Impact of inclusive jet cross sections with low transverse momenta on the determination of gluon parton distributions in pp collisions D. Sunar Cerci1 S. Cerci1 and K. Wichmann2

2025-05-08 0 0 741.31KB 13 页 10玖币

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Impact of inclusive jet cross sections with low transverse momenta

on the determination of gluon parton distributions in pp collisions

D. Sunar Cerci∗1, S. Cerci1, and K. Wichmann2

1Adiyaman University, Faculty of Arts and Sciences, Department of Physics, Turkiye

2Deutsches Elektronen-Synchrotron DESY, Hamburg, Germany

Abstract

Jet production at hadron colliders provides constraints on the parton distribution functions

(PDFs) of the proton, in particular on the gluon distribution. In the present paper, the impact

on PDF of CMS inclusive diﬀerential jet cross sections at center-of-mass energy of √s= 8

TeV for jets with low momentum pTand produced in the forward direction is investigated

at next-to leading order in perturbative quantum chromodynamics (QCD). The results of the

QCD global analysis are compared with theoretical predictions. The impact of low-pTjet

measurements on the determination of the gluon distribution is assessed. The inclusion of the

discussed measurements adds further constraints on uncertainty of the gluon distribution at

large Bjorken x > 0.1, where the low-pTdata have the largest impact.

1 Introduction

The parton distribution functions (PDFs) represent the probability densities to ﬁnd a parton in the

proton carrying a momentum fraction xat a squared energy scale and are an essential ingredient

for precise knowledge of the structure of the proton. The factorization scale dependence of PDFs is

purely perturbative and can be determined by the DGLAP evolution equations [1, 2, 3]. However,

the dependence on the momentum fraction is non-perturbative and it has to be extracted from

experimental measurements. Deep inelastic scattering (DIS) data from HERA [4] are core of any

PDF extraction, covering a big part of the kinematic phase space, with the Bjorken xdown to

x < 10−5and the negative four-momentum-transfer squared Q2up to 50000 GeV2.

With the start of LHC data taking, more and more pp data is included in the global QCD

analyses to improve determination of parton distributions in the proton. Jet and t¯

tproduction

cross sections can provide new constrain on gluon distribution. The production of W or Z bosons

at the LHC is used in particular to improve the knowledge of valence distributions. These data are

also indirectly sensitive to the strange quark distribution. The direct constrains on the strange sea

is coming from the LHC measurements of W+charm cross sections. All these data are now used in

PDF determinations of various collaborations, like CT18 [5], MSHT20 [6], NNPDF4 [7], ABMP [8],

JR [9], and CJ [10].

The xFitter [11, 12] is an open-source platform that allows to extract PDFs and to assess the

impact of new data. A variety of theoretical predictions for diﬀerent processes together with a large

number of existing methods for determining the proton and nuclear PDFs and model parameters

∗e-mail: deniz.sunar.cerci@cern.ch

arXiv:2210.04592v2 [hep-ph] 20 Nov 2022

(like the strong coupling or quark masses) are available in the modular structure of xFitter. It

is extensively used by the CMS and ATLAS collaborations to study the impact of their data in

determination of parton densities. Some examples are given here [13, 14, 15, 16, 17, 18].

2 Analysis setup

2.1 Theoretical framework

In this paper, the xFitter version 2.0.0 is used to estimate the impact of the CMS inclusive low-

pTjet cross section measurement at √s= 8 TeV [16] on the PDFs and their uncertainties. A

PDF ﬁt at next-to-leading order (NLO) is performed, using the HERA DIS cross sections [4],

and the jet cross sections [16]. In xFitter the parton distributions are evolved using the DGLAP

equations at diﬀerent orders in QCD, as implemented in the QCDNUM program [19]. The heavy-

quark contributions are treated using the generalised-mass variable-ﬂavour number Roberts-Thorne

scheme [20, 21, 22]. Here the charm and beauty quark masses are model parameters and are ﬁxed

to mc= 1.46 ±0.04 GeV and mb= 4.3±0.1 GeV, respectively, following the newest estimates from

HERA [23]. The theoretical predictions for the cross sections of jet production are calculated at

NLO by using the NLOJET++ program [24, 25] as implemented into the FASTNLO package [26].

The factorisation and renormalisation scales are set to the four-momentum transfer (Q) for the DIS

processes i.e, µf=µr=pQ2and to the jet pTin case of the CMS jet cross sections. The PDF

extraction is done using a χ2minimization method, as implemented in MINUIT [27] framework. In

the results presented here a cut on minimum Q2of the HERA data, Q2

min ≥7.5 GeV2, is required.

Also all ﬁgures presented in this study, excluding Fig. 1 are done using xFitter.

