Parton Distributions Research Articles

Krylov complexity and gluon cascades in the high energy limit

We point out an interesting connection between the mathematical framework of the Krylov basis, which is used to quantify quantum complexity, and the entanglement entropy in high energy QCD. In particular, we observe that the cascade equation of the dipole model is equivalent to the SL(2,R) Schrödinger equation in the Krylov basis. Consequently, the Krylov complexity corresponds to the average distribution of partons and the Krylov entropy is the counterpart of the entanglement entropy computations of [D. E. Kharzeev and E. M. Levin, .]. Our work not only brings new tools for exploring quantum information and complexity in QCD, but also gives hope for experimental tests of some of the recent, physical probes of quantum complexity. Published by the American Physical Society 2024

Parton distribution functions and fragmentation functions of spin-1 hadrons

Parton distribution functions and fragmentation functions of spin-1 hadrons

Transverse-momentum dependent model for hadronization in deep-inelastic lepton-nucleus scattering off heavy nuclei

Semi-inclusive deep inelastic scattering off nuclei is a unique process to study the parton propagation mechanism and its modification induced by the presence of the nuclear medium. It allows us to probe the medium properties, particularly the cold nuclear matter transport coefficient, which can be directly linked to the nuclear gluon density. We present here a model for hadron production in deep inelastic lepton-nucleus scattering, which takes into account the hadronic transverse momentum of final state particles via transverse-momentum dependent parton distributions and fragmentation functions. We implement parton energy loss and hadronic absorption with a geometrical model of the nucleus. The model is compared with the nuclear semi-inclusive deep-inelastic scattering multiplicity ratios and transverse-momentum broadening data from the CLAS, HERMES, and EMC collaborations, aiming for a simultaneous description of these data sets. We obtain a good agreement over the various nuclear targets and the wide kinematical range of those experiments. We best describe the data with a transport coefficient q̂=0.3GeV/fm2, and we highlight the importance and the role of correlations in extracting this quantity. Published by the American Physical Society 2024

Next-to-Next-to-Leading Order Global Analysis of Polarized Parton Distribution Functions.

We present a next-to-next-to-leading order (NNLO) global QCD analysis of the proton's helicity parton distribution functions, the first of its kind. To obtain the distributions, we use data for longitudinal spin asymmetries in inclusive and semi-inclusive lepton-nucleon scattering as well as in weak-boson and hadron or jet production in proton-proton scattering. We analyze the data using QCD perturbation theory at NNLO accuracy, employing approximations provided by the threshold resummation formalism in cases where full NNLO results for partonic hard-scattering functions are not readily available. Our numerical results suggest a remarkable perturbative stability of the extracted helicity parton distribution functions.

Quasiparton distributions in massive QED2: Toward quantum computation

We analyze the quasiparton distributions of the lightest η′ meson in massive two-dimensional quantum electrodynamics (QED2) by exact diagonalization. The Hamiltonian and boost operators are mapped onto spin qubits in a spatial lattice with open boundary conditions. The lowest excited state in the exact diagonalization is shown to interpolate continuously between an anomalous η′ state at strong coupling, and a nonanomalous heavy meson at weak coupling, with a cusp at the critical point. The boosted η′ state follows relativistic kinematics but with large deviations in the luminal limit. The spatial quasiparton distribution function and amplitude for the η′ state are computed numerically for increasing rapidity both at strong and weak coupling, and compared to the exact light front results. The numerical results from the boosted form of the spatial parton distributions, compare fairly with the inverse Fourier transformation of the luminal parton distributions, derived in the lowest Fock space approximation. Our analysis points out some of the limitations facing the current lattice program for the parton distributions. Published by the American Physical Society 2024

Nuclear suppression of coherent J/ψ photoproduction in heavy-ion ultraperipheral collisions and leading twist nuclear shadowing

