Gluon Distribution Research Articles

Exclusive production of ρ meson in gamma-proton collisions: dσ/dt and the role of helicity flip processes

We calculate the differential cross section dσ/dt for the diffractive photoproduction process γp→ρp and compare to recent data extracted by the CMS collaboration from ultraperipheral proton-lead collisions. Our model is based on two-gluon exchange in the nonperturbative domain. We take into account both helicity conserving and often neglected helicity-flip amplitudes in the γ→V transition. The latter can contribute at finite t. The shape of the differential cross section as well as the role of helicity flip processes is strongly related to the dependence of the unintegrated gluon distribution on transverse momenta in the nonperturbative region.

First glimpse into the kaon gluon parton distribution using lattice QCD

In this work, we present the first results on the gluon parton distribution of the kaon from lattice quantum chromodynamics. We carry out the lattice calculation at pion mass around 310~MeV and two lattice spacings, 0.15 and 0.12~fm, using $2+1+1$-flavor HISQ ensembles generated by MILC Collaboration. The kaon correlators are calculated using clover fermions and momentum-smearing sources with maximum boost momentum around 2~GeV and high statistics (up to 324,000 measurements). We study the dependence of the resulting reduced Ioffe-time pseudo-distributions at multiple boost momenta and lattice spacings. We then extract the kaon gluon distribution function in the $\overline{\text{MS}}$ scheme at $\mu = 2$~GeV, neglecting the mixing between the gluon and singlet-quark sectors. Our results at the smaller lattice spacing are consistent with phenomenological determinations.

Impact of parton energy loss and nPDFs on J/ψ production in proton-nucleus collisions

The impact of parton energy loss and nuclear parton distribution functions (nPDFs) on J/ψ production in proton-nucleus collisions are investigated by means of the E866, LHC and RHIC experimental data. By the recent EPPS21 nPDFs, a leading order phenomenological analysis of J/ψ production cross-section ratios is performed for E866 experimental data with considering the parton energy loss effect following Landau-Pomeranchuk-Migdal (LPM) regime. The gluon transport coefficient qˆg extracted from the E866 data in 0.20<xF<0.65 region is qˆg=0.35±0.01 GeV2/fm with χ2/ndf=1.01, which indicates that the significantly better-constrained gluon distributions provided by EPPS21 contribute to accurately determining the gluon energy loss. It is founded that for E866 data in 0.20<xF<0.65 the depletion induced by cc¯ energy loss is the largest, gluon energy loss is the second, and quark energy loss is the smallest. In addition, it can be seen that for LHC and RHIC experiment the role of nPDFs and gluon energy loss on J/ψ production are both significant, which indicates that operating more precise measurements at LHC and RHIC in the future can facilitate significantly better-constrained gluon energy loss and nPDFs.

Unintegrated gluon distributions from the color dipole cross section in the BGK saturation model

We evaluate the unintegrated gluon distribution of the proton starting from a parametrization of the color dipole cross section including Dokshitzer–Gribov–Lipatov–Altarelli–Parisi (DGLAP) evolution and saturation effects. To this end, we perform the Fourier-Bessel transform of σ(x,r)/α(r). At large transverse momentum of gluons we match the so-obtained distribution to the logarithmic derivative of the collinear gluon distribution. We check our approach by calculating the proton structure function FL(x,Q2) finding good agreement with HERA data.

Disentangling quarks and gluons in CMS open data

We study quark and gluon jets separately using public collider data from the CMS experiment. Our analysis is based on 2.3/fb of proton-proton collisions at 7 TeV, collected at the Large Hadron Collider in 2011. We define two non-overlapping samples via a pseudorapidity cut -- central jets with |eta| < 0.65 and forward jets with |eta| > 0.65 -- and employ jet topic modeling to extract individual distributions for the maximally separable categories. Under certain assumptions, such as sample independence and mutual irreducibility, these categories correspond to "quark" and "gluon" jets, as given by a recently proposed operational definition. We consider a number of different methods for extracting reducibility factors from the central and forward datasets, from which the fractions of quark jets in each sample can be determined. The greatest stability and robustness to statistical uncertainties is achieved by a novel method based on parametrizing the endpoints of a receiver operating characteristic (ROC) curve. To mitigate detector effects, which would otherwise induce unphysical differences between central and forward jets, we use the OmniFold method to perform central value unfolding. As a demonstration of the power of this method, we extract the intrinsic dimensionality of the quark and gluon jet samples, which exhibit Casimir scaling, as expected from the strongly-ordered limit. To our knowledge, this work is the first application of full phase space unfolding to real collider data, and one of the first applications of topic modeling to extract separate quark and gluon distributions at the LHC.

