Testing the CGC in p+Pb collisions at the LHC

Javier L Albacete

Rencontres QGP France-12. Étretat, 25-28 Sep 2012

1

What the CGC is about : coherence effects in high energy QCD (small-x)

High gluon densities in the projectile/target

Breakdown of independent particle production

!"(x,kt)! ln(x0/x)

! K " "(x,kt)# "(x,kt)2

radiation recombination

kt ! Qs(x)

A(k ! Qs) !1g

gA ! O(1)

Saturation: gluon self-interactions tame the growth of gluon densities towards small-x

2

data on charged leptons DIS with nuclear targets and Drell-Yan in proton-nucleus collisions.

Checks of the compatibility with other hard processes are also available: the inclusive particle

production at high transverse momentum from d+Au collisions at RHIC has been included in

the analysis of [25] without signs of tension among the different data sets; the compatibility with

neutrino DIS data with nuclear targets has also been checked in Ref. [29]2. Moreover, the most

recent data from Z-production at the LHC [30] also show good agreement with the factoriza-tion assumption although errors are still moderately large. In spite of these successes, the gluon

distribution remains poorly constrained for the nucleus, as can be seen in Fig. 1 where different

sets of nPDFs are shown, together with the corresponding uncertainty bands. DGLAP evolution

is, however, very efficient in removing the nuclear effects for gluons at small-x, which quicklydisappear for increasing Q2. In this way, these uncertainties become smaller for the hardest

available probes — see Fig. 1 — except for the large-x region where substantial effects couldsurvive for large virtualities. This region is, however, dominated by valence quarks which in

turn are rather well constrained by DIS data with nuclei.

An alternative approach [31] computing the small-x shadowing by its connection to thehard diffraction in electron-nucleon scattering has been used to obtain the nuclear PDF at an

initial scale Q0 which are then evolved by NLO DGLAP equations. The inputs in this calcula-

tion are the diffractive PDFs measured in DIS with protons at HERA. These distributions are

dominated by gluons, resulting in a stronger shadowing for gluons than the corresponding one

for quarks. In Fig. 1 the results from this approach for the gluon case are also plotted. The

differences at small-x become even larger at smaller virtualities (not shown) [31].

x

-510

-410

-310 -210 -110 1

0

0.2

0.4

0.6

0.8

1

1.2

1.4 EPS09

HKN

nDS

)2

=1.6

9 G

eV2

(x,Q

Pb

gR

x

-510

-410

-310 -210 -110 1

0

0.2

0.4

0.6

0.8

1

1.2

1.4 EPS09

HKN

nDS

)2

=10

0 G

eV2

(x,Q

Pb

gR

FGS10

Fig. 1: Current knowledge of nuclear PDFs, shown as the ratio of bound over free proton gluon distributions,

RPbg (x,Q2), obtained by the NLO global fits EPS09 [25], HKN07 [26] and nDS [27] at two different virtualities,

Q2 = 1.69 GeV2 and Q2=100 GeV2. Also shown for Q2 = 100 GeV2 are the results from Ref. [31] (FGS10) in

which gluon shadowing is computed from the DIS diffraction cross section measured at HERA.

It is worth noticing that in contrast to RHIC, where there are constraints at mid-rapidity

(x >! 10!2) for nuclear distributions from DIS and DY data, the LHC will probe completely

unexplored regions of phase space. This complicates the interpretation of the A+Adata before

a p+Abenchmarking programme removes these uncertainties, e.g. for the suppression of high

transverse momentum particles observed in [3]. The experimental data from d+Au collisions at

RHIC have already proven to be an appropriate testing ground for nPDFs studies: as mentioned

before, data on inclusive production at high-pT has been included in global fits, providing con-straints for gluons; nPDFs are also extensively used in phenomenological studies of hard probes

2See, however, Ref. [28] for contradicting results.

High gluon densities in the projectile/target

Breakdown of independent particle production

!"(x,kt)! ln(x0/x)

! K " "(x,kt)# "(x,kt)2

radiation recombination

kt ! Qs(x)

Saturation: gluon self-interactions tame the growth of gluon densities towards small-x

What the CGC is about : coherence effects• Nuclear shadowing, String fusion, percolation

HIC phenomenology

• Energy dependent cutoff in event generators

• Resummation of multiple scatterings

0 500 1000 1500 2000 2500

2

3

4

5

6

7

HYDJETHIJING 2.0HERWIGPYTHIAQs Pb

GeV

sqrt(s) (GeV)

energy dependence of Pt-cutoff in EG

NUCLEUS

PROTON!

s

• kt-broadening

A(k ! Qs) !1g

gA ! O(1)

3

OUTLINE

• Coherence effects are essential for the description of data in HIC collisions (RHIC, LHC)

• Is the CGC effective theory (at its present degree of accuracy) the best suited framework to quantify those coherence phenomena in LHC HI collisions?

• Pros and Cons: - Derived from QCD within a controlled approximation -> Theory driven predictive power - Systematic unified description of different observables/collision systems - Limited degree of applicability: High-(x,Q2) effects not accounted for

François Gelis

CGC

Why small-x gluons matter

Color Glass Condensate

Factorization

Stages of AA collisions

Leading Order

Leading Logs

Glasma fields

Initial color fields

Link to the Lund model

Rapidity correlations

Matching to hydro

Glasma stress tensor

Glasma instabilities

Summary

14

Initial condition from CGC: Leading Logs

• Consider now quantum corrections to the previous result,

restricted to modes with !+1 < k

+ < !+0 :

k+

P+!+

0!+1

fields sources

"TNLO

TLO

• At leading log accuracy, the contribution of the quantum

modes in that strip can be written as :

!Tµ!NLO

=!ln

"!+0

!+1

#H1 + ln

"!!0

!!1

#H2

$T

µ!LO

(FG, Lappi, Venugopalan (2008))

small-x d.o.f (dynamical) valence d.o.f (static)

LHC RHIC SPS

4

(brief and incomplete) CGC Theory Status: Entering the NLO era

Evolution Equations:

- Running coupling kernel in BK evolution for the 2-point function - Full NLO kernel for BK-JIMWLK [Balitsky Chirilli]- Analytic [ Iancu & Triantafyllopoulos’s ] and numerical [Dumitru et al] solutions of full B-JIMWLK hierarchy for n-point functions - ...

✓✕✓

Production processes

- Running coupling and full NLO corrections to kt-factorization [Kovchegov, Horowitz, Balitsky, Chirilli]- Inelastic terms in the hybrid formalism [Altinoluk and Kovner]- Hadron-hadron, hadron-photon* correlations [Heikki’s talk, Jalilian Marian’s talk]- Factorization of multiparticle production processes at NLO [Gelis et al]- DIS NLO photon impact factors [Chirilli]

dNAB!X

d3p1 . . .[!(x, k);WY ["]]

✕

✓✓

✕

! "(x, k)! ln(1/x)

= K ! "(x, k)" "2(x, k) ! W ["]! Y

= . . .

- ...

✕

Used in phenomenological works? ✓ Yes ✕ No ✓A bit :)

LO: αs ln(1/x) NLO Running coupling

Kovchegov Weigert Gardi Balitsky

G. Beuf’s Talk

5

(brief and incomplete) CGC Phenomenology StatusEmpiric information needed to constrain:

- Non-perturbative parameters: initial conditions for BK-JIMWLK evolution, impact parameter dependence - K-factors to account for higher order corrections (effectively also for missing high-(x,Q2) contributions, energy-conservation corrections etc)

proton• Abundant high quality data at small-x• Good simultaneous description of e+p and p+p data• Global rcBK fits to constrain gluon distribution

nuclei• Few data at small-x• LHC Pb+Pb data and RHIC dAu forward data troublesome (more later)

modelling!

