High energy QCD: when CGC meets experiment

Transcription

1 High energy QCD: when CGC meets experiment Javier L. Albacete IPhT CEA/Saclay Excited QCD Les Houches, February

2 OUTLINE Brief Intro [cf Larry s Talk] Running coupling corrections to the BK equation. Fits e+p data (in coll with N. Armesto, JG Milhano, P. Quiroga and C. Salgado) RHIC: Single and double inclusive yields at forward rapidities (in coll with C. Marquet) rcbk Monte Carlo: Pb+Pb multiplicities at the LHC (in coll with A. Dumitru) See also T. Ullrich s talk tomorrow

3 At high energies, or small Bjorken-x, hadron s gluon densities are large k + n = x n p + k + = x p + xg /0 xu k + 1 = x 1 p + p + xs xd Probability of n-soft gluon emission P (α s ln 1/x) n proton ugd from HERA x Multiple small-x gluon emissions are resummed by the BFKL equation φ(x, k t ) ln(x 0 /x) K φ(x, k t)

4 Non-linear QCD evolution: At small-x gluon both radiative and recombination processes Y=ln (1/x) High density CGC: JIMWLK BK Q(x) S BK-JIMWLK p + φ(x, k t ) ln(x 0 /x) K φ(x, k t) φ(x, k t ) NON PERTURBATIVE BFKL Low density Non-linear recombination corrections are demanded by UNITARITY lnλ QCD ln Q Saturation scale: transverse momentum scale which marks the onset of non-linear corrections K φ(x, Q s ) φ(x, Q s ) Nuclear enhancement: Q sa A 1/3 Q sp

5 CGC evolution: The BK equation Balitsky 96, Kovchegov 99 ln 1 x ln s Y ( large-nc limit of full JIMWLK evolution) γ q x S(x, y; Y ) = 1 N c tr{u x U y} Y = 1 N (x, y; Y ) q P y unintegrated WW gluon distribution: d r ϕ(x, k t )= eik r π r N (r, x) Increase the collision energy and resum small-x gluon radiation N (r, x) ln(x 0 /x) = d r 1 K(r, r 1,r )[N(r 1,x)+N(r,x) N (r, x) N (r 1,x)N(r,x)] perturbative kernel non-linear term The kernel: probability of small-x gluon emission at leading-logarithmic accuracy in α s ln(1/x) : K(x, y, z) = α s N c (x y) z π (x z) (z y) = + y x 5 + all possible permutations

6 NLO corrections to BK-JIMWLK equations have been calculated recently (Balitsky-Chirilli; Kovchegov-Weigert, Gardi et al). Phenomenological tool: The BK equation including only running coupling corrections in Balitsky s scheme grasps most of the NLO corrections (JLA-Kovchegov) BK eqn: N (r, x) ln(x 0 /x) = Running coupling kernel: d r 1 K(r, r 1,r )[N (r 1,x)+N (r,x) N (r, x) N (r 1,x)N (r,x)] K run (r, r 1, r )= N c α s (r ) π [ r r 1 r + 1 r 1 ( αs (r1) ) α s (r ) r ( αs (r) )] α s (r1 ) 1 LO: αs ln(1/x) small-x gluon emission NLO : αs Nf Quark loops resummed to all orders Gluon contribution: N f 6πβ

7 Running coupling corrections are large, rendering evolution compatible with experimental data. λ(y ) = d ln Q s(y ) dy λ LO 4.8 α s values compatible with DIS and HIC data Free parameters in the (x,kt)-dependence of unintegrated gluon distributions corresponds to freedom in the choice of initial conditions: MV + anomalous dimension [ ( r Q γ N (r, x = x 0 )=1 exp s0) 4 ln ( ) ] 1 r Λ + e 7

8 AAMQS Fits to e+p data: JLA, N. Armesto, J.G. Milhano, P Quiroga and C. Salgado γ q q x y σ γ h T,L (x,q )= flavours d r 1 0 dz T,L (z, r, Q ) σ dip (r, x) Ψ f,γ q q QED piece Strong interactions are here P dipole cross section: σ dip (r, x) = d b N (b, r, x) σ 0 N (b, r, x) Experimental data: ZEUS & H1 (HERA) combined data on reduced cross sections + older NMC (CERN-SPS) and E665 (Fermilab) coll. at x< x0= - and Q < 50 GeV Regularization of the coupling: α s (r ) = 1 π ( (11 N c N f ) ln ) 4 C r Λ QCD for r < r fr, with α s(rfr) α fr = 0.7 Charm contribution: Including charm in the sum over flavors we are account for charm contribution (~% of total e+p cross section) and also describe available data on Fc (extra parameters). Variable flavour number scheme for the running of the coupling