An analysis of polarized parton distribution functions with nonlinear QCD evolution equations

We present the polarized parton distribution functions from a QCD analysis of the worldwide polarized deep inelastic scattering data, based on the dynamical parton distribution model. All the sea quarks and gluons are dynamically generated from QCD radiations, with the nonperturbative input comprising only the polarized valence quark distributions. This approach leads to a simple parametrization, which has only seven free parameters. In the analysis, we apply the DGLAP equations with parton-parton recombination corrections. For the first step, the DGLAP equations, parton-parton recombination corrections, and experimental observable g1 are all evaluated at the leading order. The parameterized nonperturbative input at an extremely low Q02 reproduces well the spin-dependent structure functions measured at high Q2. Comparisons with experimental observations and some other polarized parton distribution functions are also shown. Our results are in good agreement with the experimental data and consistent with some other parameterized models. Furthermore, our analysis presents the positive polarized gluon distribution and it suggests that the gluon distribution plays an important role to the proton spin content. The polarized antiquark distributions are non-zero at high Q2 but quite small compared to polarized valence quark distributions, based on this dynamical parton model analysis. This analysis gives smaller statistical uncertainties for the polarized sea quark and gluon distributions, thanks to the fewer free parameters used for the parametrization of the initial polarized PDFs.

Exclusive J/ψ and ϒ production in high-energy pp and p -Pb collisions

We present a formalism for determining the cross section for exclusive heavy vector meson production ($J/\ensuremath{\psi},\mathrm{\ensuremath{\Upsilon}}$) as a function of rapidity, in both high-energy proton-proton and proton-heavy ion collisions, at next-to-leading order in QCD. We compare and contrast the production in $pp$ and $p$-Pb collisions and show how data for these processes can give information on the low-$x$ gluon distribution of the proton and heavy ions at a range of different scales.

Gluon dipole factorisation for diffractive dijets

Within the colour dipole picture for deep inelastic scattering at small Bjorken x, we study the production of a pair of relatively hard jets via coherent diffraction. By “relatively hard” we mean that the transverse momenta of the two jets — the quark (q) and the antiquark ( overline{q} ) generated by the decay of the virtual photon — are much larger than the target saturation momentum Qs(Yℙ) evaluated at the rapidity gap Yℙ. We argue that the typical final-state configurations are such that the hard qoverline{q} dijets are accompanied by a semi-hard gluon jet, with a transverse momentum of the order of Qs(Yℙ). The presence of this third jet ensures that the scattering is strong and thus avoids the strong suppression of exclusive (hard) dijet production due to colour transparency. For such “2+1” jet configurations, we demonstrate that both the emission of the semi-hard gluon and its scattering with the hadronic target can be factorised in terms of an effective gluon-gluon dipole. This effective description, originally proposed in [1–7], builds a bridge between the colour dipole picture and the transverse-momentum dependent (TMD) version of the collinear factorisation: the cross-section for diffractive 2+1 jets can be written as the product between a hard factor describing the qoverline{q} dijets and a semi-hard factor expressing the unintegrated gluon distribution of the Pomeron. The latter is controlled by gluon dipole scattering in the black disk limit and hence is strongly sensitive to gluon saturation. By integrating out the kinematics of the 3 jets, we obtain the qoverline{q}g contribution to the diffractive structure function in collinearly-factorised form.

