Rapidity correlations in the cgc
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N. Armesto. Rapidity correlations in the CGC. ECT* Workshop on High Energy QCD: from RHIC to LHC Trento, January 9th 2007. N éstor Armesto Departamento de Física de Partículas and Instituto Galego de Física de Altas Enerxías Universidade de Santiago de Compostela with

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Rapidity correlations in the CGC

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Rapidity correlations in the cgc

N. Armesto

Rapidity correlations in the CGC

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).

1


Contents

N. Armesto

Contents

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.

2

Rapidity correlations in the CGC


1 introduction i

N. Armesto

1. Introduction (I):

  • 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?

3

Rapidity correlations in the CGC


1 introduction ii

N. Armesto

1. Introduction (II):

  • 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.

4

Rapidity correlations in the CGC


2 lrc in the cgc i

N. Armesto

2. LRC in the CGC (I):

  • 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

5

Rapidity correlations in the CGC


2 lrc in the cgc ii

N. Armesto

2. LRC in the CGC (II):

  • 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):

6

Rapidity correlations in the CGC


2 lrc in the cgc iii

N. Armesto

2. LRC in the CGC (III):

  • 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

7

Rapidity correlations in the CGC


2 lrc in the cgc iv

N. Armesto

2. LRC in the CGC (IV):

  • 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.

8

Rapidity correlations in the CGC


3 lrc in string models i

N. Armesto

3. LRC in string models (I):

  • 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:

9

Rapidity correlations in the CGC


3 lrc in string models ii

N. Armesto

3. LRC in string models (II):

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

10

Rapidity correlations in the CGC


3 lrc in string models iii

N. Armesto

3. LRC in string models (III):

  • 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

11

Rapidity correlations in the CGC


4 some numbers at rhic and lhc i

N. Armesto

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

  • 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).

12

Rapidity correlations in the CGC


4 some numbers at rhic and lhc ii

N. Armesto

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

  • 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).

13

Rapidity correlations in the CGC


5 summary

N. Armesto

5. Summary:

  • 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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Rapidity correlations in the CGC


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