9 Reduced cross section Charm structure function c F Q =1.5 GeV Q =3.5 GeV c F Q =4 GeV Q =6.5 GeV c F Q =7 GeV Q =8.5 GeV - c F Q =11 GeV Q =1 GeV - c F Q =18 GeV Q =0 GeV - fit GBW χ c d.o.f Q s0 σ 0 γ Q s0c σ 0c γ c C m l a α fr = fixed F Q =5 GeV a α fr =0.7 (Λ mτ ) fixed b α fr = E- c α fr = fixed d χ αfit fr =1 1.1 d.o.f 0.95 Q s σ γ 0.74 Q s0c 0.6 σ 0c 0.94 γ c 3.75 C 1.351E- m l MV GBW ea α fr = fixed fa α fr =0.7 (Λ mτ ) E- fixed gb α fr =0.7 = E- fixed hc α fr = E- fixed d α fr = E- Table : Parameters from fits including charm and beauty contributions to data with x MV and and Q e α 50 GeV for different initial conditions and fixed values of the coupling in the infrared fr = fixed α fr =0.7 and. Light quark masses are fixed to m l =4 GeV in some fits and left as a free f α fr = E- -4 Q =45 GeV x - -

10 d+au and p+p collisions at RHIC RHIC Kinematics: single particle production: Small-x ~ forward production (k, y) x 1() m t s exp(± y h ) double inclusive production: Small-x ~ two particles in the forward region! (k1, y1), (k, y) x p = k 1 e y 1 + k e y s x A = k 1 e y 1 + k e y s At RHIC energies, forward measurements needed to isolate small-x (<0.01) effects

11 Forward hadron production in the CGC (Dumitru, Jalilian-Marian) large-x parton from proj. (pdf) small-x glue from target (CGC) dn h dy h d p t = K (π) q 1 x F Unintegrated gluon from running coupling BK MV Initial conditions: JLA & C. Marquet dz [ z x 1 f q / p (x 1,p t ) ÑF + x 1 f g / p (x 1,p t ) ÑA Ñ F (A) (x, k) = ( x, p t z ( x, p t z N (r, x = x 0 ) = 1 exp ) D h/q (z, p t ) ) ] D h/g (z, p t ) fragmentation d r e ik r [ 1 N F (A) (r, Y =ln(x 0 /x)) ] [ r Q 0 4 ln Two free parameters: (x0, Q0) ( )] 1 r Λ + e We use CTEQ6 pdf s and de Florian-Sassot ff s Alternative approaches: Modelization of quantum corrections (Dumitru-JalilianMarian-Hayashigaki; De Boer-Utermann-Wessels; Goncalves et al; Kharzeev-Kovchegov-Tuchin) 11

12 Comparison to RHIC forward data [ JLA, C. Marquet ] - Very good description of forward yields in proton+proton and d+au collisions - K=1 for h -. K= (0.3) for neutral pions in p+p (d+au)?? - Energy loss related to high-xf effects not taken into account ) - (GeV T p N/d!/d d proton-proton BRAHMS - h (x00);!=.; K=1 - h (x50);!=3.; K=1 STAR " 0 (x0);!=3.3; K= 0 " (x);!=3.8; K= 0 " ;!=4; K= ) - (GeV p N/d!/d d T d-au BRAHMS - h (x0);!=.; K=1 - h (x4);!=3.; K=1 STAR 0 " ;!=4; K= p (GeV) T p (GeV) T x Q s0 =0. GeV 0.01 x x Q s0 =GeV Q s0 =GeV Q s0 gluon =0.9GeV Q s0, gluon =1.15 GeV 1

13 -...by simply taking the ratio of d+au and p+p spectra we get a good description of the nuclear modification factor (not a trivial statement!!) RHIC d+au LHC p+pb R d+au 1.8 h! =.; BRAHMS h 0 "!=3.; BRAHMS <!> =4; STAR NLO-CGC JLA & C. Marquet p (GeV/c) T - We predict a similar suppression in p+pb collisions at the LHC already at central rapidities 13

14 Double Inclusive forward hadron production in the CGC x p = k 1 e y 1 + k e y s x A = k 1 e y 1 + k e y s (k1, y1), (k, y) Cyrille Marquet 07: hard quark initiating scattering Fourier transfrom coordinate space to momentum q-> qg splitting (pqcd) { Scattering of the -parton system with the CGC target Involves more than 3 and 4 point functions. Calculated in the large Nc limit 14

15 Monojets in d+au collisions at RHIC at forward rapidity Coincidence probability measured by STAR Coll. at forward rapidities: trigger φ CP( φ) = 1 dn pair N trig d φ trigger Dependence on the saturation scale of the target (centrality) CP("!) [JLA C. Marquet ] 0.0 p > GeV/c STAR PRELIMINARY T,L p+p ( ) 1 GeV/c < p <p T,S T,L d+au central ( ) Increasing Qs d+au p+p "! Effect of enhanced pedestal due to double parton interactions not taken into account 15

