Dijet azimuthal correlations in p-p and p-Pb collisions at forward LHC calorimeters M. Abdullah Al-MashadaA. van HamerencH. KakkaddP. Kotkod

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Dijet azimuthal correlations in p-p and p-Pb collisions at

forward LHC calorimeters

M. Abdullah Al-Mashad aA. van Hameren cH. Kakkad dP. Kotko d

K. Kutak c,e P. van Mechelen bS. Sapeta c

aFayoum University, Center for High Energy Physics (CHEP-FU),

Department of Physics, Faculty of Science,

Fayoum 63514, Egypt

bAntwerp University, Particle Physics group

Groenenborgerlaan 171, 2020 Antwerpen, Belgium

cInstitute of Nuclear Physics, Polish Academy of Sciences

Radzikowskiego 152, 31-342 Krak´ow, Poland

dAGH University Of Science and Technology,

Faculty of Physics and Applied Computer Science,

al. Mickiewicza 30, 30-059 Krak´ow, Poland

eBrookhaven National Laboratory,

Physics Department, Bldg. 510A,

20 Pennsylvania Street, 30-059 Upton, NY 11973 USA

IFJPAN-IV-2022-17

Abstract

We present a state-of-the-art computation for the production of forward dijets in proton-

proton and proton-lead collisions at the LHC, in rapidity domains covered by the ATLAS

calorimeter and the planned FoCal extension of the ALICE detector. We use the small-x

improved TMD (ITMD) formalism, together with collinearly improved TMD gluon distribu-

tions and full b-space Sudakov resummation, and discuss nonperturbative corrections due to

hadronization and showers using the Pythia event generator. We observe that forward dijets

in proton-nucleus collisions at moderately low pTare excellent probes of saturation eﬀects, as

the Sudakov resummation does not alter the suppression of the cross section.

1 Introduction

One of the current experimental challenges in Quantum Chromodynamics (QCD) are searches for

clean signals of gluon saturation, i.e. a signature of gluon recombination in a dense nuclear system.

Gluon saturation has been predicted from QCD long time ago [1] and has been systematically

studied over the years, in particular using the Color Glass Condensate (CGC) eﬀective theory

(see e.g. [2]). Although there is no doubt that the growth of gluon distributions has to be tamed

at some point due to the unitarity of a scattering matrix, and while there are strong hints for

occurrence of saturation in data [3–10] (see [11] for a review), there is no complete consensus

on how the very small xlimit is reached. Moreover, it is expected to see the onset of Balitsky-

Fadin-Kuraev-Lipatov (BFKL) dynamics [12,13], even before saturation dynamics. One example is

Mueller-Navalet jet production [14–16] in the kTfactorization formalism [17] (see also [18] for recent

arXiv:2210.06613v2 [hep-ph] 26 Oct 2022

developments) [19] for BFKL resummation in collinear factorization or central-forward inclusive

jets at the LHC [20–22].

However, there is an important diﬀerence between BFKL and saturation physics, which could

potentially allow for saturation to be seen more directly. Saturation phenomena manifest them-

selves through the high energy evolution equations, similar to BFKL, but nonlinear (the Balitsky-

Kovchegov (BK) equation [23,24] and the B-JIMWLK equations [23, 25–31]. The strength of the

nonlinearity taming the growth of gluon distributions strongly depends on the target size – for

large systems with Anuclei it is expected to be enhanced by roughly A1/3. Therefore, compar-

ing observables computable within the high energy QCD limit for a proton and for large nuclear

targets is potentially the best way to ﬁnd evidence for saturation. Such dependence of the cross

section for production of forward π0in p+A was recently reported in [32], providing strong signs

of saturation. It is important to mention that there might be other mechanisms giving suppres-

sion of nuclear parton distribution functions (PDFs), notably the so-called leading twist nuclear

shadowing [33] which is used within collinear factorization. However, at present its connection to

saturation is unclear, although one has to keep in mind that the saturation for dijet production is

also the leading power eﬀect.

In our work we are interested in dijet production as a probe of saturation (see [34–38] for earlier

works on this subject) in hadro-production. We thus require the ﬁnal state partons to have rather

large transverse momenta PT. Naturally, the scale set by the jets is larger than the saturation scale

Qs, but not asymptotically larger, so that the saturation eﬀects are not neglected. Such limit is

well deﬁned within the CGC theory, and is precisely the leading power limit kT/PT1, where kT

is the dijet imbalance [39]. In our computations we go beyond the leading power, by including the

kinematic twists – such approach gives more precise predictions for the dijet correlation spectra.

The adequate formalism is known as the small-ximproved Transverse Momentum Dependent

(ITMD) factorization [40, 41] (for further developments of both the ITMD and the leading power

limit see [42–52]).

For dijet imbalance observables it is necessary to perform a suitable resummation of the Sudakov

logs. This can be done in at least two ways. First method relies on including the Sudakov form

factor as a source of the hard scale evolution, similar to what is being done in parton shower

algorithms. Such approach has been used for instance in [38, 53–55]. Another approach relies on

the soft gluon resummation technique in b-space [56, 57], which in general provides resummation

beyond simple double Sudakov logs (see e.g. [9,58,59]. In the present work, we shall apply the full

b-space resummation approach, as a current state-of-the-art result.

