Star azimuthal correlations of forward di pions in d au collisions in the color glass condensate
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STAR azimuthal correlations of forward di-pions in d+Au collisions in the Color Glass Condensate. Cyrille Marquet. Institut de Physique Théorique, CEA/Saclay. - but single particle production probes limited information about the CGC. (only the 2-point function).

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STAR azimuthal correlations of forward di-pions in d+Au collisions in the Color Glass Condensate

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STAR azimuthal correlations of forward di-pions ind+Au collisions in theColor Glass Condensate

Cyrille Marquet

Institut de Physique Théorique, CEA/Saclay

- but single particle production probes limited information about the CGC

(only the 2-point function)

to strengthen the evidence, we need to studymore complex observables to be measured with the new d+Au run

- I will focus on di-hadron azimuthal correlations

a measurement sensitive to possible modificationsof the back-to-back emission pattern in a hard process

d Au → h1 h2 X


- after the first d+Au run at RHIC, there was a lot of new results on

single inclusive particle production at forward rapidities

d Au → h X

the spectrum and

the modification factor were studied

y increases

the suppressed production (RdA < 1) was predicted in the

Color Glass Condensate picture of the high-energy nucleus


  • Introduction to parton saturation

    - the hadronic/nuclear wave function at small-x

    - non-linear parton evolution in QCD

    - the saturation scale and the unintegrated gluon distribution

  • Di-hadron correlation measurements

    - at high-pT/central rapidities in p+p collisions : high-x physics

    - at low-pT/forward rapidities in p+p collisions : small-x physics

    - at low-pT/forward rapidities in d+Au collisions : saturation physics

  • Comparing d+Au data with CGC predictions

    - parameters fixed with single particle spectra (Javier’s talk, last meeting)

    - forward di-pion correlations : monojets are produced in central d+Au

the saturation regime: for with

gluon density per unit area

it grows with decreasing x

recombination cross-section

recombinations important when

this regime is non-linear

yet weakly coupled

Parton saturation

x : parton longitudinal momentum fraction

kT: parton transverse momentum

the distribution of partons

as a function of x and kT :

QCD linear evolutions:

DGLAP evolution to larger kT (and a more dilute hadron)

BFKL evolution to smaller x (and denser hadron)

dilute/dense separation characterized by the saturation scale Qs(x)

QCD non-linear evolution:meaning

Di-hadron correlation measurements

Di-hadron final-state kinematics

final state :

  • scanning the wave-function

xp ~ 1, xA << 1

xp ~ xA < 1

forward rapidities probe small x

high pT’s probe large x

  • azimuthal correlations

- are only a small part of the information contained in

- but are very sensitive to possible non-linear effects (modification of the back-to-back

emission pattern in a hard process)


Dijets in standard (linear) pQCD

in pQCD calculations based on collinear factorization, dijets are back-to-back

this is supported by Tevatron data

transverse view

peak narrower with higher pT


(near side)


(away side)


Azimuthal correlations in p+p

typical measurement in p+p collisions at RHIC:



at RHIC this is done

with low-pT pions

this is probing small-x, but not quite the saturation regime

rather one is sensitive to the growth of the gluon distribution


(near side)


(away side)



Azimuthal correlations in d+Au

the evidence for parton saturation:


d+Au central

transverse view

Comparison with CGC predictions

the large-x hadron should be described by

standard leading-twist parton distributions

the small-x hadron/nucleus should be

described by a Color Glass Condensate

the cross-section:

single gluon production

probes only the (unintegrated)

gluon distribution

Forward particle production

forward rapidities probe small values of x

kT , y

transverse momentum kT, rapidity y > 0

values of x probed in the process:

NLO-BK description of d+Au data

Albacete and C.M. (2010)

the shapes and normalizations are well

reproduced, except the 0 normalization

the speed of the x evolution and of

the pT decrease are predicted

this fixes the two parameters of the theory:

- the value of x at which one starts to trust (and therefore use) the CGC description

- and the saturation scale at that value of x

in very forward particle production in p+p collisions at RHIC (where NLO DGLAP fails), using this formalism to describe the (small-x) proton also works

Betemps, Goncalves, de Santana Amaral (2009)