6

The baseline: proton collisions1. Global fits to e+p data at small-x

5 3

0.5

1

1.5 DataTheory

r!

2=0.85 GeV2Q

0.5

1

1.5

r!

2=4.5 GeV2Q

0.5

1

1.5

r!

2=10.0 GeV2Q

5 3

0.5

1

1.5

r!

2=15.0 GeV2Q

−510 −410 −310 −210

0.5

1

1.5

r!

2=35 GeV2Q

x

5 3

2=2.0 GeV2Q

2=8.5 GeV2Q

2=12.0 GeV2Q

5 3

2=28.0 GeV2Q

−410 −310 −210

2=45 GeV2Q

x

Fit including heavy quarks

! 1k2!t

! > 1

accordingly, the BK equation equation including running coupling corrections (referred to as rcBKin what follows) reads

!NF (r, x)

! ln(x0/x)=

!d2r1 K

run(r, r1, r2) [NF (r1, x) +NF (r2, x)!NF (r, x)!NF (r1, x)NF (r2, x)] (1)

where r = r1+ r2 (we use the notation v " |v| for two-dimensional vectors throughout the paper)and Krun is the evolution kernel including running coupling corrections:

Krun(r, r1, r2) =Nc "s(r2)

2#2

"1

r21

#"s(r21)

"s(r22)! 1

$+

r2

r21 r22

+1

r22

#"s(r22)

"s(r21)! 1

$%. (2)

In practical implementaions, the running coupling in Eq. (2) is regularized in the infrared byfreezing it to a constant value "fr = 0.7.

Solving the BK equation is an initial value problems, i.e. it is well defined only after initialconditions at the initial evolution scale, x0 = 10!2 in the AAMQS fits, and for all values of the thedipole size r have been provided. This introduces free parameters, ultimately of non-perturbativeorigin, to be fitted to data. In the AAMQS rcBK fits to HERA data the initial conditions aretaken in the form

NF (r, x=x0) = 1! exp

&!'r2Q2

s0,proton

(!

4ln

#1

! r+ e

$), (3)

where ! = 0.241 GeV, Q2s0,proton is the saturation scale at the initial scale x0 and $ is a dimen-

sionless parameter that controls the steepness of the unintegrated gluon distribution for momentaabove the saturation scale kt > Qs0. Both Q2

s0 and $ are fitted to data. Although the the AAMQSfits clearly favor values $ > 1, they do not uniquely determine its optimal value (and neither doso the analysis of forward RHIC data performed in [?]). Rather, di"erent pairs of (Q2

s0,proton, $)-values that provide comparably good values of %2/d.o.f # 1 are found, the reason being that theyare correlated with other parameters, as the overall normalization, and also that HERA data istoo inclusive to constrain exclusive features of the proton UGD. In order to account for such un-certainty, we shall consider two of the AAMQS sets, corresponding to (Q2

s0,proton, $)=(0.168 GeV2,1.119) and (0.157 GeV2, 1.101). Additionally we shall also consider the McLerran Venugopalan(MV) model, which corresponds to Eq. (3) evaluated at $ = 1, since it provides contact with amodel well established theoretically. Besides, it should be noticed that values $ > 1 for the protonmay arise due to higher order in density corrections to the MV model, as recently demonstratedin [?]. Such corrections are expected to the decrease with increasing atomic number. Thereforeit is conceivable that the dipole nucleus scattering amplitude may be better represented by theMV model than by initial conditions with $ > 1, an option we shall consider later on (?). The(Q2

s0,proton, $)-values we shall considered are shown in Table 1.

Set Q2s0,proton (GeV2) $

MV 0.2 1h 0.168 1.119h’ 0.157 1.101

Table 1: Summary of the parameters of the three sets for the dipole-proton scattering amplitude con-sidered in this work

5

2. Extract NP fit parameters(initial conditions for evolution)

JLA, Armesto, Milhano, Quiroga, Salgado

!!kt,x0 = 10!2,Q2

s0, ", ..."

!!!P["(kt,x)]!"(x,kt)! ln(x0/x)

! K " "(x,kt)# "(x,kt)2

initial conditions rcBK evolution e+p x-section

7

The baseline: proton collisions1. Global fits to e+p data at small-x

5 3

0.5

1

1.5 DataTheory

r!

2=0.85 GeV2Q

0.5

1

1.5

r!

2=4.5 GeV2Q

0.5

1

1.5

r!

2=10.0 GeV2Q

5 3

0.5

1

1.5

r!

2=15.0 GeV2Q

−510 −410 −310 −210

0.5

1

1.5

r!

2=35 GeV2Q

x

5 3

2=2.0 GeV2Q

2=8.5 GeV2Q

2=12.0 GeV2Q

5 3

2=28.0 GeV2Q

−410 −310 −210

2=45 GeV2Q

x

Fit including heavy quarks

! 1k2!t

! > 1

accordingly, the BK equation equation including running coupling corrections (referred to as rcBKin what follows) reads

!NF (r, x)

! ln(x0/x)=

!d2r1 K

run(r, r1, r2) [NF (r1, x) +NF (r2, x)!NF (r, x)!NF (r1, x)NF (r2, x)] (1)

where r = r1+ r2 (we use the notation v " |v| for two-dimensional vectors throughout the paper)and Krun is the evolution kernel including running coupling corrections:

Krun(r, r1, r2) =Nc "s(r2)

2#2

"1

r21

#"s(r21)

"s(r22)! 1

$+

r2

r21 r22

+1

r22

#"s(r22)

"s(r21)! 1

$%. (2)

In practical implementaions, the running coupling in Eq. (2) is regularized in the infrared byfreezing it to a constant value "fr = 0.7.

Solving the BK equation is an initial value problems, i.e. it is well defined only after initialconditions at the initial evolution scale, x0 = 10!2 in the AAMQS fits, and for all values of the thedipole size r have been provided. This introduces free parameters, ultimately of non-perturbativeorigin, to be fitted to data. In the AAMQS rcBK fits to HERA data the initial conditions aretaken in the form

NF (r, x=x0) = 1! exp

&!'r2Q2

s0,proton

(!

4ln

#1

! r+ e

$), (3)

where ! = 0.241 GeV, Q2s0,proton is the saturation scale at the initial scale x0 and $ is a dimen-

sionless parameter that controls the steepness of the unintegrated gluon distribution for momentaabove the saturation scale kt > Qs0. Both Q2

s0 and $ are fitted to data. Although the the AAMQSfits clearly favor values $ > 1, they do not uniquely determine its optimal value (and neither doso the analysis of forward RHIC data performed in [?]). Rather, di"erent pairs of (Q2

s0,proton, $)-values that provide comparably good values of %2/d.o.f # 1 are found, the reason being that theyare correlated with other parameters, as the overall normalization, and also that HERA data istoo inclusive to constrain exclusive features of the proton UGD. In order to account for such un-certainty, we shall consider two of the AAMQS sets, corresponding to (Q2

s0,proton, $)=(0.168 GeV2,1.119) and (0.157 GeV2, 1.101). Additionally we shall also consider the McLerran Venugopalan(MV) model, which corresponds to Eq. (3) evaluated at $ = 1, since it provides contact with amodel well established theoretically. Besides, it should be noticed that values $ > 1 for the protonmay arise due to higher order in density corrections to the MV model, as recently demonstratedin [?]. Such corrections are expected to the decrease with increasing atomic number. Thereforeit is conceivable that the dipole nucleus scattering amplitude may be better represented by theMV model than by initial conditions with $ > 1, an option we shall consider later on (?). The(Q2

s0,proton, $)-values we shall considered are shown in Table 1.