2.2 Jet data

In this paper the CMS inclusive jet measurement at 8 TeV [16] is considered. It includes two sets

of jet data, one of which is named high-pTand the other is low-pT. The pTranges considered

in the low-pTand high-pTjet analyses are 21 −74 GeV and 74 −2500 GeV, respectively. These

double-diﬀerential inclusive jet cross sections are shown in Fig. 1 [16]. The data included in the

high-pTjet measurement are collected using six single-jet triggers in the high-level trigger system

requiring at least one jet in the event with jet pT>40,80,140,200,260,and 320 GeV, while events

for the low-pTjet analysis are selected online in an unbiased way by triggering the low average

number of pp interactions per bunch crossing, or pileup.

The infrared and collinear safe anti-kTjet clustering algorithm [28] is used to reconstruct jets

with a distance parameter of R= 0.7. The inputs to the jet clustering algorithm are the four-

momentum vectors of particle-ﬂow objects. Individual particles (leptons, photons, charged and

neutral hadrons) are reconstructed with the particle-ﬂow technique [29] which combines the infor-

mation from several sub-detectors.

In order to account for various experimental eﬀects, the raw jet pTspectra are corrected. The

reconstructed jet energy is calibrated with correction factors derived using real data, via a pT-

balancing method in dijet and in photon-jet events, as well as from MC simulations [30, 31]. The

jet energy scale (JES) correction is applied to the jet four-momentum vector as a multiplicative

factor. It depends on the ηand pTof the jet. The JES corrections are diﬀerent for both analyzes,

especially in pT-dependent components. This also contributes to ﬂuctuations in the transition

between the low- and high-pTjet regions. Although this causes some discontinuity to be observed

in the measured values, both analyzes are generally compatible in terms of total experimental

uncertainties. Since the initial part of the 2012 low pileup data sample was used in the low-pT

[GeV]

Jet p

30 40 100 200 300 1000 2000

GeV

dp σ

7−

4−

1−

10 8 TeV

CMS

-1

= 5.6 pb

int

Open: L -1

= 19.7 fb

int

Filled: L

EWK ⊗ NP ⊗CT10 NLO NP ⊗CT10 NLO

)

10×|y| < 0.5 ( )

10×0.5 < |y| < 1.0 ( )

10×1.0 < |y| < 1.5 ( )

10×1.5 < |y| < 2.0 ( )

10×2.0 < |y| < 2.5 ( )

10×2.5 < |y| < 3.0 ( )

10×3.2 < |y| < 4.7 (

Figure 1: CMS double-diﬀerential inclusive jet cross sections at 8 TeV [16] shown as function of jet

pT. The low-pTdata are represented by open points and the high-pTdata by ﬁlled points.

jet analysis, there is no JES time dependence and the pileup-related corrections are negligible.

Systematic uncertainty sources for the high-pTand low-pTjet data sets are treated as correlated,

except for those with the pileup-related corrections and JES time dependence which are assumed

to be uncorrelated.

The high-pTjet data set has already been used in a global QCD analysis in the CMS publi-

cation [16] to extract parton densities and αs(M2

Z). This analysis illustrated that the high-pTjet

cross sections provide important constraints on the gluon distributions in a new corner of kinematic

phase space.

2.3 Parameterisation

In the QCD analysis we use the approach of HERAPDF [4], where the PDFs of the proton, xf,

are parameterised at the starting scale µ2

f0= 1.9 GeV2in a general way as

xf(x) = AxB(1 −x)C(1 + Dx +Ex2).(1)

Here xis the fraction of the proton’s momentum taken by the struck parton in the inﬁnite momen-

tum frame. The parameterisations for the following PDFs are used: the gluon distribution, xg, the

valence quark distributions, xuv,xdv, and the u-type and d-type anti-quark distributions, x¯

U,x¯

We assume that x¯

U=x¯uand x¯

D=x¯

d+x¯sat the starting scale µ2

f0.

The nominal parameterisation used in the studies presented here is

xg(x) = AgxBg(1 −x)Cg−A0

gxB0

g(1 −x)C0

g,(2)

xuv(x) = AuvxBuv(1 −x)Cuv1 + Duvx+Euvx2,(3)

xdv(x) = AdvxBdv(1 −x)Cdv,(4)

x¯

U(x) = A¯

UxB¯

U(1 −x)C¯

U(1 + D¯

Ux),(5)

x¯

D(x) = A¯

DxB¯

D(1 −x)C¯

D1 + E¯

Dx2.(6)

As can be seen from Eq. 2 the gluon distribution, xg, is an exception from Eq. 1, from which an

additional term of the form A0

gxB0

g(1 −x)C0

gis subtracted1.Auv, AdvandAgare the normalisation

1In this analysis, C0

gis ﬁxed to C0

g= 25 [32], following [4].

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ImpactofinclusivejetcrosssectionswithlowtransversemomentaonthedeterminationofgluonpartondistributionsinppcollisionsD.SunarCerci*1,S.Cerci1,andK.Wichmann21AdiyamanUniversity,FacultyofArtsandSciences,DepartmentofPhysics,Turkiye2DeutschesElektronen-SynchrotronDESY,Hamburg,GermanyAbstractJetproductionat...

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Impact of inclusive jet cross sections with low transverse momenta on the determination of gluon parton distributions in pp collisions D. Sunar Cerci1 S. Cerci1 and K. Wichmann2

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