CroninEffectandHigh-pTSuppressioninpACollisions

Click to edit Master title style,Click to edit Master text styles,Second level,Third level,Fourth level,Fifth level,*,Cronin Effect and High-p,T,Suppression in pA Collisions,Yuri Kovchegov,University of Washington,Based on work done in collaboration with,Dmitri Kharzeev and Kirill Tuchin, hep-ph/0307037,1,Gluon Production in pA: McLerran-Venugopalan model,Classical gluon production: we,need to resum only the,multiple rescatterings of the,gluon on nucleons. Heres one,of the graphs considered.,Yu. K., A.H. Mueller,hep-ph/9802440,Resulting inclusive gluon production cross section is given by,With the gluon-gluon dipole-nucleus,forward scattering amplitude,2,McLerran-Venugopalan model:Cronin Effect,Defining,we can plot it for the quasi-classical,cross section calculated before.,One can actually do the integration,analytically obtaining,(Y.K., A. M. 98),Classical gluon production leads to Cronin effect!,(see also B. Kopeliovich et al, 02, R. Baier et al, 03),3,Proof of Cronin Effect,Plotting a curve is not a proof of,Cronin effect: one has to trust the,plotting routine.,To prove that Cronin actually,does take place one has to study the,behavior of,R,pA,at large,k,T,(cf.,Dumitru,Gelis,Jalilian,-Marian,quark production, 02-03):,R,pA,approaches 1 from above at high p,T, there is an enhancement!,Note the sign!,4,Cronin Effect,The,height,and,position,of the Cronin maximum are,increasing,functions of,centrality,!,The position of the Cronin,maximum is given by,k,T, Q,S, A,1/6,as,Q,S,2, A,1/3,.,Using the formula above we see,that the height of the Cronin,peak is,R,pA,(k,T,=Q,S,) ln Q,S, ln A,.,5,Including Quantum Evolution,To understand the energy,dependence of particle,production in pA one needs to,include quantum evolution,resumming graphs like this one.,This resums powers of,a,ln 1/x =,a,Y.,This has been done in Yu. K.,K. Tuchin, hep-ph/0111362.,The rules accomplishing the inclusion of quantum corrections are,where the dipole-nucleus amplitude N is to be found from,(Yu. K., Balitsky),Protons,LO wave function,Protons BFKL,wave function,and,6,Including Quantum Evolution,In the traditional fan diagram language the calculated gluon,production cross section is pictured above for DIS.,Produced Gluon,Can be proton or deuteron.,7,Including Quantum Evolution,Amazingly enough, gluon production cross section,reduces to k,T,factorization expression:,with the proton and nucleus “unintegrated,distributions” defined by,with N,G,p,A,the amplitude of a GG dipole on a p or A.,8,Phase Diagram of High Energy QCD,Moderate Energy,or Rapidity,Cronin effect and low-p,T,suppression,Q,S,High Energy or,Rapidity,Q,S,k,geom,= Q,S,2,/,L, p,T,2,I,II,III,9,Region I: Double Logarithmic Approximation,At very high momenta,p,T, k,geom, the gluon production is given by the,double logarithmic approximation, resumming powers of,Resulting produced particle multiplicity scales as,with,where y=ln(1/x) is rapidity and Q,S0, A,1/6,is the saturation scale of,McLerran-Venugopalan model. For pp collisions Q,S0,is replaced by,L,leading to,as Q,S0,L.,R,pA, 1 in Region I, There is suppression in DLA region!,10,The resulting gluon production cross section scales as,Region II: Anomalous Dimension,Kharzeev, Levin, McLerran,hep-ph/0210332,At somewhat lower but still large momenta,Q,S, k,T, k,geom, the BFKL,evolution introduces anomalous dimension for gluon distributions:,such that,For large enough nucleus,R,pA, Q,S, Q,S0,. Shouldnt R,pA, k,T,/ Q,S0,be,greater than 1 ?,with BFKL,g,=1/2 (DLA,g,=1),11,Region II: Anomalous Dimension,R,pA,is also a,decreasing,function of energy,leveling off to a constant,R,pA, A,-1/6,at very high energy.,R,pA,is a,decreasing,function of both,energy,and,centrality,at high energy / rapidity.,(D. Kharzeev, Yu. K., K. Tuchin, hep-ph/0307037),A more detailed analysis,gives the following ratio in,the extended geometric,scaling region our region II:,12,Region III: What Happens to Cronin Peak?,The position of Cronin peak is given by saturation scale Q,S, such that the,height of the peak is given by,R,pA,(,k,T,= Q,S,(y), y).,It appears that to find out what happens to Cronin maximum we need to,know the gluon distribution function of the nucleus at the saturation scale ,f,A,(,k,T,= Q,S, y).,For that we would have to solve nonlinear BK evolution,equation a very difficult task.,Instead we can use the scaling property of the solution of BK equation,which leads to,Levin, Tuchin 99,Iancu, Itakura, McLerran, 02,We do not need to know,f,A,to determine how Cronin peak scales with,energy and centrality! (The constant carries no dynamical information.),13,Our Prediction,Toy Model!,Our analysis shows that as,energy/rapidity increases,the,height of the Cronin peak,decreases,. Cronin maximum,gets progressively lower and,eventually disappears.,Corresponding R,pA,levels,off at roughly at,D. Kharzeev, Yu. K., K. Tuchin, hep-ph/0307037; (see also numerical,simulations by Albacete, Armesto, Kovner, Salgado, Wiedemann,hep-ph/0307179 and Baier, Kovner, Wiedemann hep-ph/0305265 v2.),At,high energy / rapidity,R,pA,at the Cronin peak becomes a,decreasing,function of both,energy,and,centrality,.,R,pA,k / Q,S,energy / rapidity,increases,14,Overall Picture,At moderately high energy/rapidity one has to use McLerran-Venugopalan model to calculate gluon production. In McLerran-Venugopalan model one gets Cronin effect only. The height of the Cronin peak is an,increasing,function of,centrality.,As energy/rapidity increases quantum effects due to BK evolution become important introducing high-,p,T,suppression. Cronin peak gradually disappears.,R,pA,becomes a,decreasing,function of,energy and centrality,.,15,Other Predictions,Color Glass Condensate /,Saturation physics,predictions,are in,sharp contrast,with other,models.,The prediction presented here,uses a Glauber-like model for,dipole amplitude with energy,dependence in the exponent.,figure from I. Vitev, nucl-th/0302002,see also a review by,M. Gyulassy, I. Vitev, X.-N. Wang, B.-W. Zhang, nucl-th/0302077,16,Forward Rapidity Data,BRAHMS collaboration preliminary data,presented by R. Debbe at DNP 03,Suppression!,17,It is very likely (pending final data) that,Color,Glass,Condensate,has just been,discovered,by dAu experiments at RHIC !,18,