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Rapidity correlations in the CGC

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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/0607345).

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N. Armesto

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/0611329).

4. Some numbers at RHIC and the LHC.

5. Summary.

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- 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?

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- One source characterized by exponentially damped rapidity correlations:
* Old multiperipheral models.

* e+e- collisions in two-jet events: string models very successful.

D2BF=<nBnF> - <nB><nF>

D2=D2FF=<nF2> - <nF>2

<nF>(nB)=a+bnB

sFB=b=D2BF/D2:

correlation strength

- In hadronic collisions, D2FF characterizes the short range correlations,
related with the number of emitted particles per cluster, while D2BF, long

range for a gap > 1.5-2, is related with the number of sources,

provided SRC >> LRC as experimentally seen.

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Rapidity correlations in the CGC

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- The picture of an AB collision in the CGC (the glasma) corresponds to
the creation at short times t~exp(-k/as) 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 Qs between projectile and target, in a
transverse region of size a~1/Qs the multiplicity becomes

KN

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- LRC come from production from different sources in the same transverse
region a~1/Qs. For gluons:

O(g)

- In the region where the classical fields are
rapidity invariant:

O(1/g)

- Note that for quarks (baryon production):

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- k~1, and the correlated dNcor/dy is order
as 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 Dy/(Dy=0), we get

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- For large enough Dy, so SRC are absent and LRC, which should be little
affected by hadronic rescattering, dominate, and assuming that Qs sets the

scale for as, Qs growing with energy and Npart:

* sFB increases with centrality.

* sFB increases with energy.

* sFB decreases with Dy.

- All said above applies for gluons (mesons); for baryon production, the
1/as factor in coherent production is absent, so the dependence with energy

and centrality should be milder.

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Rapidity correlations in the CGC

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- 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:

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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 Ncoll and Npart ~ 2A.

- h ~ 3 for central AuAu at
at RHIC, and BDD assume

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- 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 ~ hg, g>1/2):

percolation

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- Just to illustrate the results (no errors considered, no direct work on
experimental data with nevertheless are preliminary, no variations of

the phenomenological input).

- Scaleof as is Qs2 = (Npart/2)1/3 (Ecm/200 AGeV)0.288.
- We use the BDD results for b=sFB as input to adjust ours for AuAu
collisions at 200 AGeV, considering Dh=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).

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- Qs2 ~ LQCD2 for Npart=2
at 200 GeV.

- c ~ 5.
- The behavior with
centrality may be made

similar, the behavior

with energy cannot

(for K ~ h).

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- 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=sFB

* 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.

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