Set Q2s0,proton (GeV2) $

MV 0.2 1h 0.168 1.119h’ 0.157 1.101

Table 1: Summary of the parameters of the three sets for the dipole-proton scattering amplitude con-sidered in this work

5

2. Extract NP fit parameters(initial conditions for evolution)

JLA, Armesto, Milhano, Quiroga, Salgado

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

10-4

10-3

10-2

dre

l -

DG

LA

P

x

Q2=3.5 GeV

2

Q2=6.5 GeV

2

Q2=10.0 GeV

2

Q2=15.0 GeV

2

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

10-4

10-3

10-2

dre

l -

rcB

K

x

Q2=3.5 GeV

2

Q2=6.5 GeV

2

Q2=10.0 GeV

2

Q2=15.0 GeV

2

Q2=35.0 GeV

2

DGLAP rcBK

rcBK fits more stable than DGLAP fits at small-x

Q2 [G

eV2 ]

10-2

10-1

100

101

102

103

104

105

10-7 10-6 10-5 10-4 10-3 10-2 10-1 100 101

x

DGLAP fitted region

rcBK fitted region

unfitted region

(xcut , Q2)

combined HERA data+ DGLAP evolutionrcBK evolution

rcBK

DGLAP

3. Run consistency and stability checks

JLA, Milhano, Quiroga, Rojo

8

The baseline: proton collisions1. Global fits to e+p data at small-x

5 3

0.5

1

1.5 DataTheory

r!

2=0.85 GeV2Q

0.5

1

1.5

r!

2=4.5 GeV2Q

0.5

1

1.5

r!

2=10.0 GeV2Q

5 3

0.5

1

1.5

r!

2=15.0 GeV2Q

−510 −410 −310 −210

0.5

1

1.5

r!

2=35 GeV2Q

x

5 3

2=2.0 GeV2Q

2=8.5 GeV2Q

2=12.0 GeV2Q

5 3

2=28.0 GeV2Q

−410 −310 −210

2=45 GeV2Q

x

Fit including heavy quarks

! 1k2!t

! > 1

accordingly, the BK equation equation including running coupling corrections (referred to as rcBKin what follows) reads

!NF (r, x)

! ln(x0/x)=

!d2r1 K

run(r, r1, r2) [NF (r1, x) +NF (r2, x)!NF (r, x)!NF (r1, x)NF (r2, x)] (1)

where r = r1+ r2 (we use the notation v " |v| for two-dimensional vectors throughout the paper)and Krun is the evolution kernel including running coupling corrections:

Krun(r, r1, r2) =Nc "s(r2)

2#2

"1

r21

#"s(r21)

"s(r22)! 1

$+

r2

r21 r22

+1

r22

#"s(r22)

"s(r21)! 1

$%. (2)

In practical implementaions, the running coupling in Eq. (2) is regularized in the infrared byfreezing it to a constant value "fr = 0.7.

Solving the BK equation is an initial value problems, i.e. it is well defined only after initialconditions at the initial evolution scale, x0 = 10!2 in the AAMQS fits, and for all values of the thedipole size r have been provided. This introduces free parameters, ultimately of non-perturbativeorigin, to be fitted to data. In the AAMQS rcBK fits to HERA data the initial conditions aretaken in the form

NF (r, x=x0) = 1! exp

&!'r2Q2

s0,proton

(!

4ln

#1

! r+ e

$), (3)

where ! = 0.241 GeV, Q2s0,proton is the saturation scale at the initial scale x0 and $ is a dimen-

sionless parameter that controls the steepness of the unintegrated gluon distribution for momentaabove the saturation scale kt > Qs0. Both Q2

s0 and $ are fitted to data. Although the the AAMQSfits clearly favor values $ > 1, they do not uniquely determine its optimal value (and neither doso the analysis of forward RHIC data performed in [?]). Rather, di"erent pairs of (Q2

s0,proton, $)-values that provide comparably good values of %2/d.o.f # 1 are found, the reason being that theyare correlated with other parameters, as the overall normalization, and also that HERA data istoo inclusive to constrain exclusive features of the proton UGD. In order to account for such un-certainty, we shall consider two of the AAMQS sets, corresponding to (Q2

s0,proton, $)=(0.168 GeV2,1.119) and (0.157 GeV2, 1.101). Additionally we shall also consider the McLerran Venugopalan(MV) model, which corresponds to Eq. (3) evaluated at $ = 1, since it provides contact with amodel well established theoretically. Besides, it should be noticed that values $ > 1 for the protonmay arise due to higher order in density corrections to the MV model, as recently demonstratedin [?]. Such corrections are expected to the decrease with increasing atomic number. Thereforeit is conceivable that the dipole nucleus scattering amplitude may be better represented by theMV model than by initial conditions with $ > 1, an option we shall consider later on (?). The(Q2

s0,proton, $)-values we shall considered are shown in Table 1.

Set Q2s0,proton (GeV2) $

MV 0.2 1h 0.168 1.119h’ 0.157 1.101

Table 1: Summary of the parameters of the three sets for the dipole-proton scattering amplitude con-sidered in this work

5

2. Extract NP fit parameters(initial conditions for evolution)

JLA, Milhano, Quiroga, Rojo0 2 4 6 8 10 12

1x10-7

1x10-6

0.00001

0.0001

0.001

0.01

0.1

1 CMS data |eta|<2.4MV DSS-NLOg1.119 DSS-NLO, calc(y=y*0.9)g1.101 DSS-NLOMV KKPg1.119 KKP g1.101 KKP

d2 Nch

/d2 p td!

(1/G

eV2 )

7 TeVsame K-factors as for 1.96 TeV

pt (GeV)

4. Apply gained knowledge in the study of other systems (theory driven extrapolation)

LO kt-factorization: dNg

d!d2pt! K"s(Q2

r )#(x1,kt)" #(x2,kt # pt)" FF(Q2f )

proton-protonproton-proton

0 2 4 6 8 10 12

1x10-7

1x10-6

0.00001

0.0001

0.001

0.01

0.1

1 CDF data |eta|< 1MV DSS-NLO K=1.08g1.119 DSS-NLO K=3.10g1.101 DSS-NLO K=2.33MV DSS-LOg1.119 DSS-LOg1.101 DSS-LOMV KKP K=0.42g1.119 KKP K= 1.45g1.101 KKP K=1

d2 Nch

/d2 p td!

(1/G

eV2 )

1.96 TeVFF(Q)

pt (GeV)

proton-proton

JLA, Dumitru, Fujii, Nara

9

!B

!Pb(x0,kt,B) = !p(x0,kt; {Q2s0,p ! Q2

s0,Pb(B)); "}

Q2s0,Pb(B) = TA(B)Q2

s0,p

Q2s0,Pb(B) = TA(B)1/! Q2

s0,p

!Pb = !p(> 1)

!Pb = 1(MV) +#

A2/3

!Pb(x,kt,B) = rcBK[!Pb(x0,kt,B)]

A) Most “natural” option:

PROBLEM: yields RpPB > 1 at high transverse momentum

B) Possible solution and/or

Modeling the impact parameter dependence

13

! " # $ % &

!'!!!!"

!'!!!"

!'!!"

!'!"

!'"

"

"!

"!!

"!!!

()*+,-.!/#'#.01.23#!!4'.56789:;</"

()*+,-.!/$'#.01.23&!4'.56789:;</"

-=*).!/%.">!'.56789:;</!'%

,?

@8AA8/"'""B

CC.D.#!!.EF?

2;GHI.FH8J:K9.:F<A4

C:.2EF?4

LMNL!NL#C:.2EF?6#4

! " # $ %

&'&&&&!

&'&&&!

&'&&!

&'&!

&'!

!

!&

!&&

!&&&

()*+,-.!/"'".01.23"&&4'.56789:;</!

()*+,-.!/#'".01.23%&4'.56789:;</!