16 Multiplicities at RHIC and the LHC - Most of particles produced in the collision originate from small-x gluons in the saturation domain - Other sources (genuinely soft processes, contribution from valence quarks etc) neglected - Initial gluon production is calculated via kt-factorization and then mapped to final hadron spectra assuming local parton-hadron duality KLN model ϕ A (x, p t,b) dσ A+B g dy d p t d R = κ 1 C F p t pt d k t 4 h x 1() =(p t / s NN ) exp(±y) d b α s (Q) ϕ( p t + k t,x 1 ; b) ϕ( p t k t,x ; R b), unintegrated gluon distributions ϕ B (x, p t,b) Observed hadrons Hadron phase Scaling toy model: N_part scaling: dn AA dη Q sa( s, b) s λ N part η=0 QGP

17 Nuclear geometry in rcbk approaches JLA 007 JLA & Dumitru 0 Homogeneous disk nucleus characterized by a single initial saturation scale, Qs ~ 1 GeV, adjusted to reproduce RHIC most central data Q sa Monte Carlo treatment of nuclear geometry x y Q sa(r) r i R This approach underestimates data 17

18 y x r i rcbk Monte Carlo (JLA & Dumitru 0) R 1. Generate configurations for the positions of nucleons in the transverse plane (ri, i=1...a). Wood-Saxons thickness function TA(R). Count the number of nucleons at every point in the transverse grid, R. N(R) = A Θ i=1 ( ) σ0 π R r i independent σ 0 4 mb 3. Assign a local initial (x=x0=0.01) saturation scale at every point in the transverse grid, R: Q s0 (R) =N(R) Q s0, nucl Q s0, nucl =0. GeV, ven nucleus which o ϕ(x 0 =0.01,k t, R) ϕ(x, k t, R) rcbk equation

19 y x r i R rcbk Monte Carlo 1. Generate configurations for the positions of nucleons in the transverse plane (ri, i=1...a). Wood-Saxons thickness function TA(R). Count the number of nucleons at every point in the transverse grid, R. N(R) = A Θ i=1 ( ) σ0 π R r i independent σ 0 4 mb 3. Assign a local initial (x=x0=0.01) saturation scale at every point in the transverse grid, R: Q s0 (R) =N(R) Q s0, nucl Q s0, nucl =0. GeV, ven nucleus which o ϕ(x 0 =0.01,k t, R) rcbk equation ϕ(x, k t, R) 4. Gluon production is calculated at each transverse point according to kt-factorization r i b R dσ A+B g dy d p t d R = κ 1 C F dn ch dη = p t pt d k t 4 ± cosh η dn ch cosh η + m /P dy d b α s (Q) ϕ( p t + k t,x 1 ; b) ϕ( p t k t,x ; R b), m = 350 MeV and P = 400 MeV

20 rcbk Monte Carlo dn ch /d! / N part MV initial conditions: Good description of Npart dependence of RHIC Au+Au and Cu+Cu and LHC Pb+Pb multiplicities: RHIC Au+Au, 00 GeV Cu+Cu, 00 GeV rcbk Au rcbk Cu KLN Au KLN Cu N part ( ) - Systematics: Changing the model parameters (average hadron mass, pt-cutoff...) yield an equally good description of RHIC and LHC data by just adjusting the normalization (i.e the gluon to hadron ratio) κ 4.5 7

21 dn ch /d!d p T (1/GeV ) Constraining the initial conditions: p+p yields at the LHC Steeper initial conditions than the MV model are needed to get a good description of p+p yields MV CMS NSD! =, 7 TeV CMS NSD! <.4, 7 TeV rcbk-disc rcbk-g0 rcbk-g p T (GeV) dn ch /d!d p T (1/GeV ) MV + gamma=1.119 CMS NSD! =, 7 TeV CMS NSD! <.4, 7 TeV MV + rcbk p T (GeV) Steeper initial conditions also provide a good description of RHIC and LHC multiplicity data: /N part dn ch /d! LHC Pb+Pb.76 TeV RHIC Au+Au 00 GeV N part

22 Conclusions Running coupling corrections bring the CGC to a new period of quantitative and predictive phenomenology The CGC at its present degree of accuracy consistently describes data in the small-x region for a variety of colliding systems (e+p, p+p d+au) However: - Alternative physics scenarios have been proposed for those different observables - HERA and RHIC data probe a relatively small range of energy evolution. - LHC data should offer much more constraints to model - A first successful test: description of multiplicities Still, many things remain to be done to refine the CGC as a precise phenomenological tool... Thanks!!!

23 Back up slides