Exploring the phenomena of Gluon saturation via dijet production in proton-proton and proton-lead collisions at the LHC

The differential cross sections with respect to the azimuthal angle between two jets were computed using the KaTie Monte Carlo program (downloaded from https://bitbucket.org/hameren/katie/downloads/) within the Small-x Improved TMD (ITMD) factorization. We considered the proton-proton and proton-lead collisions at √s=5.02TeV, 8.16 TeV, and 8.8 TeV per nucleon. For proton-proton collisions, we also computed the proton-proton differential cross section for √s=14 TeV. To define the leading and the sub-leading jet, we used the anti-kT jet clustering algorithm with a radius of R = 0.4.

Motivated by the current and planned LHC experiments, we applied the following cuts to the transverse momentum of these jets:
i) 28 GeV < pT 1, pT 2 < 35 GeV,
ii ) 35 GeV < pT 1, pT 2 < 45 GeV,
iii ) 35 GeV < pT 1 < 45 GeV and 28 GeV < pT 2 < 35 GeV,
iv ) pT 1, pT 2 > 10 GeV,
v ) pT 1, pT 2 > 20 GeV.
Specifically, we used the first three cuts i) − iii) for the transverse momentum of the jets in the rapidity range 2.7 < y⋆1 , y⋆2 < 4.0, both for proton-proton and proton-lead collisions at √s =8.16 TeV. These cuts correspond to the FCal calorimeter of the ATLAS detector. The last two cuts iv)−v) were applied in the rapidity range 3.8 < y⋆1 , y⋆2 <5.1, both for proton-proton and proton-lead collisions at √s = 5.02 TeV, and 8.8 TeV energies per nucleon. These correspond to the planned FoCal extension of the ALICE detector. For the same kinematic domain (rapidity and transverse momentum cuts for the jets), we also considered protons collisions at √s = 14 TeV (proton-lead collisions are not feasible at this energy).

The factorization and renormalization scales were set using the transverse momentum of the leading and the sub-leading jets μ = (pT 1 + pT 2)/2. To account for errors we vary this value by a factor of 1/2 and 2. That is, for each cut we run KaTie 3 times for the three values of the factorization scale. For the TMD gluon distributions, we used the Kutak-Sapeta (KS) gluons (downloaded from http://nz42.ifj.edu.pl/~sapeta/itmd-KS.tar.gz). For the collinear PDFs, we used the CTEQ10NLO PDF set from LHAPDF6 (https://lhapdf.hepforge.org/pdfsets.html). In our computations, we used the ITMD factorization alone, without parton shower or hadronization corrections. To assess this effect, we computed cross section with PYTHIA (available at https://pythia.org/) version 8.307 with the default tunes. We used the NNPDF23NLO set to describe the proton structure, and nCTEQ15WZ set for the nuclear PDF necessary for the simulation of p-Pb collisions. We computed cross sections with all corrections turned on in PHYTIA, and then just with initial-state parton shower. The latter roughly corresponds to the TMD framework, therefore both calculations allow for the extraction of a “correction factor”. We repeated the same procedure using the nucler PDFs in PYTHIA. We then applied that correction to KaTie results.

All the data files generated are attached below.