-=*).!/$.">&'.56789:;</&'$

,?.@'9

A8BB8/!'!!C

A8BB8/!'!!C.B;D

E:.2FG?4

DHID!ID"E:.2FG?6"4

D*J.K."&&.FG?

2;LMN.GM8O:@9.:G<B4

FIG. 8: Comparison of the rcBK-MC results obtained with only the elastic term of the hybrid formalism, Eq. (19), tothe RHIC forward data on single inclusive charged hadron (BRAHMS data [51]) and neutral pion yields in p+p (left) andd+Au collisions (right). Solid lines correspond to the ! = 1.119 i.c., dashed-dotted to also ! = 1.119 i.c but using theprescription in Eq. (10) for the initial saturation scale. Dotted lines correspond to MV i.c.

In Fig. 8 we compare our results for single inclusive charged hadron (BRAHMS data [51]) and neutral pion(STAR data [52]) distributions measured in p+p and d+Au collisions at RHIC. In this figure we include only theelastic component of the hybrid formalism. In what follows we adopt the DSS-NLO fragmentation functions as thedefault ones for all the calculations performed within the hybrid formalism. Our results show a good agreementwith data. However, the figure also illustrates that RHIC forward data does not constrain well the initial conditionsfor the evolution of nuclear wave functions: both the UGD MV and g1119 sets (using either the natural, Eq. (9),or the modified, Eq. (10), ansatz for the initial saturation scale at every point in the transverse plane) yield acomparably good description of data. This is due to the fact that transverse momentum distributions in theforward region do not probe the kT ! Qs tails of the UGDs.

Similar to previous phenomenological works, we found that no K-factors are needed to describe data at rapidities! = 2.2 and 3. However, STAR data at more forward rapidities can only be well described if a K-factor " 0.4is introduced. This may be an indication that large-x phenomena non included in the CGC may be relevant inthe region close to the kinematic limit of phase space. Note, however, that the value of the K-factor dependssignificantly both on the UGD and on the FF.

In Fig. 9 we show the comparison to the same RHIC forward data, now also including the inelastic term inthe hybrid formalism. We explore both fixed "s = 0.1 as well as one-loop running coupling at the scale Q. Weobserve that the e!ect of this additional term can be very large, especially at large transverse momentum. Wenote that, despite the fact that the coupling decreases with increasing transverse momentum, the running couplingprescription causes a larger e!ect than the fixed coupling one.

We observe that the inelastic term exhibits a harder pT -dependence than the elastic contribution, and at sometransverse momentum it overwhelms the elastic contribution. The crossing point depends on the particular choiceof UGD. The e!ects from the inelastic corrections are stronger for the steeper g1119 initial conditions than forthe MV ones over the entire range of transverse momentum shown in Fig. 9. Also, the importance of the inelasticterm depends on the collision system or, equivalently, on the target saturation scale: it is stronger for p+p thanfor d+Au collisions. For p+p collisions in particular it appears that the present formalism does not provide astable result as the inelastic correction overwhelms the leading elastic contribution already at moderate valuesof transverse momentum. This not a completely unexpected result since, parametrically, the inelastic term isproportional to ln(pt/Qst), with Qst the target saturation scale, while the elastic term scales as ln(pt/"QCD) (seediscussion in [31]). Given the importance and magnitude of the inelastic term, our findings call for a completephenomenological analysis of the full NLO corrections.

We now proceed to p+Pb collisions at LHC energy,#

s = 5 TeV. In Figs. 10 and 11 we show our results for thesingle inclusive charged hadrons yields in p+p and minimum bias p+Pb collisions and the nuclear modificationfactor Rp+Pb for minimum bias collisions respectively. We compare also to Rp+Pb from collinear factorizationusing EPS09 nPDFs [53, 54] as well as to results from the “IP-sat” model and from an independent rcBK imple-

RHIC data does not constrain much the i.c. for BK evolution. K-factor needed at most forward rapidity

dNg

dyhd2kt! xq(x1,k!)" !A(x2,kt)hybrid formalism:

10

The effect of NLO corrections to the hybrid formalism can be very large!!!. Full NLO analyses needed

Effect of NLO corrections

1 2 3 4 5

0.00001

0.0001

0.001

0.01

0.1

1

10

100

1000BRAHMS !=2.2 h± (x200). K-factor=1BRAHMS !=3.2 h± (x50). K-factor=1STAR !=4 "'0. K-factor=0.4only elasticelas+inelas #=0.1elas+inelas #(Q=pt)

pt (GeV)

dN/d!/

d2 pt (

GeV

-2)

dAu @ 200 GeV g=1.119 i.c

0 1 2 3 4 5

0.00001

0.0001

0.001

0.01

0.1

1

10

100

1000BRAHMS !=2.2 h± (x200). K-factor=1BRAHMS !=3.2 h± (x50). K-factor=1STAR !=4 "'0. K-factor=0.4only elasticelas+inel #=0.1elas+inel #(Q=pt)

pp @ 200 GeV(g=1.119 i.c)

pt (GeV)

dN/d!/

d2 pt (

GeV

-2)

11

Multiplicities

x1(2) =kt!se±yh

-6 -4 -2 0 2 4 6!

0

5

10

15

20

25

30

dN

ch/d!

BRAHMSPHOBOSMCrcBK (Albacete & Dumitru, arXiv:1011.3820)

b-CGC (Rezaeian, arXiv:1111.2312)

KLN (Dumitru et al., arXiv:1111.3031)

IP-Sat (Tribedy & Venugopalan, arXiv:1112.2445)

p(d)+A, Mini Bias

4.4 TeV

0.2 TeV

Overall, different CGC works predict dNchpPb

d!

!!!!!!=0

(5 TeV) ! 17± 2we’ll know the answer very soon!!

dNg

dyhd2kt! !sCF

k2t

"p(x1,kt)" "A(x2,kt)Kt-factorization:

dNgluons

d! d2b

!!!!!=0

! Q2s ("

s,b) #"

s0.3 Npart

• In the CGC, multiplicities rise proportional to the (local) saturation scaleb

R

ri

LHC Pb-Pb

RHIC Au+Au

rcBK

12

0 2 4 6 8 10 120

0.5

1

1.5

2

0

0.5

1

1.5

2

IP-Sat (Tribedy & Venugopalan)rcBK (Tribedy & Venugopalan)

RpPb(!=0)ch

EPS09 nPDF

pt (GeV/c)

rcBK-MC kt-factorization

0 2 4 6 8 10 120

0.5

1

1.5

2

0

0.5

1

1.5

2

IP-Sat (Tribedy & Venugopalan)rcBK (Tribedy & Venugopalan)

RpPb(!=0)ch

EPS09 nPDF

pt (GeV/c)

rcBK-MC kt-factorization

!Pb(x0,kt,B) = !p(x0,kt; {Q2s0,p ! Q2

s0,Pb(B)); "}

Q2s0,Pb(B) = TA(B)Q2

s0,p

Q2s0,Pb(B) = TA(B)1/! Q2

s0,p

Setting up the evolution

!Pb = !p(> 1)

!Pb = 1(MV) +#

A2/3

!Pb(x,kt,B) = rcBK[!Pb(x0,kt,B)]

A) Most “natural” option:

!B

PROBLEM: yields RpPB > 1 at high transverse momentum

B) Possible solution and/or

Nuclear ugd’s and nuclear modification factors

A) B)

13

!Pb(x0,kt,B) = !p(x0,kt; {Q2s0,p ! Q2

s0,Pb(B)); "}

Q2s0,Pb(B) = TA(B)Q2

s0,p

Q2s0,Pb(B) = TA(B)1/! Q2

s0,p

Setting up the evolution

!Pb = !p(> 1)

