STAR azimuthal correlations of forward di-pions ind+Au collisions in the

Color Glass Condensate

Cyrille Marquet

Institut de Physique Théorique, CEA/Saclay

the spectrum and

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

single inclusive particle production at forward rapidities

kdyddN

kdyddN

NR

hXpphXdA

colldA 22

1

the suppressed production (RdA < 1) was predicted in the Color Glass Condensate picture of the high-energy nucleus

d Au → h X

y increases

the modification factor were studied

- but single particle production probes limited information about the CGC(only the 2-point function)to strengthen the evidence, we need to study

more 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

Outline

• 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

Parton saturationx : parton longitudinal momentum fraction

kT : parton transverse momentum

the distribution of partons

as a function of x and kT :

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

QCD linear evolutions:

DGLAP evolution to larger kT (and a more dilute hadron)BFKL evolution to smaller x (and denser hadron)

QCD non-linear evolution: meaning

recombination cross-section

gluon density per unit areait grows with decreasing x

recombinations important when

the saturation regime: for with

this regime is non-linearyet weakly coupled

Di-hadron correlation measurements

Di-hadron final-state kinematics11 , yk 22 , yk

s

ekekx

yy

p

21 21

s

ekekx

yy

A

21 21

final state :

forward rapidities probe small x

xp ~ 1, xA << 1

• azimuthal correlations

• scanning the wave-function

high pT’s probe large x

xp ~ xA < 1

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

emission pattern in a hard process)

- are only a small part of the information contained in

Dijets in standard (linear) pQCD

this is supported by Tevatron data

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

transverse view

peak narrower with higher pT

Azimuthal correlations in p+ptypical measurement in p+p collisions at RHIC:

coincidenceprobability

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)

(rad)

at RHIC this is done

with low-pT pions

Azimuthal correlations in d+Authe evidence for parton saturation:

d+Au central

(near side)

(away side)

(rad)

p+p

transverse view

Comparison with CGC predictions

Forward particle production

kT , y

yT eksx 1

transverse momentum kT, rapidity y > 0

yT eksx 2

forward rapidities probe small values of x

values of x probed in the process:

),(),( 22

212

2TT

TT kxfkxg

dykd

dk

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

NLO-BK description of d+Au data

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

Albacete and C.M. (2010)

Betemps, Goncalves, de Santana Amaral (2009)

the shapes and normalizations are wellreproduced, except the 0 normalization

the speed of the x evolution and of

the pT decrease are predicted

Forward di-hadron production

the CGC cannot be describedby a single gluon distribution

involves 2-, 4- and 6- point functions

no kT factorization

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

the saturation regime is better probedcompared to single particle production

a good test for the theory

C. M. (2007)

The two-particle spectrum

collinear factorization of quark density in deuteron Fourier transform k┴ and q┴

into transverse coordinates

pQCD q → qg wavefunction

b: quark in the amplitudex: gluon in the amplitudeb’: quark in the conj. amplitudex’: gluon in the conj. amplitude

interaction with hadron 2 / CGC

n-point functions that resums the powers of gS A and the powers of αS ln(1/xA)

computed with JIMWLK evolution at NLO (in the large-Nc limit),and MV initial conditions no parameters

Monojets in central d+Au• in central collisions where Qs is the biggest

there is a very good agreement of thesaturation predictions with STAR data

suppressed away-side peak

an offset is needed toaccount for the background

• the focus is on the away-side peak

where non-linearities have the biggest effect

to calculate the near-side peak, oneneeds di-pion fragmentation functions

standard (DGLAP-like) QCD calculations cannot reproduce this

The centrality dependenceit can be estimated by modifying the initial condition for NLO-BK evolution

for a given impact parameter,the initial saturation scale used is

no data yet,

but hopefully soon

peripheral collisions are like p+p collisions

the away-side peak is reappearing

when decreasing the centrality

with higher pT, one goes away from the saturation regime

the away-side peak is restored at higher pT

The pT dependence

so far, only p+p data have been shown

Conclusions

• 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

The non-linear QCD evolution

)()( )( )( )()()(

)(

2 )( 22

22 yzzxyxyzzx

yzzxyx

yx

YYYYYY NNNNNzdNdYd

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

• BK equation in coordinate space

• the unintegrated gluon distribution

Balitsky-Kovchegov x evolution

BK evolution at NLO has been calculated

one should obtain from the evolution equation

• 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)

before

nowBalitsky-Chirilli (2008)

BK evolution at NLO• running coupling (RC) corrections to the BK equation

taken into account by the substitution

Kovchegov

Weigert

Balitsky

RC corrections represent most of the NLO contribution

(2007)

• the begining of saturation phenomenology at NLO

first numerical solution

first phenomenological implementation

Albacete and Kovchegov (2007)

to successfully describe the proton structure function F2 at small x

Albacete, Armesto, Milhano and Salgado (2009)

2- 4- and 6-point functionsthe 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)

Blaizot, Gélis and Venugopalan (2004)

need more than the 2-point function: no kT factorization same conclusions in sea quark

production

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

Jalilian-Marian and Kovchegov (2004)

Baier, Kovner, Nardi and Wiedemann (2005)

we will now include the xA evolution

Performing the CGC average

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

• a Gaussian distribution of color sources

is the two-dimensional massless propagator

• applying Wick’s theorem

when expanding in powers of α and averaging,

all the field correlators can be expressed in terms of ),'(),( yx zz dc

the difficulty is to deal with the color structure

Fujii, Gelis and Venugopalan (2006)

MV model and BK evolution

in the large-Nc limitis related to in the following way

With this model for the CGC wavefunction squared, it is possible to compute then-point functions:

Blaizot, Gélis and Venugopalan (2004)

and obeys the BK equation:

we will use the MV initial condition: McLerran and Venugopalan (1994)

with the initial saturation scale

→