We determine the nuclear suppression factor SPb(x), where x=MJ/ψ2/Wγp2 with MJ/ψ the J/ψ mass and Wγp the photon-nucleon energy, for the cross section of coherent J/ψ photoproduction in heavy-ion ultraperipheral collisions at the Large Hadron Collider and Relativistic Heavy Ion Collider by performing the χ2 fit to all available data on the cross section dσAA→J/ψAA/dy as a function of the J/ψ rapidity y and the photoproduction cross section σγA→J/ψA(Wγp) as a function of Wγp. We find that while the dσAA→J/ψAA/dy data alone constrain SPb(x) for x≥10−3, the combined dσAA→J/ψAA/dy and σγA→J/ψA(Wγp) data allow us to determine SPb(x) in the wide interval 10−5<x<0.05. In particular, the data favor SPb(x), which decreases with a decrease of x in the 10−4<x<0.01 interval and can be both decreasing or constant for x<10−4. Identifying SPb(x) with the ratio of the gluon distributions in Pb and the proton Rg(x,Q02)=gA(x,Q02)/[Agp(x,Q02)], we demonstrate that the leading twist approximation for nuclear shadowing provides a good description of all the data on dσAA→J/ψAA/dy and σγA→J/ψA(Wγp) as well as on the experimental values for SPb(x) derived from σγA→J/ψA(Wγp). We also show that modern nuclear parton distributions reasonably reproduce SPb(x) as well. Published by the American Physical Society 2024

TMD Relations: Insights from a Light-Front Quark–Diquark Model

Abstract In this work, we have established the relations between the T-even proton transverse-momentum-dependent parton distributions (TMDs) at all twist levels up to twist-4 using the light-front quark–diquark model. From the parameterization equations of TMDs, we have found that there are multiple ways by which a particular TMD can be expressed in terms of the initial and final helicity states of the proton. For the first time, we have presented a parameterization table that can be applied to the derivation and recognition of proton TMDs based on their helicity. We have constructed the linear and quadratic relationships of TMDs at the intra- and intertwist levels within the same model. We have also looked at the inequality relations that TMDs follow. Additionally, to provide easy access to the calculations, amplitude matrices have been expressed in the form of TMDs over all the possible helicities of the diquark.

Valence quark PDFs of the proton from two-current correlations in lattice QCD

Following previous works on that topic, we consider Euclidean hadronic matrix elements in position space of two spatially separated local currents on the lattice, in order to extract the x dependence of parton distribution functions (PDFs). The corresponding approach is often referred to by the term . In this work we will consider valence quark PDFs of an unpolarized proton. We adapt the previously established formalism to our choice of operators. The calculation of the two-current matrix elements requires the evaluation of four-point functions. The corresponding calculation is carried out on a nf=2+1 gauge ensemble with lattice spacing a=0.0856 fm and pseudoscalar masses mπ=355 MeV and mK=441 MeV. The four-point functions have been evaluated in a previous project. The lattice data is converted to the MS¯ scheme at a scale μ=2 GeV and improved with respect to lattice artifacts. We use a common model as fit ansatz for the lattice data in order to extract the PDFs. Published by the American Physical Society 2024

An FONLL prescription with coexisting flavor number PDFs

We present a new prescription to account for heavy quark mass effects in the determination of parton distribution functions (PDFs) based on the FONLL scheme. Our prescription makes explicit use of the freedom to choose the number of active flavors at a given scale and, thus, use coexisting PDFs with different active flavor number. This new prescription is perturbatively equivalent to the former but improves the implementation in two ways. First, it can be naturally generalized to account simultaneously for multiple heavy quark effects, such as charm and bottom effects, which can both be relevant at the same scale due to the small mass difference. Second, it can be trivially generalized to use at any fixed-order or collinear resummed accuracy, while previous prescriptions required ad-hoc expansions of the DGLAP evolution kernels for each coefficient. We supplement the paper with codes for the computation of deep inelastic scattering observables in this new prescription.

Nonlocal chiral contributions to generalized parton distributions of the proton at nonzero skewness

We compute the one-loop contributions to spin-averaged generalized parton distributions (GPDs) in the proton from pseudoscalar mesons with intermediate octet and decuplet baryon states at nonzero skewness. Our framework is based on nonlocal covariant chiral effective theory, with ultraviolet divergences regularized by introducing a relativistic regulator derived consistently from the nonlocal Lagrangian. Using the splitting functions calculated from the nonlocal Lagrangian, we find the nonzero skewness GPDs from meson loops by convoluting with the phenomenological pion GPD and the generalized distribution amplitude, and verify that these satisfy the correct polynomiality properties. We also compute the lowest two moments of GPDs to quantify the meson loop effects on the Dirac, Pauli, and gravitational form factors of the proton. Published by the American Physical Society 2024