Exclusive J/ψ photoproduction in ultraperipheral Pb+Pb collisions at the CERN Large Hadron Collider calculated at next-to-leading order perturbative QCD

We present the first next-to-leading-order (NLO) perturbative QCD (pQCD) study of rapidity-differential cross sections of coherent exclusive photoproduction of $J/\psi$ mesons in heavy-ion ultraperipheral collisions (UPCs) at the LHC, $d\sigma/dy(\text{Pb} + \text{Pb} \rightarrow \text{Pb} + J/\psi + \text{Pb})$. For this, we account for the photon-nucleon NLO cross sections at the forward limit, the $t$ dependence using a standard nuclear form factor, and the photon fluxes of the colliding nuclei. Approximating the generalized parton distributions with their forward-limit parton distribution functions (PDFs), we quantify the NLO contributions in the cross sections, show that the real part of the amplitude and quark-PDF contributions must not be neglected, quantify the uncertainties arising from the scale-choice and PDFs, and compare our results with ALICE, CMS and LHCb $J/\psi$ photoproduction data in Pb+Pb UPCs, exclusive $J/\psi$ photoproduction data from HERA, and LHCb data in p+p. The scale dependence in $d\sigma/dy(\text{Pb} + \text{Pb} \rightarrow \text{Pb} + J/\psi + \text{Pb})$ is significant, but we can find a scale-choice that reproduces the Pb+Pb UPC data both at 2.76 and 5.02 TeV collision energies. This process has traditionally been suggested to be a direct probe of nuclear gluon distributions. We show that the situation changes rather dramatically from LO to NLO: the NLO cross sections reflect the nuclear effects of both gluons and quarks in a complicated manner where the relative signs of the LO and NLO terms in the amplitude play a significant role.

Anomalous diffusion in QCD matter

We study the effects of quantum corrections on transverse momentum broadening of a fast parton passing through dense QCD matter. We show that, at leading logarithmic accuracy the broadening distribution tends at late times or equivalently for large system sizes $L$ to a universal distribution that only depends on a single scaling variable $k^2_\perp/Q^2_s$ where the typical transverse momentum scale increases with time as $\ln Q_s^2 \simeq (1+2 \beta ) \ln L - \frac{3}{2}(1+\beta )\,\ln\ln L$ up to non-universal terms, with an anomalous dimension $\beta \sim \sqrt{\alpha_s} $. This property is analogous to geometric scaling of gluon distributions in the saturation regime and traveling waves solutions to reaction-diffusion processes. We note that since $\beta >0$ the process is super-diffusive, which is also reflected at large transverse momentum where the scaling distribution exhibits a heavy tail $k_\perp^{4-2\beta }$ akin to L\'{e}vy random walks.

Nuclear transverse momentum broadening in the color dipole approach at the LHC regime

Transverse momentum broadening of a parton propagating through a large nucleus is evaluated in the color dipole approach using different models for the dipole cross section or unintegrated gluon distribution, which lead to different values of the coefficient . Numerical calculations are compared to data extracted from LHCb, ALICE and PHENIX experiments for the nuclear broadening of J/ψ mesons. We find that different models which describe the small-x data predict values of nuclear broadening of transverse momentum that agree reasonably well with experiment. The centrality dependence was also analysed and the models are consistent with the ALICE measurements. Available experimental results, however, are not able to clearly distinguish the performance of the considered models.

D-meson production in high energy pA collisions within the QCD color dipole transverse momentum representation

The D-meson production is investigated by considering the unintegrated gluon distribution within the dipole approach in the momentum representation. We analyze the D-meson spectrum accounting for the effects of nonlinear behavior of the QCD dynamics which can be accordingly addressed in the dipole framework. The unintegrated gluon distribution is obtained by using geometric scaling property and the results are compared to the Glauber–Gribov framework. The absolute transverse momentum spectra and the nuclear modification ratios are investigated. Predictions are compared with the experimental measurements by the ALICE and LHCb Collaborations in pA collisions for different rapidity bins.