Forward di-hadron production

a good test for the theory

C. M. (2007)

the saturation regime is better probed

compared to single particle production

is sensitive to multi-parton distributions, and not only to the gluon distribution

the CGC cannot be described

by a single gluon distribution

no kT factorization

involves 2-, 4- and 6- point functions

Fourier transform k┴ andq┴

into transverse coordinates

collinear factorization of quark density in deuteron

pQCD q→ qg


interaction with hadron 2 / CGC

n-point functions that resums the powers ofgS A and the powers ofαS ln(1/xA)

computed with JIMWLK evolution at NLO (in the large-Nc limit),

and MV initial conditionsno parameters

The two-particle spectrum

b: quark in the amplitude

x: gluon in the amplitude

b’: quark in the conj. amplitude

x’: gluon in the conj. amplitude

to calculate the near-side peak, one

needs di-pion fragmentation functions

standard (DGLAP-like) QCD calculations cannot reproduce this

Monojets in central d+Au

  • in central collisions where Qs is the biggest

an offset is needed toaccount for the background

there is a very good agreement of the

saturation predictions with STAR data

  • the focus is on the away-side peak

where non-linearities have the biggest effect

suppressed away-side peak

The centrality dependence

it can be estimated by modifying the initial condition for NLO-BK evolution

for a given impact parameter,

the initial saturation scale used is

peripheral collisions are like p+p collisions

the away-side peak is reappearing

when decreasing the centrality

no data yet,

but hopefully soon

The pT dependence

with higher pT, one goes away from the saturation regime

the away-side peak is restored at higher pT

so far, only p+p data have been shown


  • New d+Au RHIC data show evidence for parton saturation

  • Single particle production at forward rapidities

    - the suppressed production at forward rapidities was predicted

    - there is a good agreement with NLO-BK calculations

  • Two-particle correlations at forward rapidities

    - probe the theory deeper than single particle measurements

    - mono-jets were predicted and are now seen in central d+Au collisions

    - first theory(CGC)/data comparison successful, more coming

Back-up slides

  • modeling the unintegrated gluon distribution

the numerical solution of the BK equation is not useful for phenomenology(because this is a leading-order calculation)


instead, saturation models are used for (with a few parameters adjusted to reproduce the data)

BK evolution at NLO has been calculated

one should obtain from the evolution equation

Balitsky-Chirilli (2008)


The non-linear QCD evolution

  • the unintegrated gluon distribution

Balitsky-Kovchegov x evolution

  • BK equation in coordinate space

this is a leading-order equation in which the coupling doesn’t run

  • the begining of saturation phenomenology at NLO

first numerical solution

Albacete and Kovchegov (2007)

first phenomenological implementation

Albacete, Armesto, Milhano and Salgado (2009)

to successfully describe the proton structure function F2 at small x

BK evolution at NLO

  • running coupling (RC) corrections to the BK equation

taken into account by the substitution





RC corrections represent most of the NLO contribution

need more than the 2-point function: no kT factorization

same conclusions in sea quark production

and two-gluon production

Blaizot, Gélis and Venugopalan (2004)

Jalilian-Marian and Kovchegov (2004)

using Fierz identities that relate WA and WF, we recover the z→ 0 (soft gluon) limit

Baier, Kovner, Nardi and Wiedemann (2005)

we will now include the xA evolution

2- 4- and 6-point functions

the scattering off the CGC is expressed through the following correlators of Wilson lines:

if the gluon is emitted before the interaction, four partons scatter off the CGC

if the gluon is emitted after the interaction, only the quarks interact with the CGC

interference terms, the gluon interacts in the amplitude only (or c.c. amplitude only)

  • applying Wick’s theorem

Fujii, Gelis and Venugopalan (2006)

when expandingin powers of α and averaging,

all the field correlators can be expressed in terms of

is the two-dimensional massless propagator

the difficulty is to deal with the color structure

Performing the CGC average

  • a Gaussian distribution of color sources

characterizes the density of color charges along the projectile’s path

with this model for the CGC wavefunction squared, it is possible to compute n-point functions

and obeys the BK equation:

in the large-Nc limit

we will use the MV initial condition:

McLerran and Venugopalan (1994)


the initial saturation scale

MV model and BK evolution

With this model for the CGC wavefunction squared, it is possible to compute the

n-point functions:

Blaizot, Gélis and Venugopalan (2004)

is related to in the following way

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