Generalized Valon Model for Double Parton Distributions

We present the construction of unintegrated double parton distribution\nfunctions which include dependence on transverse momenta of partons. We extend\nthe formulation which was used to obtain the single unintegrated parton\ndistributions from the standard, integrated parton distribution functions.\nStarting from the homogeneous part of the evolution equations for the\nintegrated double parton distributions, we construct the unintegrated double\nparton distributions as the convolutions of the integrated double distributions\nand the splitting functions, multiplied by the Sudakov form factors. We show\nthat there exist three domains of external hard scales which require three\ndistinct forms of the unintegrated double distributions. The additional\ntransverse momentum dependence which arises through the Sudakov form factors\nleads to non-trivial correlations in the parton momenta. We also discuss the\nnon-homogeneous contribution to the unintegrated double parton distributions,\nwhich arises due to the splitting of a single parton into daughter partons with\nhigh transverse momenta. We analyze two cases, the unfolding of the transverse\nmomenta dependence from the last step of the evolution of two partons, and the\ncase where the transverse momenta are generated directly from the single parton\nsplitting.\n

Double parton scattering (DPS) has become very relevant as a background to interesting analyses performed by the experiments at the LHC. It encodes knowledge of correlations between the proton constituents not accessible in single parton scattering. Within perturbative QCD DPS is described in terms of partonic subprocesses and double parton distributions (DPDs). There exists a large number of different DPDs describing the different possible states of two partons inside a proton. They include correlations between the two partons and interferences between the two hard subprocesses. Taking the probability interpretation of the DPDs as starting point, we derive limits on the interference DPDs and thereby constrain the size of correlations between two partons inside an unpolarized proton.

In this paper, we address double parton scattering (DPS) in pA collisions. Within the Light-Front approach, we formally derive the two contributions to the nuclear double parton distribution (DPD), namely: DPS1, involving two partons from the same nucleon, and DPS2, where the two partons belong to different parent nucleons. We then generalize the sum rule for hadron DPDs to the nuclear case and analytically show how all contributions combine to give the expected results. In addition partial sum rules for the DPDs related to DPS1 and DPS2 mechanisms are discussed for the first time. The deuteron system is considered for the first calculation of the nuclear DPD by using a realistic wave function obtained from the very refined nucleon-nucleon AV18 potential, embedded in a rigorous Poincaré covariant formalism. Results are used to test sum rules and properly verify that DPS1 contribution compares with the DPS2 one, although smaller. We also introduce EMC-like ratios involving nuclear and free DPDs to address the potential role of DPS in understanding in depth the EMC effect.

We study parton distributions for two partons, a quark and a gluon, in the light-front dressed quark model, with focus on correlations between the two partons. The model calculation leads to sizable spin-spin and spin-kinematic correlations of interest for studies of double parton scattering (DPS) in high-energy collisions. In particular, we find that the transverse dependence of the double parton distributions (DPDs) does not factorize within the model. The results gives insight to the strengths of correlations in different kinematical regions, which can help in constructing input DPDs in cross section calculations.

This contribution to CIPANP 2012 highlights what we have learned about the asymmetric parton distributions of the nucleon over the past 20 years. These distributions include the transverse momentum dependent parton distributions describing spin-orbit correlations, but also their generalized parton and Wigner distribution analogues. Besides quark distributions, also gluon distributions are discussed, in particular the distribution of linearly polarized gluons inside unpolarized nucleons and its applications, such as at LHC in Higgs production and at a future Electron-Ion Collider in heavy quark production.

A bstract Reconstructing Mellin moments of double parton distributions from calculations on a Euclidean lattice requires taking an integral over a variable that may be regarded as a Ioffe time. The Fourier conjugate of this variable plays the role of a kinematic skewness in the double parton distributions. We discuss the skewness dependence of the relevant hadronic correlation functions. Using several models, we study the impact of this dependence on extracting moments of double parton distributions from existing lattice data.

Valence quark distributions of pion at very low resolution scale Q02∼0.1 GeV2 are deduced from a maximum entropy method, under the assumption that pion consists of only a valence quark and a valence anti-quark at such a low scale. Taking the obtained initial quark distributions as the nonperturbative input in the modified Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (with the GLR-MQ-ZRS corrections) evolution, the generated valence quark distribution functions at high Q2 are consistent with the measured ones from a Drell-Yan experiment. The maximum entropy method is also applied to estimate the valence quark distributions at relatively higher Q2=0.26GeV2. At this higher scale, other components (sea quarks and gluons) should be considered in order to match the experimental data. The first three moments of pion quark distributions at high Q2 are calculated and compared with the other theoretical predictions.