!Pb = 1(MV) +#

A2/3

!Pb(x,kt,B) = rcBK[!Pb(x0,kt,B)]

A) Most “natural” option:

!B

PROBLEM: yields RpPB > 1 at high transverse momentum

B) Possible solution and/or

Nuclear ugd’s and nuclear modification factors

2 4 6 8 10 121x10-13

1x10-12

1x10-11

1x10-10

1x10-9

1x10-8

1x10-7

1x10-6

0.00001

0.0001

0.001

0.01

0.1

1

10

rcBK-MC, kt-fact. MV i.c.!=0 (x 50)

!=2

!=4 (x 50)

!=6 (x 4•10-4)d2 Nch

/d2 p t/d

! (1

/GeV

2 )

pt (GeV/c)

rcBK-MC, kt-fact

rcBK-MC, hybrid (only elastic)

p+p collisionscme= 5 TeV

2 4 6 8 10 121x10-13

1x10-12

1x10-11

1x10-10

1x10-9

1x10-8

1x10-7

1x10-6

0.00001

0.0001

0.001

0.01

0.1

1

10

rcBK-MC, kt-fact. MV i.c!=0 (x 50)

!=2

!=4 (x 50)

!=6 (x 4•10-4)

d2 Nch

/d2 p t/d

! (1

/GeV

2 )

pt (GeV/c)

rcBK-MC, kt-fact

rcBK-MC, hybrid (only elastic)

p+Pb collisionscme= 5 TeV

The yields themselves carry very valuable information!

14

Moving forward

Yet another issue: Where to switch from kt-factorization to hybrid formalism? x1(2) !mt"

sexp(± yh)

dNg

d!d2pt! "p(x1)" "Pb(x2)

dNd!d2pt

! pdfp(x1)" "Pb(x2)

(pt, yh>>0)

Midrapidity: kt-factorization: Forward rapidity: hybrid formalism

JLA-Dumitru-Fujii-NaranPDF EPS09 results by P Quiroga

0 2 4 6 8 10 120

0.5

1

1.5

2

0

0.5

1

1.5

2

RpPb(!=2)ch

rcBK-MC, hyb LO+inel. term "=0.1

pt (GeV/c)

rcBK-MC, hybrid LOrcBK-MC, kt-factorization

EPS09 nPDF

15

Moving forward: Testing the non-linear evolution

0 2 4 6 8 10 120

0.5

1

1.5

2

0

0.5

1

1.5

2

RpPb(!=4) rcBK-MC, min bias

rcBK-MC, LO+inelastic term "=0.1

pt (GeV/c)

rcBK-MC, Npart >10ch

cme= 5 TeV

EPS09 nPDF

0 2 4 6 8 10 120

0.5

1

1.5

2

0

0.5

1

1.5

2

RpPb(!=6) rcBK-MC, min bias

rcBK-MC, LO+inelastic term "=0.1

pt (GeV/c)

rcBK-MC, Npart >10ch

cme= 5 TeV

EPS09 nPDF

0 2 4 6 8 10 120

0.5

1

1.5

2

0

0.5

1

1.5

2

RpPb(!=2)ch

rcBK-MC, hyb LO+inel. term "=0.1

pt (GeV/c)

rcBK-MC, hybrid LOrcBK-MC, kt-factorization

EPS09 nPDF

0 2 4 6 8 10 120

0.5

1

1.5

2

0

0.5

1

1.5

2

IP-Sat (Tribedy & Venugopalan)rcBK (Tribedy & Venugopalan)

RpPb(!=0)ch

EPS09 nPDF

pt (GeV/c)

rcBK-MC kt-factorization

(pt, yh>>0)

16

Forward di-hadron angular correlations

At small-x, the transverse momentum transfer is controlled by the saturation scale. CGC description: A quark (gluon) emits a gluon. The pair scatters independently off the target

xp =|k1|ey1 + |k2|ey2

!s

xA =|k1|e!y1 + |k2|e!y2

!s

Angular decorrelation happens if QPbs (xA) ! (k1,k2)

Ergo, decorrelation should be stronger with • Increasing rapidity of the pair • Increasing collision centrality • Decreasing hadron momentum

CP (!!) =1

Ntrig

dNpair

d!!!!

trigger➡ Coincidence probability

Marquet ’07, Dominguez et al

17

6

Au nucleus.

Aufragx

-310 -210

dA

J

-110

1

T

fwdd+Au 60-88 p

0.5-0.75 GeV/c

0.75-1.0 GeV/c

1.0-1.5 GeV/c

T

fwdd+Au 0-20 p

0.5-0.75 GeV/c

0.75-1.0 GeV/c

1.0-1.5 GeV/c

FIG. 4: (color online). JdA versus xfragAu for peripheral (60–

88%) and central (0–20%) d+Au collisions at!sNN = 200

GeV. The statistical error bars and systematic uncertaintyboxes are the same as in Fig. 3. Above xfrag

Au > 10!3, some

data points were o!set from their true xfragAu to avoid overlap.

The leftmost point in each group of three is at the correctxfragAu .

Because the fragmentation hadrons on average carry amomentum fraction !z" < 1, xfrag

Au will be smaller than!xAu". Based on previous studies by PHENIX at midra-pidity, the mean fragmentation !z" is expected to be be-tween 0.5-0.75 [22]. In general the theoretical extrac-tion of xAu from the measured pT and ! will di!er fromthe leading order QCD picture of 2#2 processes usedabove. Also, at modest pT ’s the interpretation of themeasured correlation functions as high energy 2#2 par-ton scattering accessing low x may be limited by con-tributions from processes with small momentum transferQ2. Future theoretical analysis will be necessary to eval-uate these and other contributions from di!erent nucleare!ects [4–10] on the observed large suppression in JdA.These analyses could additionally be complicated by thepresence of hadron pairs originating from multiparton in-teractions [23] that might not probe gluon structure atlow xAu.In summary, measurements of the inclusive "0 yield

at forward rapidity, of the back-to-back correlated yieldof cluster-"0 pairs in the forward-rapidity region, and ofthe correlated yield of forward-rapidity "0’s with midra-pidity "0’s or hadrons in p+p and d+Au collisions at$sNN = 200 GeV were presented. The correlated yields

of back-to-back pairs were analyzed for various kinematicselections in pT and rapidity. The forward-central pairmeasurements show no increase in the azimuthal angularcorrelation width within experimental uncertainties. Thecorrelated yield of back-to-back pairs in d+Au collisionsis observed to be substantially suppressed relative to p+pcollisions with a suppression that is observed to increasewith decreasing impact parameter selection and for pairs

probing more forward rapidities.

We thank the sta! of the Collider-Accelerator andPhysics Departments at Brookhaven National Labora-tory and the sta! of the other PHENIX participatinginstitutions for their vital contributions. We acknowl-edge support from the O"ce of Nuclear Physics in theO"ce of Science of the Department of Energy, the Na-tional Science Foundation, Abilene Christian UniversityResearch Council, Research Foundation of SUNY, andDean of the College of Arts and Sciences, Vanderbilt Uni-versity (U.S.A), Ministry of Education, Culture, Sports,Science, and Technology and the Japan Society for thePromotion of Science (Japan), Conselho Nacional de De-senvolvimento Cientıfico e Tecnologico and Fundacao deAmparo a Pesquisa do Estado de Sao Paulo (Brazil), Nat-ural Science Foundation of China (P. R. China), Min-istry of Education, Youth and Sports (Czech Repub-lic), Centre National de la Recherche Scientifique, Com-missariat a l’Energie Atomique, and Institut Nationalde Physique Nucleaire et de Physique des Particules(France), Ministry of Industry, Science and Tekhnolo-gies, Bundesministerium fur Bildung und Forschung,Deutscher Akademischer Austausch Dienst, and Alexan-der von Humboldt Stiftung (Germany), Hungarian Na-tional Science Fund, OTKA (Hungary), Department ofAtomic Energy and Department of Science and Technol-ogy (India), Israel Science Foundation (Israel), NationalResearch Foundation and WCU program of the MinistryEducation Science and Technology (Korea), Ministry ofEducation and Science, Russian Academy of Sciences,Federal Agency of Atomic Energy (Russia), VR and theWallenberg Foundation (Sweden), the U.S. Civilian Re-search and Development Foundation for the IndependentStates of the Former Soviet Union, the US-HungarianFulbright Foundation for Educational Exchange, and theUS-Israel Binational Science Foundation.

