Parton distributions from lattice QCD

We extract the x dependence of the valence nonsinglet u - d distribution function in the nucleon from the lowest few moments calculated on the lattice, using an extrapolation formula which ensures the correct behavior in the chiral and heavy quark limits. We discuss the implications for the quark mass dependence of meson masses lying on the J^PC = 1^{– -} Regge trajectory.     

Parton distributions in hadrons

We use the statistical model of Zhang et al. [Y.-J. Zhang, B. Zhang, B.-Q. Ma, Phys. Lett. B 523 (2001) 260; Y.-J. Zhang, B.-S. Zou, L.-M. Yang, Phys. Lett. B 528 (2002) 228; Y.-J. Zhang, W.-Z. Deng, B.-Q. Ma, Phys. Rev. D 65 (2002) 114005] to calculate parton distributions in hadrons. The model does reasonably well in predicting the distributions of partons in the proton, including the excess in the proton sea. We extend the model to calculate quark and gluon distributions in the pion, kaon, lambda and the pentaquark. The hadrons are described in terms of a Fock expansion in quark and gluon states. Detailed balance between each pair of states is assumed, from which the coefficients of the Fock state expansion are determined. The parton distribution functions are found in the hadron rest frame from a Monte Carlo calculation. The results are evolved to appropriate QCD scales for comparison with experiment. This project has included significant participation by undergraduates at Seattle University, made possible by support from the Research in Undergraduate Institutions Program of the National Science Foundation.     

Parton distributions for LO generators

We present a study of the results obtained by combining LO partonic matrix elements with either LO or NLO parton distributions. These are compared to the best prediction using NLO for both matrix elements and parton distributions. The aim is to determine which parton distributions are most appropriate to use in those cases where only LO matrix elements are available, e.g. as in many Monte Carlo generators. Both LO and NLO parton distributions have flaws, sometimes serious, for some processes, so a modified optimal LO set is suggested. We investigate a wide variety of processes, and the new modified LO* PDF works at least as well as, and often better than, both LO and NLO PDFs in nearly all cases.     

Parton distributions in the photon

We discuss in detail the photon structure function beyond the leading logarithm approximation. Of special concern is the factorization scheme and the hadronic input; we show how to naturally absorb large terms due to the factorization scheme in a modified hadronic component. The effect of the charm quark mass threshold is also discussed in relation to the phenomenology. A comparison with data shows that the modified hadronic component can be reasonably described by a VDM-type input.URA 14-36 du CNRS, associée à l'Ecole Normale Supérieure de Lyon, et au Laboratoire d'Annecy-le-Vieux de Physique des Particules     

Parton distributions for the LHC

We present updated leading-order, next-to-leading order and next-to-next-to-leading order parton distribution functions (“MSTW 2008”) determined from global analysis of hard-scattering data within the standard framework of leading-twist fixed-order collinear factorisation in the [`(MS)]\overline{\mathrm{MS}} scheme. These parton distributions supersede the previously available “MRST” sets and should be used for the first LHC data taking and for the associated theoretical calculations. New data sets fitted include CCFR/NuTeV dimuon cross sections, which constrain the strange-quark and -antiquark distributions, and Tevatron Run II data on inclusive jet production, the lepton charge asymmetry from W decays and the Z rapidity distribution. Uncertainties are propagated from the experimental errors on the fitted data points using a new dynamic procedure for each eigenvector of the covariance matrix. We discuss the major changes compared to previous MRST fits, briefly compare to parton distributions obtained by other fitting groups, and give predictions for the W and Z total cross sections at the Tevatron and LHC.     

Parton distributions incorporating QED contributions

We perform a global parton analysis of deep inelastic and related hard-scattering data, including corrections to the parton evolution. Although the quality of the fit is essentially unchanged, there are two important physical consequences. First, the different DGLAP evolution of u and d type quarks introduces isospin violation, i.e. , which is found to be unambiguously in the direction to reduce the NuTeV anomaly. A second consequence is the appearance of photon parton distributions of the proton and the neutron. In principle these can be measured at HERA via the deep inelastic scattering processes ; our predictions are in agreement with the present data.Received: 3 November 2004, Published online: 11 January 2005R.S. Thorne: Royal Society University Research Fellow.     

