Rapidity correlations in the CGC N. Armesto ECT* Workshop on High Energy QCD: from RHIC to LHC Trento, January 9th 2007 Néstor Armesto Departamento de Física de Partículas and Instituto Galego de Física de Altas Enerxías Universidade de Santiago de Compostela with Larry McLerran (BNL) and Carlos Pajares (Santiago de Compostela) Based on Nucl. Phys. A781 (2007) 201 (hep-ph/ ). 1

Contents N. Armesto Rapidity correlations in the CGC 1. Introduction (see Capella and Krzywicki '78). 2. Long-range rapidity correlations (LRC) in the CGC (see also Kovchegov, Levin, McLerran '01). 3. LRC in string models (based on Brogueira and Dias de Deus, hep-ph/ ). 4. Some numbers at RHIC and the LHC. 5. Summary. 2

1. Introduction (I): N. Armesto Rapidity correlations in the CGC 3 ● Correlations have always been expected to reflect the features of multiparticle production, including eventual phase transitions. ● Simplistic, multipurpose picture of multiparticle production: first formation of sources, then coherent decay of the sources into particles. ● Correlations in rapidity characterize, in principle, the process of formation and decay of such clusters: how many of them, which size i. e. how many particles do they produce?

1. Introduction (II): N. Armesto Rapidity correlations in the CGC 4 ● One source characterized by exponentially damped rapidity correlations: * Old multiperipheral models. * e + e - collisions in two-jet events: string models very successful. D 2 BF = - D 2 =D 2 FF = - 2 (n B )=a+bn B  FB =b=D 2 BF /D 2 : correlation strength ● In hadronic collisions, D 2 FF characterizes the short range correlations, related with the number of emitted particles per cluster, while D 2 BF, long range for a gap > 1.5-2, is related with the number of sources, provided SRC >> LRC as experimentally seen.

2. LRC in the CGC (I): N. Armesto Rapidity correlations in the CGC 5 ● The picture of an AB collision in the CGC (the glasma) corresponds to the creation at short times t~exp(-k/  s ) of a central region with longitudinal fields (strings, flux tubes) from the passage of the transverse nuclear fields one through each other (Lappi, McLerran '06). ● Neglecting the difference in Q s between projectile and target, in a transverse region of size a~1/Q s the multiplicity becomes KN

2. LRC in the CGC (II): N. Armesto Rapidity correlations in the CGC 6 ● LRC come from production from different sources in the same transverse region a~1/Q s. For gluons: O(g) O(1/g) ● In the region where the classical fields are rapidity invariant: ● Note that for quarks (baryon production):

2. LRC in the CGC (III): N. Armesto Rapidity correlations in the CGC 7 ●  ~1, and the correlated dN cor /dy is order  s with respect to the uncorrelated one. ● Both diagrams do not interfere, as the average over an odd number of sources in the same nucleus vanish. ● Adding the correlated and uncorrelated pieces at  y/(  y=0), we get

2. LRC in the CGC (IV): N. Armesto Rapidity correlations in the CGC 8 ● For large enough  y, so SRC are absent and LRC, which should be little affected by hadronic rescattering, dominate, and assuming that Q s sets the scale for  s, Q s growing with energy and N part : *  FB increases with centrality. *  FB increases with energy. *  FB decreases with  y. ● All said above applies for gluons (mesons); for baryon production, the 1/  s factor in coherent production is absent, so the dependence with energy and centrality should be milder.

3. LRC in string models (I): N. Armesto Rapidity correlations in the CGC 9 ● We assume the existence of N sources (strings – longitudinal flux tubes). The multiplicity is: single source (SRC) number of sources (LRC) ● For Poissonian sources, ● So, for forward and backward rapidity windows, with a large enough gap between them:

3. LRC in string models (II): N. Armesto Rapidity correlations in the CGC 10 Finally ● The (AGK) proportionality of the multiplicity with the number N of strings is corrected by a transverse surface geometric factor computed in 2d percolation: shadowing corrections interpolating between N coll and N part ~ 2A. ●  ~ 3 for central AuAu at at RHIC, and BDD assume

3. LRC in string models (III): N. Armesto Rapidity correlations in the CGC 11 ● Comparison (fit) to STAR preliminary, nucl-ex/ for charged: ● b increases with centrality (faster in the non-percolation case): ● b decreases with energy (provided K ~  ,  >1/2): percolation

4. Some numbers at RHIC and LHC (I): N. Armesto Rapidity correlations in the CGC 12 ● Just to illustrate the results (no errors considered, no direct work on experimental data with nevertheless are preliminary, no variations of the phenomenological input). ● Scale of  s is Q s 2 = (N part /2) 1/3 (E cm /200 AGeV) ● We use the BDD results for b=  FB as input to adjust ours for AuAu collisions at 200 AGeV, considering  =1.6 as large enough; We then go to the LHC, 5.5 ATeV, to see the difference in results between string models (BDD) and ours (AMP).

4. Some numbers at RHIC and LHC (II): N. Armesto Rapidity correlations in the CGC 13 ● Q s 2 ~  QCD 2 for N part =2 at 200 GeV. ● c ~ 5. ● The behavior with centrality may be made similar, the behavior with energy cannot (for K ~  ).

5. Summary: N. Armesto Rapidity correlations in the CGC 14 ● Correlations in rapidity provide information about the dynamics of multiparticle production in hadronic collisions: distribution and nature of the sources (strings, classical fields,...) of particles. ● Within the CGC, the qualitative behavior is well defined: The LRC strength b=  FB * Increases with increasing energy. * Increases with increasing centrality. * Decreases with increasing rapidity gap. * Should be smaller for baryons (quarks) than for mesons (gluons). ● String models show similar trends except (maybe) the increase with increasing energy. ● For quantitative comparisons, the role of hadronic FSI must be considered.