Forward jets have been already measured at LHC, with inconclusive result regarding the satu-

ration signal. For example, the CMS-CASTOR calorimeter [60] measured single inclusive jets [61]

in proton-lead collision, but the lack of the proton-proton study makes it very diﬃcult to assess if

saturation is present. This is mainly due to the fact that at present all saturation-based calculations

are parton-level and thus the comparison with data is burdened with large uncertainties [62–64]

. Further, the ATLAS collaboration measured forward-forward and forward-central dijets [65] for

both proton-proton and proton-lead, but no cross section measurement has been done, and thus

no nuclear modiﬁcation ratio was provided. The visible nuclear broadening has been claimed to

be negligible within the error bars, despite being consistent with saturation and Sudakov resum-

mation [55]. Finally, the CMS collaboration recently measured exclusive dijet production [66] in

ultra-peripheral collisions, where, again, only the photon-lead sample is studied, without a photon-

proton reference. Interestingly, a comparison with a Monte Carlo describing the photoproduction

on proton targets seems to imply strong nuclear broadening.

In the present work we provide predictions for a potential new study of forward dijets with

ATLAS FCal kinematics, as well as for the planned FoCal upgrade of ALICE [67], assuming that

both proton-proton and proton-lead cross sections will be measured. Our paper is organized as

follows. In the next Section we brieﬂy review the ITMD framework and modify it accordingly to

include the Sudakov resummation. Next, in Section 3we specify our kinematic cuts in detail and

present our results. We delegate the discussion of the results to Section 4.

2 Small-xImproved TMD Factorization

The ITMD factorization formula for the production of two jets with momenta p1and p2, and

rapidities y1and y2, reads

dσpA→j1j2+X

d2PTd2kTdy1dy2

a,c,d

xpfa/p(xp, µ)

i=1 K(i)

ag∗→cd (PT, kT;µ) Φ(i)

ag→cd (xA, kT),(1)

where for jets with transverse momenta ~pT1and ~pT2we deﬁned ~

PT=~pT1−~pT2and the dijet

transverse momentum imbalance ~

kT=~pT1+~pT2. The longitudinal fractions of partons extracted

from proton and nucleus are, respectively, xpand xA, with a restriction that xAxp. Further-

more, fa/pare collinear PDFs, Kag∗→cd are oﬀ-shell gauge invariant hard factors and Φ(i)

ag→cd are

the TMD gluon distributions that correspond to distinct color ﬂows for each partonic channel. The

hard factors and the TMD gluon distributions were computed in [40].

The resummation of the Sudakov logarithms is performed following the perturbative calculation

presented in [56], where the calculations have been done in the impact parameter space (here, the

impact parameter bTis the Fourier conjugate to the gluon kT). The derivation has been done

in the back-to-back regime, that is to leading power. Since the Sudakov factors are negligible for

kT∼PT, it can be straightforwardly extended to the ITMD formula (1).

dσpA→j1j2+X

d2PTd2kTdy1dy2

a,c,d

i=1 K(i)

ag∗→cd (PT, kT;µ)

×ˆdbTbTJ0(bTkT)fa/p(xp, µb)e

Φ(i)

ag→cd (xA, bT)e−Sag→cd (µ,b⊥),(2)

where e

Φ(i)

ag→cd is the Fourier transform of the TMD gluon distributions and Sag→cd are the Sudakov

factors deﬁned below. The scale µbis essentially the inverse of the impact parameter:

µb= 2e−γE/b∗(3)

with

b∗=bT/q1 + b2

T/b2

max .(4)

With such a choice, the scale µbfreezes in the limit of large bT, where it takes the value 2e−γE/bmax 

ΛQCD. Following Ref. [68], in our calculation we shall use the value bmax = 0.5 GeV−1.

For each channel, the Sudakov factors can be written as

Sab→cd(µ, b⊥) = X

i=a,b,c,d

p(µ, b⊥) + X

i=a,c,d

np(µ, b⊥),(5)

where Si

pand Si

np are the perturbative and non-perturbative contributions. It was argued in Ref. [59],

that the non-perturbative Sudakov should not be included for a small-xparton b. The perturbative

Sudakov factors, including double and single logarithms, are given by [56,57]

Sqg→qg

p(µ, b⊥) = ˆµ2

µ2

dq2

T2(CF+CA)αs

2πln µ2

T−3

2CF+CAβ0αs

π,(6)

Sgg→gg

p(µ, b⊥) = ˆµ2

µ2

dq2

T4CA

αs

2πln µ2

T−3CAβ0

αs

π,(7)

where β0= (11 −2nf/Nc)/12. The gg →q¯qchannel is negligible for the kinematic domain of this

study1.

Let us notice, that in (2) the collinear PDF depends on the impact parameter. This complicates

the Monte Carlo implementation of the factorization approach. Therefore we investigate a choice

1The single logarithm accuracy terms have been recently obtained at leading power within the small-xCGC

formalism for di-jet production in e-A at NLO accuracy [69].

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Dijetazimuthalcorrelationsinp-pandp-PbcollisionsatforwardLHCcalorimetersM.AbdullahAl-MashadaA.vanHamerencH.KakkaddP.KotkodK.Kutakc;eP.vanMechelenbS.SapetacaFayoumUniversity,CenterforHighEnergyPhysics(CHEP-FU),DepartmentofPhysics,FacultyofScience,Fayoum63514,EgyptbAntwerpUniversity,ParticlePhysicsgro...

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Dijet azimuthal correlations in p-p and p-Pb collisions at forward LHC calorimeters M. Abdullah Al-MashadaA. van HamerencH. KakkaddP. Kotkod

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