Universality aspects of quantum corrections to transverse momentum broadening in QCD media

We study non-linear quantum corrections to transverse momentum broadening (TMB) of a fast parton propagating in dense QCD matter in the leading logarithmic approximation. These non-local corrections yield an anomalous super-diffusive behavior characterized by a heavy tailed distribution which is associated with Lévy random walks. Using a formal analogy with the physics of traveling waves, we show that at late times the transverse momentum distribution tends to a universal scaling regime. We derive analytic solutions in terms of an asymptotic expansion around the scaling limit for both fixed and running coupling. We note that our analytic approach yields a good agreement with the exact numerical solutions down to realistic values of medium length. Finally, we discuss the interplay between system size and energy dependence of the diffusion coefficient hat{q} and its connection with the gluon distribution function that is manifest at large transverse momentum transfer.

QCD factorization of quasi generalized quark distributions

We study the factorization of quasi generalized quark distributions with twist-2 generalized parton distributions. We use an approach which is different than that used in literature. Using the approach we derive the factorization relations of all quasi generalized quark distributions at one-loop. The contributions from twist-2 generalized gluon distributions are included. Our results apply not only to the quasi distributions of a spin-1/2 hadron but also to those of a hadron with any spin.

T-odd quark-gluon-quark correlation function in the light-front quark-diquark model

We have scrutinized the transverse momentum dependent quark–gluon–quark correlation function. We have utilized the light-front quark-diquark model to study the time-reversal-odd interaction-dependent twist-3 gluon distributions which we have obtained from the disintegration of the transverse momentum dependent quark–gluon–quark correlator. Specifically, we have studied the behavior of \tilde{e}_{L}ẽL and \tilde{e}_{T}ẽT while considering our diquark to be an axial-vector.

Exclusive emissions of rho-mesons and the unintegrated gluon distribution

Exclusive emissions of vector mesons in forward directions of rapidity offer us a faultless chance to probe the proton structure at small xx. A high-energy factorization formula is established within BFKL, given as the convolution of an impact factor depicting the forward-meson emission and of an unintegrated gluon distribution (UGD) driving the gluon evolution at small xx. As a nonperturbative quantity, the UGD is not well known and several models for it exist. We present recent progresses on the study of the exclusive forward \rhoρ-meson leptoproduction at HERA and EIC energies, showing how osbervables sensitive to different polarization states of the \rhoρ-particle act as discriminators for the existing UGD models.

Azimuthal correlations in diffractive scattering at the Electron-Ion Collider

We calculate azimuthal correlations between the exclusively produced vector meson and the scattered electron in Deep Inelastic Scattering processes at the future Electron-Ion Collider (EIC). We identify ``kinematical'' and ``intrinsic'' contributions to these correlations, and show that the correlations are sensitive to the non-trivial correlations in the gluon distribution of the target. Realistic predictions at the EIC kinematics are provided using two different approaches to describe the dipole-proton interaction at relatively small x.

Central exclusive production of $\eta_c$ and $\chi_{c0}$ in the light-front k$_{\perp}-factorization approach

We study the exclusive production of J^{PC} = 0^{++},0^{-+}JPC=0++,0−+ charmonium states in proton-proton collisions at the LHC energies. The pp \to pp\eta_cpp→ppηc reaction is discussed for the first time. We observe a substantial contribution from the nonperturbative domain of gluon virtualities, especially for \eta_cηc production. To model the nonperturbative region better, we utilize models of the unintegrated gluon distribution based on parametrizations of the color dipole cross-section.

A novel formulation of the unintegrated gluon distribution for DIS

In this talk, we revisit inclusive DIS in the small x limit and derive a new factorization formula that accounts for leading powers in both Bjorken and Regge limits. In this semi-classical description, we obtain a new unintegrated gluon distribution which encompasses both the dipole operator and the gluon Parton Distribution Function with an explicit dependence on the longitudinal momentum fraction x.

Dijet production at EIC and interplay of Sudakov and saturation effects in Weizsacker-Williams TMD gluon distribution

We study production of dijets at the EIC using the small-x Improved Transverse Momentum Dependent factorization (ITMD), which is a framework based on the Color Glass Condensate theory. Dijet production in DIS is the simplest process directly coupled to the Weizsäcker-Williams TMD gluon distribution, which is the only small-x gluon distribution possessing the gluon number density interpretation. We study various observables sensitive to the interplay of the Sudakov effects and the nonlinear effects, in particular the azimuthal correlations between the jet system and the scattered electron.