, as in arxiv:.3665 (ALICE) mult : less than minimum bias => string decay (a) (a) (b) mult 8: five time minimum bias => plasma decay (b)

Non-Peturb QCD, IAP Paris, Klaus WERNER, Subatech, Nantes -8 Classical three dimensional analysis: Correlation function parametrized as C(P, q) =+ λ exp ( ) Rout qout Rside qside Rlong qlong long: beam direction out: parallel to projection of P perpendicular to the beam Fit parameters λ, R out, R side, and R long are determined for different centrality classes and for different k T, with k T = ( p T (hadron ) + p T (hadron ) ).

Non-Peturb QCD, IAP Paris, Klaus WERNER, Subatech, Nantes -9 3 mult mult 4 mult 7 mult 8 Rout (fm) Rout (fm) Rout (fm) Rout (fm) 3 Rside (fm) Rside (fm) Rside (fm) Rside (fm) 3 Rlong (fm) Rlong (fm) Rlong (fm) Rlong (fm)..4..4..4..4.7 k T (GeV/c) k T (GeV/c) k T (GeV/c) k T (GeV/c)

Non-Peturb QCD, IAP Paris, Klaus WERNER, Subatech, Nantes -3 Decreasing radii with k T : flow effect Pairs of radial flow vectors on sufaces with different radii (assuming lenths r) with constant difference, for two different radii two vectors in more distant compared to

Non-Peturb QCD, IAP Paris, Klaus WERNER, Subatech, Nantes -3 Summary Multiple scattering approach => multiple flux tubes, used as initial conditions for hydrodynamical evolution, realized in an event-by-event mode, in pp and AA explains naturally nontrivial features as ridge correlations in HI collisions explains also some nontrivial pp phenomena (ridge, BE correlations) Thank you!!

Non-Peturb QCD, IAP Paris, Klaus WERNER, Subatech, Nantes -3 Summary Multiple scattering approach => multiple flux tubes, used as initial conditions for hydrodynamical evolution, realized in an event-by-event mode, in pp and AA explains naturally nontrivial features as ridge correlations in HI collisions explains also some nontrivial pp phenomena (ridge, BE correlations) Thank you!!