The strangeness degrees of freedom in the parton structure of the nucleon are explored in the global analysis framework, using the new CTEQ6.5 implementation of the general mass perturbative QCD formalism of Collins. We systematically determine the constraining power of available hard scattering experimental data on the magnitude and shape of the strange quark and anti-quark parton distributions. We find that current data favor a distinct shape of the strange sea compared to the isoscalar non-strange sea. A new reference parton distribution set, CTEQ6.5S0, and representative sets spanning the allowed ranges of magnitude and shape of the strange distributions, are presented. Some applications to physical processes of current interest in hadron collider phenomenology are discussed.

In this paper we derive an integral equation for the evolution of unintegrated (longitudinally) polarized quark and gluon parton distributions. The conventional Catani-Ciafaloni-Fiorani-Marchesini (CCFM) framework is modified at small x in order to incorporate the QCD expectations concerning the double ${\mathrm{ln}}^{2}(1/x)$ resummation at low x for the integrated distributions. Complete Altarelli-Parisi splitting functions are included that makes the formalism compatible with the leading order Altarelli-Parisi evolution at large and moderately small values of x. The obtained modified polarized CCFM equation is shown to be partially diagonalized by the Fourier-Bessel transformation. Results of the numerical solution for this modifed polarized CCFM equation for the nonsinglet quark distributions are presented.

While the form factors and parton distributions provide separately the shape of the proton in coordinate and momentum spaces, a more powerful imaging of the proton structure can be obtained through quantum phase-space distributions. Here we introduce the Wigner-type quark and gluon distributions which depict a full-3D proton at every fixed Feynman momentum, like what is seen through momentum(“color”)-filters. After appropriate reductions, the phase-space distributions are related to the generalized parton distributions (GPDs) and transverse-momentum dependent parton distributions measurable in high-energy experiments.

We present a next-to-leading-order QCD structure-function analysis of deep-inelastic muon and neutrino scattering data. In particular, we incorporate new $\frac{{F}_{2}^{\ensuremath{\mu}n}}{{F}_{2}^{\ensuremath{\mu}p}}$ data and take account of a recent reanalysis of SLAC data. The fit is performed simultaneously with next-to-leading-order fits to recent prompt photon and Drell-Yan data. As a result we are able to place tighter constraints on the quark and gluon distributions. Two definitive sets of parton distributions are presented according to whether the European Muon Collaboration or Bologna-CERN-Dubna-Munich-Saclay Collaboration muon data are included in the global fit. Comparisons with distributions obtained in earlier analyses are made and the consistency of data sets is investigated.

Nucleon structure functions, as measured in lepton-nucleon scattering, have historically provided a critical observable in the study of partonic dynamics within the nucleon. However, at very large parton momenta, it is both experimentally and theoretically challenging to extract parton distributions due to the probable onset of nonperturbative contributions and the unavailability of high-precision data at critical kinematics. Extraction of the neutron structure and the d quark distribution have been further challenging because of the necessity of applying nuclear corrections when utilizing scattering data from a deuteron target to extract the free neutron structure. However, a program of experiments has been carried out recently at the energy-upgraded Jefferson Lab electron accelerator aimed at significantly reducing the nuclear correction uncertainties on the d quark distribution function at large partonic momentum. This allows leveraging the vast body of deuterium data covering a large kinematic range to be utilized for d quark parton distribution function extraction. In this Letter, we present new data from experiment E12-10-002, carried out in Jefferson Lab Experimental Hall C, on the deuteron to proton cross section ratio at large Bjorken x. These results significantly improve the precision of existing data and provide a first look at the expected impact on quark distributions extracted from parton distribution function fits.

It is shown that the previously noted extreme perturbative NNLO/NLO instability of the longitudinal structure function F_L(x,Q^2) is a mere artefact of the commonly utilized `standard' gluon distributions. In particular it is demonstrated that using the appropriate -- dynamically generated -- parton distributions at NLO and NNLO, F_L(x,Q^2) turns out to be perturbatively rather stable already for Q^2 $\geq$ O(2-3 GeV^2).

New parton distribution functions for the photon

Gluon distributions in real and virtual photons are calculated using evolution equations in the NLO approximation. The quark distributions in the photon determined on the basis of the QCD sum rule approach in [1] are taken as an input. It is shown that gluon distribution in the photon can be reliably determined up tox=0.03÷0.05, much lower than the corresponding values in the case of quark distributions. Two variants of the calculations are considered: (1) it is assumed that there are no intrinsic gluons in the photon at some low normalization pointQ 2=Q 20 ∼1GeV2; (2) it is assumed that gluonic content of the photon at lowQ 20 is described by gluonic content of vector mesonsρ, ω, ϕ. The gluon distributions in these two variants appear to be different. This fact permits one to clarify the origin of nonperturbative gluonic content of the photon by comparing the results with experiment. Structure functionsF 2(x) for real and virtual photon are calculated and it is shown that in the regionx≥0.2 where QCD approach is valid, there is a good agreement with experiment.