" Deceased† PHENIX spokesperson. jacak@skipper.physics.sunysb.edu

[1] I. Arsene et al. (BRAHMS Collaboration), Phys. Rev.Lett. 93, 242303 (2004).

[2] J. Adams et al. (STAR Collaboration), Phys. Rev. Lett.97, 152302 (2006).

[3] S. S. Adler et al. (PHENIX Collaboration), Phys. Rev.Lett. 94, 082302 (2005).

[4] I. Vitev, Phys. Rev. C 75, 064906 (2007).[5] L. Frankfurt and M. Strikman, Phys. Lett. B645, 412

(2007).[6] R. C. Hwa, C. B. Yang, and R. J. Fries, Phys. Rev. C

71, 024902 (2005).[7] V. Guzey, M. Strikman, and W. Vogelsang, Phys. Lett.

B603, 173 (2004).[8] J. Qiu and I. Vitev, Phys. Lett. B632, 507 (2006).[9] L. Gribov, E. Levin, and M. Ryskin, Phys.Rept. 100, 1

(1983).

Forward di-hadron angular correlations in RHIC dAu data

Observed decorrelation IS stronger with • Increasing rapidity of the pair • Increasing collision centrality • Decreasing hadron momentum

forward-forward

central-forward

PHENIX data

peripheral

central

4

1 2 3 4 5 6

0

0.01

0.02

0.03

0.04

0.05

0.06(pp) = 0.084

0b

(dA 60-88) = 0.1340

b

(dA 0-20) = 0.1800

b

0.5-0.75 GeV/c!4-7

1 2 3 4 5 6

0

0.01

0.02

0.03

0.04

0.05

0.06(pp) = 0.086

0b

(dA 60-88) = 0.1330

b

(dA 0-20) = 0.1850

b

0.5-0.75 GeV/c!3-4

0 1 2 3 4 5 6

0

0.01

0.02

0.03

0.04

0.05

0.06 = 0.088

0b

= 0.1350

b

= 0.1840

b

p+p

d+Au 60-88d+Au 0-20

0.5-0.75 GeV/c!2.5-3

(rad)"#

fwd

$ d

Tfwd

) d

p"

#N

/d(

3d

mid

1/N

FIG. 1: (color online). Pedestal-subtracted !0-!0 per-triggercorrelation functions for, as indicated, p+p, d+Au periph-eral (60–88% centrality) and d+Au central (0–20% central-ity) collisions at

!sNN = 200 GeV; the associated !0’s

of pT = 0.5–0.75 GeV/c are measured at forward rapidity(3.0 < " < 3.8) and the triggered !0’s are measured atmidrapidity (|"| < 0.35) for the indicated pT ranges. Thesubtracted pedestal values, b0, are also indicated.

-1 0 1 2 3 4

0

0.02

0.04

0.06

0.08

0.1

= 0.0590

pp b

= 0.1060

dA 60-88b

= 0.1420

dA 0-20 b

0.5-0.75 GeV/c!2-5

-1 0 1 2 3 4

0

0.02

0.04

0.06

0.08

0.1

= 0.0790

pp b

= 0.1270

dA 60-88b

= 0.1630

dA 0-20 b

0.5-0.75 GeV/c!1.6-2

-1 0 1 2 3 4

0

0.02

0.04

0.06

0.08

0.1

= 0.0950

pp b

= 0.1410

dA 60-88b

= 0.1760

dA 0-20 b

p+p

d+Au 60-88

d+Au 0-20

0.5-0.75 GeV/c!1.1-1.6

(rad)"#

0%$

dT

0%

) d

p"

#N

/d(

3 d

clu

s1

/N

FIG. 2: (color online). Pedestal-subtracted cluster-!0 per-trigger correlation functions measured at forward rapidity(3.0 < " < 3.8) for, as indicated, p+p, d+Au peripheral(60–88% centrality) and d+Au central (0-20% centrality) col-lisions at

!sNN = 200 GeV; the correlation functions are for

associated !0’s of pT = 0.5–0.75 GeV/c and trigger clustersover the indicated pT ranges. Systematic uncertainties of upto 30% on the near side (|!#| < 0.5) are not shown. Thesubtracted pedestal values, b0, are also indicated.

tion make it di!cult to reconstruct photon pairs from !0

decays at high pT . For example at pT = 1 GeV/c, ap-proximately 30% of the photon cluster pairs are mergedand cannot be reconstructed separately in the MPC. Toextend the pT range and the pair yield, single electromag-netic clusters are used as trigger particles to constructcluster-!0 dihadron pairs in the MPC. These trigger clus-ters are treated assuming that they are all !0’s. How-ever, pythia studies indicate that >! 80% of these trig-ger clusters are from !0’s with the rest being dominantlysingle photons from asymmetric decays of " mesons ordirect photons; thus, according to these studies a rela-tively small contamination remains. The cluster energywas corrected to the true !0 energy to account for themerging e"ects of the two photons from !0 decay. Thesecorrections were determined by embedding Monte Carlogenerated !0’s into real data, as well as from pythia

tuned to match the data.Figure 1 shows the azimuthal angle correlations be-

tween midrapidity and forward-rapidity !0 pairs, per !0

trigger detected at midrapidity, in p+p, peripheral d+Au,and central d+Au collisions for varying trigger !0 pT .Figure 2 shows the same correlations for trigger clusterswhere the cluster-!0 pairs are both detected at forwardrapidity. The constant pedestal, b0, was subtracted fromthe correlation function. The correlations were correctedfor the forward !0 detection e!ciency and for the combi-natoric background beneath the !0 peaks in the photon-pair invariant mass spectra. This background is deter-mined by measurement of the azimuthal correlations forphoton-pair mass selections adjacent to the !0 mass win-dow and from studies of simulated jet events from pythia

events processed through PISA.For the midrapidity/forward-rapidity correlations

(Fig. 1), due to the large pseudorapidity gap of #"!3.3between the hadrons, only an away-side peak (##=!)is seen. For the forward-forward correlations a near-sidepeak (##=0) is also present (see Fig. 2). The yieldsand widths of the correlated pairs are extracted by fitsto an away-side Gaussian signal shape plus a constantbackground (b0). The fit to the forward-forward corre-lations has an additional Gaussian signal for the near-side peak. The pedestal is determined from a fit in themidrapidity/forward-rapidity correlations and is consis-tent with the pedestal level found based on the assump-tion that the signal yield is 0 at the minimum of the cor-relation function - zero yield at minimum (ZYAM) [20].In the forward-forward correlations the ZYAM pedestalis used in the yield extraction. Additional systematicuncertainties of up to 30% (not shown in Fig. 2) areascribed to the near-side peak due to corrections forresonance decays that contaminate the jet signal, anddue to the acceptance loss around the trigger particle of##"#" # 0.5" 0.5 rad, resulting from the minimumseparation cut of one tower between cluster peaks in theMPC. The acceptance loss gives rise to the decrease ob-served for the near side peak.Figures 1 and 2 show that the away-side peak for d+Au

central collisions is suppressed compared to p+p colli-sions and peripheral d+Au collisions. This e"ect is largefor the midrapidity/forward-rapidity correlations (Fig. 1)and becomes even larger when both particles are requiredto be in the forward-rapidity region (Fig. 2).For the midrapidity/forward-rapidity correlations,

within their large uncertainties the Gaussian widths ofthe away-side correlation peak remain the same be-tween p+p and central d+Au and the broadening pre-dicted in the CGC framework in Ref. [11] is not ob-served. For example, in d+Au central collisions, $ =0.93±0.09stat±0.139syst for pfwd