Moments of parton distribution functions of any order from lattice QCD

We describe a procedure to determine moments of parton distribution functions of any order in lattice quantum chromodynamics (QCD). The procedure is based on the gradient flow for fermion and gauge fields. The flowed matrix elements of twist-2 operators renormalize multiplicatively, and the matching with the physical matrix elements can be obtained using continuum symmetries and the irreducible representations of Euclidean 4-dimensional rotations. We calculate the matching coefficients at one-loop in perturbation theory for moments of any order in the flavor nonsinglet case. We also give specific examples of operators that could be used in lattice QCD computations. It turns out that it is possible to choose operators with identical Lorentz indices and still have a multiplicative matching. One can thus use twist-2 operators exclusively with temporal indices, thus substantially improving the signal-to-noise ratio in the computation of the hadronic matrix elements. Published by the American Physical Society 2024

Study of intrinsic-kT in the Parton Branching Method

The work presented here focuses on the production of Drell-Yan lepton pairs in hadron-hadron collisions with very low transverse momentum which is sensitive to the contribution from the non-perturbative transverse motion of partons inside hadrons as well as to the multiple soft gluon emissions which have to be resumed. To study the two contributions, we use Parton Branching Method which describes the evolution of transverse momentum dependent parton distributions and provides very precise predictions for inclusive observables such as the Drell–Yan cross section as a function of transverse momentum. In this study, we tune a parameter that describes the internal transverse motion of partons within hadron (intrinsic-kT) depending on the soft gluon contribution which is varied applying a lower limit to the transverse momentum of the emitted parton in branching up to 2 GeV. It will be shown that the parameter presented by the width of the Gaussian distribution increases with the minimal transverse momentum. This means that by reducing the contribution of soft gluons, more intense internal transverse motion is required (larger intrinsic-kT) to describe experimental data. Moreover, it was observed that the value of the intrinsic-kT increases with the collision energy and such a trend is more pronounced when the minimum transverse momentum of the parton at the branching is higher.

Factorization for J/ψ leptoproduction at small transverse momentum

Nonrelativistic Quantum Chromodynamics (NRQCD) breaks down in the region of low transverse momentum, where the transverse momentum of the produced quarkonium state is sensitive to multiple scattering with the incoming hadron and to soft gluon radiation. In this kinematic regime, the transverse-momentum-dependent (TMD) factorization framework is required, promoting the long-distance matrix elements (LDMEs) of NRQCD to the so-called TMD shape functions (TMDShFs), which encode both the soft gluon radiation and the formation of the heavy-quark bound state. In this work, we apply an effective-field theory approach (combining NRQCD and SCET) to the photon-gluon fusion process in inclusive J/ψ leptoproduction. We derive a factorization theorem for the cross section in terms of TMDShFs, compute these quantities at next-to-leading order, establish their evolution, and study their matching onto the corresponding LDMEs in the high-transverse-momentum region. Our results are particularly relevant to the Electron-Ion Collider, where J/ψ leptoproduction can be used to probe gluon transverse-momentum-dependent parton distribution functions (gluon TMDPDFs).

Twist analysis of the spin-orbit correlation in QCD

We present a QCD analysis of the twist-three parton distribution functions associated with the spin-orbit correlation of quarks and gluons in spin-12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\frac{1}{2} $$\\end{document} and spin-0 hadrons. We derive exact non-perturbative identities decomposing the spin-orbit correlations into the Wandzura-Wilczek part and the genuine twist-three part. In the spin-12\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\frac{1}{2} $$\\end{document} case, the result is partially related to the kinematical twist-three part of the gT (x) distribution familiar in the context of transverse spin physics. We use these identities to obtain a novel longitudinal momentum sum rule which may be regarded as the momentum version of the Jaffe-Manohar spin sum rule. We explore the physical interpretation of the sum rule and make a connection to the color Lorentz forces and their associated potential energies.

Exclusive photoproduction of ηcγ pairs with large invariant mass

In this manuscript, we analyze the exclusive photoproduction of ηcγ pairs in the collinear factorization framework and evaluate its cross section in leading order in the strong coupling αs. We found that this channel is mostly sensitive to the behavior of the unpolarized gluon generalized parton distributions Hg in the Efremov-Radyushkin-Brodsky-Lepage kinematics. We estimated numerically the cross section and the expected counting rates in the kinematics of middle-energy photoproduction experiments, which can be realized at the future Electron-Ion Collider or in the ultraperipheral collisions at LHC. We found that the cross section is sufficiently large for dedicated experimental study. We also estimated the role of this process as a potential background to ηc photoproduction, which is considered as one of the possible gateways for studies of t-channel odderons. We found that the contribution of ηcγ (with undetected photon) is on par with expected contributions of odderons in the kinematics of small momentum transfer |t|≲0.5 GeV2, though decreases rapidly at larger |t|. Published by the American Physical Society 2024

