Rapidity correlations in the CGC

N. Armesto

ECT* Workshop on High Energy QCD: from RHIC to LHCTrento, January 9th 2007

Néstor Armesto

Departamento de Física de Partículasand

Instituto Galego de Física de Altas EnerxíasUniversidade de Santiago de Compostela

with

Larry McLerran (BNL) and Carlos Pajares (Santiago de Compostela)

Based on Nucl. Phys. A781 (2007) 201 (hep-ph/0607345).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 Diasde Deus, hep-ph/0611329).

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 ofmultiparticle production, including eventual phase transitions.

● Simplistic, multipurpose picture of multiparticle production: firstformation of sources, then coherent decay of the sources into particles.

● Correlations in rapidity characterize, in principle, the process offormation and decay of such clusters: how many of them, which sizei. e. how many particles do they produce?

1. Introduction (II):

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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.

D2BF

=<nBn

F> - <n

B><n

F>

D2=D2FF

=<nF

2> - <nF>2

<nF>(n

B)=a+bn

B

FB

=b=D2BF

/D2:correlation strength

● In hadronic collisions, D2FF

characterizes the short range correlations, related with the number of emitted particles per cluster, while D2

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):

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Rapidity correlations in the CGC 5

● The picture of an AB collision in the CGC (the glasma) corresponds tothe creation at short times t~exp(-k/

s) of a central region with

longitudinal fields (strings, flux tubes) from the passage of the transversenuclear fields one through each other (Lappi, McLerran '06) .

● Neglecting the difference in Qs between projectile and target, in a

transverse region of size a~1/Qs the multiplicity becomes

KN

2. LRC in the CGC (II):

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Rapidity correlations in the CGC 6

● LRC come from production from different sources in the same transverseregion 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):

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Rapidity correlations in the CGC 7

● ~1, and the correlated dNcor

/dy is order

s with respect to the uncorrelated one.

● Both diagrams do not interfere, as theaverage over an odd number of sources inthe same nucleus vanish.

● Adding the correlated and uncorrelated pieces at y/(y=0), we get

2. LRC in the CGC (IV):

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Rapidity correlations in the CGC 8

● For large enough y, so SRC are absent and LRC, which should be littleaffected 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, the1/

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 fluxtubes). The multiplicity is:

single source (SRC)

number of sources (LRC)

● For Poissonian sources,

● So, for forward and backward rapidity windows, with a large enoughgap between them:

3. LRC in string models (II):

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Rapidity correlations in the CGC 10

Finally

● The (AGK) proportionality of the multiplicity with the number N of stringsis corrected by a transverse surface geometric factor computed in 2dpercolation: shadowing corrections interpolating between N

coll and N

part ~ 2A.

● ~ 3 for central AuAu atat RHIC, and BDD assume

3. LRC in string models (III):

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Rapidity correlations in the CGC 11

● Comparison (fit) to STAR preliminary, nucl-ex/0606018 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):

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Rapidity correlations in the CGC 12

● Just to illustrate the results (no errors considered, no direct work onexperimental data with nevertheless are preliminary, no variations ofthe phenomenological input).

● Scale of s is Q

s2 = (N

part/2)1/3 (E

cm/200 AGeV)0.288.

● We use the BDD results for b=FB

as input to adjust ours for AuAucollisions at 200 AGeV, considering =1.6 as large enough;

We then go to the LHC, 5.5 ATeV, to see the difference in results betweenstring models (BDD) and ours (AMP).

4. Some numbers at RHIC and LHC (II):

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Rapidity correlations in the CGC 13

● Qs2 ~

QCD2 for Npart=2

at 200 GeV.

● c ~ 5.

● The behavior withcentrality may be madesimilar, the behaviorwith energy cannot(for K ~ ).

5. Summary:N. Armesto

Rapidity correlations in the CGC 14

● Correlations in rapidity provide information about the dynamics ofmultiparticle production in hadronic collisions: distribution and natureof the sources (strings, classical fields,...) of particles.

● Within the CGC, the qualitative behavior is well defined: The LRCstrength 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 withincreasing energy.

● For quantitative comparisons, the role of hadronic FSI must be considered.