T = 1.25 GeV/c and trig-ger particle momentum 2.5 < ptT < 3.0 GeV/c, while$ = 0.97±0.07stat±0.08syst for p+p collisions. For theforward-forward correlations, the measurement does not

4

1 2 3 4 5 6

0

0.01

0.02

0.03

0.04

0.05

0.06(pp) = 0.084

0b

(dA 60-88) = 0.1340

b

(dA 0-20) = 0.1800

b

0.5-0.75 GeV/c!4-7

1 2 3 4 5 6

0

0.01

0.02

0.03

0.04

0.05

0.06(pp) = 0.086

0b

(dA 60-88) = 0.1330

b

(dA 0-20) = 0.1850

b

0.5-0.75 GeV/c!3-4

0 1 2 3 4 5 6

0

0.01

0.02

0.03

0.04

0.05

0.06 = 0.088

0b

= 0.1350

b

= 0.1840

b

p+p

d+Au 60-88d+Au 0-20

0.5-0.75 GeV/c!2.5-3

(rad)"#

fwd

$ d

Tfwd

) d

p"

#N

/d(

3d

mid

1/N

FIG. 1: (color online). Pedestal-subtracted !0-!0 per-triggercorrelation functions for, as indicated, p+p, d+Au periph-eral (60–88% centrality) and d+Au central (0–20% central-ity) collisions at

!sNN = 200 GeV; the associated !0’s

of pT = 0.5–0.75 GeV/c are measured at forward rapidity(3.0 < " < 3.8) and the triggered !0’s are measured atmidrapidity (|"| < 0.35) for the indicated pT ranges. Thesubtracted pedestal values, b0, are also indicated.

-1 0 1 2 3 4

0

0.02

0.04

0.06

0.08

0.1

= 0.0590

pp b

= 0.1060

dA 60-88b

= 0.1420

dA 0-20 b

0.5-0.75 GeV/c!2-5

-1 0 1 2 3 4

0

0.02

0.04

0.06

0.08

0.1

= 0.0790

pp b

= 0.1270

dA 60-88b

= 0.1630

dA 0-20 b

0.5-0.75 GeV/c!1.6-2

-1 0 1 2 3 4

0

0.02

0.04

0.06

0.08

0.1

= 0.0950

pp b

= 0.1410

dA 60-88b

= 0.1760

dA 0-20 b

p+p

d+Au 60-88

d+Au 0-20

0.5-0.75 GeV/c!1.1-1.6

(rad)"#

0%$

dT

0%

) d

p"

#N

/d(

3 d

clu

s1

/N

FIG. 2: (color online). Pedestal-subtracted cluster-!0 per-trigger correlation functions measured at forward rapidity(3.0 < " < 3.8) for, as indicated, p+p, d+Au peripheral(60–88% centrality) and d+Au central (0-20% centrality) col-lisions at

!sNN = 200 GeV; the correlation functions are for

associated !0’s of pT = 0.5–0.75 GeV/c and trigger clustersover the indicated pT ranges. Systematic uncertainties of upto 30% on the near side (|!#| < 0.5) are not shown. Thesubtracted pedestal values, b0, are also indicated.

tion make it di!cult to reconstruct photon pairs from !0

decays at high pT . For example at pT = 1 GeV/c, ap-proximately 30% of the photon cluster pairs are mergedand cannot be reconstructed separately in the MPC. Toextend the pT range and the pair yield, single electromag-netic clusters are used as trigger particles to constructcluster-!0 dihadron pairs in the MPC. These trigger clus-ters are treated assuming that they are all !0’s. How-ever, pythia studies indicate that >! 80% of these trig-ger clusters are from !0’s with the rest being dominantlysingle photons from asymmetric decays of " mesons ordirect photons; thus, according to these studies a rela-tively small contamination remains. The cluster energywas corrected to the true !0 energy to account for themerging e"ects of the two photons from !0 decay. Thesecorrections were determined by embedding Monte Carlogenerated !0’s into real data, as well as from pythia

tuned to match the data.Figure 1 shows the azimuthal angle correlations be-

tween midrapidity and forward-rapidity !0 pairs, per !0

trigger detected at midrapidity, in p+p, peripheral d+Au,and central d+Au collisions for varying trigger !0 pT .Figure 2 shows the same correlations for trigger clusterswhere the cluster-!0 pairs are both detected at forwardrapidity. The constant pedestal, b0, was subtracted fromthe correlation function. The correlations were correctedfor the forward !0 detection e!ciency and for the combi-natoric background beneath the !0 peaks in the photon-pair invariant mass spectra. This background is deter-mined by measurement of the azimuthal correlations forphoton-pair mass selections adjacent to the !0 mass win-dow and from studies of simulated jet events from pythia

events processed through PISA.For the midrapidity/forward-rapidity correlations

(Fig. 1), due to the large pseudorapidity gap of #"!3.3between the hadrons, only an away-side peak (##=!)is seen. For the forward-forward correlations a near-sidepeak (##=0) is also present (see Fig. 2). The yieldsand widths of the correlated pairs are extracted by fitsto an away-side Gaussian signal shape plus a constantbackground (b0). The fit to the forward-forward corre-lations has an additional Gaussian signal for the near-side peak. The pedestal is determined from a fit in themidrapidity/forward-rapidity correlations and is consis-tent with the pedestal level found based on the assump-tion that the signal yield is 0 at the minimum of the cor-relation function - zero yield at minimum (ZYAM) [20].In the forward-forward correlations the ZYAM pedestalis used in the yield extraction. Additional systematicuncertainties of up to 30% (not shown in Fig. 2) areascribed to the near-side peak due to corrections forresonance decays that contaminate the jet signal, anddue to the acceptance loss around the trigger particle of##"#" # 0.5" 0.5 rad, resulting from the minimumseparation cut of one tower between cluster peaks in theMPC. The acceptance loss gives rise to the decrease ob-served for the near side peak.Figures 1 and 2 show that the away-side peak for d+Au

central collisions is suppressed compared to p+p colli-sions and peripheral d+Au collisions. This e"ect is largefor the midrapidity/forward-rapidity correlations (Fig. 1)and becomes even larger when both particles are requiredto be in the forward-rapidity region (Fig. 2).For the midrapidity/forward-rapidity correlations,

within their large uncertainties the Gaussian widths ofthe away-side correlation peak remain the same be-tween p+p and central d+Au and the broadening pre-dicted in the CGC framework in Ref. [11] is not ob-served. For example, in d+Au central collisions, $ =0.93±0.09stat±0.139syst for pfwd

T = 1.25 GeV/c and trig-ger particle momentum 2.5 < ptT < 3.0 GeV/c, while$ = 0.97±0.07stat±0.08syst for p+p collisions. For theforward-forward correlations, the measurement does not