Spin-orbit correlations in the nucleon in the large- Nc limit

We study the twist-3 spin-orbit correlations of quarks described by the nucleon matrix elements of the parity-odd rank-2 tensor QCD operator (the parity-odd partner of the QCD energy-momentum tensor). Our treatment is based on the effective dynamics emerging from the spontaneous breaking of chiral symmetry and the mean-field picture of the nucleon in the large-Nc limit. The twist-3 QCD operators are converted to effective operators, in which the QCD interactions are replaced by spin-flavor-dependent chiral interactions of the quarks with the pion field. We compute the nucleon matrix elements of the twist-3 effective operators and discuss the role of the chiral interactions in the spin-orbit correlations. We derive the first-quantized representation in the mean-field picture and develop a quantum-mechanical interpretation. The chiral interactions give rise to new spin-orbit couplings and qualitatively change the correlations compared to the quark model picture. We also derive the twist-3 matrix elements in the topological soliton picture where the quarks are integrated out (skyrmion). The methods used here can be extended to other QCD operators describing higher-twist nucleon structure and generalized parton distributions. Published by the American Physical Society 2024

AAK24: Global QCD analysis on polarized parton distribution in the presence of $$A_2$$ asymmetry measurements

AAK24: Global QCD analysis on polarized parton distribution in the presence of $$A_2$$ asymmetry measurements

Chiral-odd GPDs in the bag model

A study of chiral-odd generalized parton distributions (GPDs) of the nucleon is presented in the bag model demonstrating that in this model all four chiral-odd GPDs are nonzero contrary to other claims in literature. The bag model results for the GPDs HTq(x,ξ,t), ETq(x,ξ,t), H˜Tq(x,ξ,t) agree with other models within a typical quark model accuracy. We present one of the few quark model calculations where polynomiality is satisfied and the sum rule ∫dxE˜Tq(x,ξ,t)=0 holds. We confront our results with predictions from the large-Nc limit, and with lattice QCD calculations. We conclude that the bag model successfully catches the main features of chiral-odd GPDs. Published by the American Physical Society 2024

LO, NLO, and NNLO parton distributions for LHC event generators

We present NNPDF4.0MC, a variant of the NNPDF4.0 set of parton distributions (PDFs) at LO, NLO and NNLO, with and without inclusion of the photon PDF, suitable for use with Monte Carlo (MC) event generators, which require PDFs to satisfy additional constraints in comparison to standard PDF sets. These requirements include PDF positivity down to a low scale Q ~ 1 GeV, smooth extrapolation in the very small and large x regions, and numerically stable results even in extreme regions of phase space for all PDFs. We compare the NNPDF4.0MC PDFs to their baseline NNPDF4.0 counterparts, and to the NNPDF2.3LO set entering the Monash tune of the Pythia8 event generator. We briefly assess the phenomenological impact of these PDFs on the cross-sections for hard and soft QCD processes at the LHC.

Effect of anisotropy on the formation of heavy quarkonium bound states

We study the real part of the static potential of a heavy quark-antiquark system in an anisotropic plasma medium. We use a quasiparticle approach where the collective dynamics of the plasma constituents is described using hard-loop perturbation theory. The parton distribution function is characterized by a set of parameters that can accurately describe the anisotropy of the plasma produced in a heavy ion collision. We calculate the potential numerically in strongly anisotropic systems and study the angular dependence of the distortion of the potential relative to the isotropic one. We obtain an analytic expression for the real part of the heavy quark potential in the limit of weak anisotropy using a model that expresses the potential in terms of effective screening masses that depend on the anisotropy parameters and the orientation of the quark-antiquark pair. A one-dimensional potential is formulated in terms of angle averaged screening masses that incorporate the anisotropy of the medium into a radial coordinate. We solve the corresponding Schrödinger equation and show that the magnitude of the binding energy typically increases with anisotropy. Anisotropy can play an important role, especially in states with nonzero angular momentum. This means that the number of bound states that are formed could depend on specific characteristics of the anisotropy of the plasma. Our study suggests that plasma anisotropy plays an important role in the dynamics of heavy quarkonium and motivates further study. Published by the American Physical Society 2024