5

4 6 8 10 12 14 16

0.5

1

1.5

2 = 0.5-0.75 GeV/cT

fwdp T

fwd2Cluster p

1.1-1.6 GeV/c1.6-2.0 GeV/c2.0-5.0 GeV/c

0! dAfwd

R

4 6 8 10 12 14 16

0.5

1

1.5

2 = 0.75-1.0 GeV/c

T

fwdp

4 6 8 10 12 14 16

0.5

1

1.5

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T

fwdp

4 6 8 10 12 14 16

0.5

1

1.5

2 = 0.5-0.75 GeV/cT

fwdp T

mid p±h

0.5-1 GeV/c1-2 GeV/c2-4 GeV/c

0! dAfwd

RT

mid p0!2.5-3 GeV/c3-4 GeV/c4-7 GeV/c

4 6 8 10 12 14 16

0.5

1

1.5

2 = 0.75-1.0 GeV/c

T

fwdp

4 6 8 10 12 14 16

0.5

1

1.5

2 = 1.0-1.5 GeV/c

T

fwdp

"coll

N#

dA

J

Mid-Forward Forward-Forward

FIG. 3: (color online). Relative yield JdA versus !Ncoll" for forward-rapidity (3.0 < ! < 3.8) "0’s paired with (left) midrapidity(|!| < 0.35) hadrons and "0’s and (right) forward-rapidity (3.0 < ! < 3.8) cluster-"0 pairs for the indicated combinations ofpT ranges. Also plotted as inverted solid triangles are the values of the forward "0 RdA. Around each data point the verticalbars indicate statistical uncertainties and the open boxes indicate point-to-point systematic uncertainties. The gray bar atthe left in each panel represents a global systematic scale uncertainty of 9.7%. Additional centrality dependent systematicuncertainties of 7.5%, 5.1%, 4.1%, and 4.8% for the peripheral to central bins, respectively, are not shown. The !Ncoll" valueswithin a centrality selection are o!set from their actual values for visual clarity (see text for actual !Ncoll" values).

discern whether there is appreciable broadening betweend+Au and p+p collisions, as the ZYAM pedestal deter-mination can bias the widths to smaller values.The observed suppression is quantified by studying

the relative yield, JdA [21], of correlated back-to-backhadron pairs in d+Au collisions compared to p+p colli-sions scaled with !Ncoll",

JdA = IdA #RtdA =

1

!Ncoll"!pairdA /!dA

!pairpp /!pp

, (1)

where RtdA = (1/!Ncoll") · (!t

dA/!dA)/(!tpp/!pp) is the

usual nuclear modification factor for trigger particles t,and !, !t, and !pair are the cross sections (or normalizedyields) for the full event selection, trigger particle eventselection, and dihadron pair event selection. IdA is theratio of conditional hadron yields, CY , for d+Au andp+p collisions:

CY =

!d(!")[dN/d(!") $ b0]

N t # #a #!$a #!paT, (2)

with the acceptance corrected dihadron correlation func-tion dN/d(!"), the number of trigger particles N t, thedetection e"ciency for the associated particle #a and thelevel of the uncorrelated pedestal in the correlation func-tions b0. The integral is taken over the Gaussian fit ofthe away-side peak. The JdA uncertainties include a sys-tematic uncertainty from the ZYAM pedestal subtrac-tion. In determining this uncertainty it was assumed that

changes between d+Au and p+p in the Gaussian away-side width remain below a factor two. This upper limitis based on the small observed changes in width in themidrapidity/forward-rapidity correlations and the corre-lations studied previously with the PHENIX muon spec-trometers [14]. The JdA is calculated from the measuredIdA and Rt

dA for the forward-rapidity trigger correlationswith the new %0 RdAu = Rt

dAu determined in the MPC.For the midrapidity trigger correlations, published valuesfor RdA from the 2003 RHIC run [15, 16] were used.

Figure 3 presents JdA versus !Ncoll" for forward-rapidity %0’s paired with midrapidity hadrons and %0’s,and for %0’s and clusters paired at forward rapidity. TheJdA decreases with an increasing number of binary col-lisions, !Ncoll", or equivalently with increasing nuclearthickness. The suppression also increases with decreas-ing particle pT and is significantly larger for forward-forward hadron pairs than for midrapidity/forward-rapidity pairs. The observed suppression of JdA ver-sus nuclear thickness, pT and $ points to large coldnuclear matter e#ects arising at high parton densitiesin the nucleus probed by the deuteron, consistent withpredictions from CGC [12]. This trend is seen moreclearly in Fig. 4 where JdA is plotted versus xfrag

Au =(!pT1"e!"!1# + !pT2"e!"!2#)/

%sNN for all pair selections

in $ and pT . In the case of 2&2 parton scattering, wheretwo final state hadrons carry the full parton energy, z=1,the variable xfrag

Au would be equal to !xAu", which is theaverage momentum fraction of the struck parton in the

18

Forward di-hadron angular correlations in RHIC dAu data

-1 0 1 2 3 4 5

0.014

0.016

0.018

0.02

0.022

0.024

0.026STAR Preliminary

CP

(!"

)

!"

CGC calculations

Stasto et al

Albacete-Marquet

Central dAu collisions

pt < 2 GeV/c <#t> = 3.2

pt > pa > 1 GeV/c <#a>=3.2

"non-CGC" calculations

Kang et al

Uncertainties in current CGC phenomenological works: • Need for a better description of n-point functions: [H Mantysaari & T. Lappi] • Better determination of the pedestal: K-factors in single inclusive production? Role of double parton scattering?

• Alternative descriptions including resummation of multiple scatterings, nuclear shadowing and cold nuclear matter energy loss seem possible... [Kang et al]

correlated uncorrelated

Double parton scattering

Background (pedestal) contribution to coincidence probability: twohadrons are produced independently

!

!

" "

! !

"

#

!"

!

$%& $'& $(&

!

# !

"

#

!

!

"

!

##

"

Strikman, Vogelsang, 1009.6123

Heikki Mantysaari (JYFL) Azimuthal angle correlations 31.5.2012 9 / 18

19

di-hadron angular correlations at the LHC

• Analogous decorrelation phenomena should be seen at the LHC• The increase in collision energy implies that they should be visible at * Lower rapidities of the produced pair * Higher transverse momentum• All previously mentioned details are been taken care of. Stay tuned!!!

20

hadron-photon* correlations in pPb collisions at the LHC • hadron-dilepton pair • hadron-photon

Stasto et al 1204.4861 Jalilian-Marian, Rezaeian

Y! = Y" = 4

M = 8 GeV

M = 4 GeV

These processes are theoretically cleaner: Only knowledge of 2-point needed!!

21

✔ Important steps have been taken in promoting GCG to an useful quantitative tool - Continuos progress on the theoretical side - Phenomenological effort to systematically describe data from different systems (e+p, e+A, p+p, d+Au, Aa+Au and Pb+Pb) in an unified framework

Outlook

Merci!!

✔ Current predictions carry some uncertainty due to lack of data to constrain NP aspects of nuclear UGD. This problem can be largely fixed through the measurement of simple observables (i.e. single inclusive spectra) in p+Pb collisions

✔ Phenomenological implementation of recent theoretical progress needed

✔ Most solid CGC predictions for the upcoming p+Pb run: - Suppression of nuclear modification factors at moderate pt already at mid-rapidity - Stronger suppression at more forward rapidities (evolution) - Suppression of di-hadron and photon-hadron angular correlations

22

If these data are confirmed... ALL initial state models are in trouble!!

23

2 4 6 8 100

0.5

1

1.5

2

0

0.5

1

1.5

2

RpPb(!=0) rcBK-MC, Min. bias

pt (GeV/c)

rcBK-MC, Npart > 10ch

cme= 5 TeVQs2(b) ~ TA(b)

rcBK-MC, Npart < 5

2 4 6 8 100

0.5

1

1.5

2

0

0.5

1

1.5

2

RpPb(!=2) rcBK-MC, Min. bias

pt (GeV/c)

rcBK-MC, Npart > 10ch

cme= 5 TeVQs2(b) ~ TA(b)

rcBK-MC, Npart < 5

24