Parton distributions for high energy collisions

Recent data from deep inelastic scattering experiments atx10^–2 are used to fix the parton distributions down tox10^–4 andQ ²0.3 GeV². The predicted extrapolations are uniquely determined by the requirement of avalence-like structure ofall parton distributions at some low resolution scale and are furthermore shown to be insensitive in the small-x region, 10^–4x10^–2, to the detailed experimental input at the presently accessiblex>10^–2. Simple parameterizations of the resulting parton distributions are presented in the range 10^–5x<1 and=">Q ²10⁸ GeV² as obtained from the leading- and higher-order evolution equations.     

Parton distributions: a new global analysis

We present a new analysis of parton distributions of the proton. This incorporates a wide range of new data, an improved treatment of heavy flavours and a re-examination of prompt photon production. The new set (MRST) shows systematic differences from previous sets of partons which can be identified with particular features of the new data and with improvements in the analysis. We also investigate the sensitivities of the results to (i) the uncertainty in the determination of the gluon at large , (ii) the value of and (iii) the minimum cut on the data that are included in the global fit. Received: 23 March 1998 / Published online: 23 June 1998     

Parton distributions in the small-x region within LLX approximation

The solutions of Lipatov-Fadin-Kuraev equation (LFK) within LLX approximation for gluon distributions are studied. The results are based on the semiphenomenological boundary conditions taken from LLQ² analysis. We find, that pure theoretical LLX approach can reproduce the form of singular small-x behaviour of gluon and sea-quark distributions obtained within LLQ²A with singular input parametrizations. Some remarks about shadowing corrections are presented.     

Parton distributions from a global QCD analysis of deep inelastic scattering and lepton-pair production

Parton distribution functions consistent with neutrino and muon deep inelastic scattering as well as Drell-Yan pair production results have been extracted. This analysis incorporates experimental systematic errors which are the dominant errors in recent deep inelastic scattering experiments. The dependence of the results on factors such as kinematic cuts in the data, heavy target corrections, and choice of initial functional form are also explored. The form adopted is motivated by perturbative QCD and particularly useful in exploring the small-x extrapolation of the distributions. This is crucial for studying the range of predictions for Collider, HERA, and SSC/LHC cross sections. Representative distribution function sets are presented in a very compact parametrized form both in the DIS and MS-bar renormalization schemes.This work is partially supported by the National Science Foundation under Grant No. PHY89-05161. This work was also supported by Argonne National Laboratory during the 1988–89 academic year when the author was on Sabbatical leave at the Laboratory from IIT     

Parton distributions and the LHC: W and Z production

W and Z bosons will be produced copiously at the LHC proton-proton collider. We study the parton distribution dependence of the total production cross sections and rapidity distributions, paying particular attention to the uncertainties arising from uncertainties in the parton distributions themselves. Variations in the gluon, the strong coupling, the sea quarks and the overall normalisation are shown to lead to small but non-negligible variations in the cross section predictions. Ultimately, therefore, the measurement of these cross sections will provide a powerful cross check on our knowledge of parton distributions and their evolution. Received: 23 November 1999 / Published online: 6 April 2000     

Calculating statistical distributions from operator relations: The statistical distributions of various intermediate statistics

In this paper, we give a general discussion on the calculation of the statistical distribution from a given operator relation of creation, annihilation, and number operators. Our result shows that as long as the relation between the number operator and the creation and annihilation operators can be expressed as a^†b=Λ(N)$a^{†}b=\Lambda \left(N\right)$ or N=Λ⁻¹(a^†b)$N={\Lambda }^{-1}\left(a^{†}b\right)$, where N$N$, a^†$a^{†}$, and b$b$ denote the number, creation, and annihilation operators, i.e., N$N$ is a function of quadratic product of the creation and annihilation operators, the corresponding statistical distribution is the Gentile distribution, a statistical distribution in which the maximum occupation number is an arbitrary integer. As examples, we discuss the statistical distributions corresponding to various operator relations. In particular, besides the Bose–Einstein and Fermi–Dirac cases, we discuss the statistical distributions for various schemes of intermediate statistics, especially various q$q$-deformation schemes. Our result shows that the statistical distributions corresponding to various q$q$-deformation schemes are various Gentile distributions with different maximum occupation numbers which are determined by the deformation parameter q$q$. This result shows that the results given in much literature on the q$q$-deformation distribution are inaccurate or incomplete.     

Parton distributions,small-x physics and the spin structure of the nucleon

Several theoretical aspects in leading (1-loop) and higher (2-loop) order as well as various approaches of extracting leading twist-2 parton distributions from structure function measurements are discussed and summarized. Their implications for the small-x region (x⩽10⁻²) are analyzed and compared with alternative approaches where higher twist contributions (‘fans’) are added to the twist-2 LO terms in the evolution equations. The second part of these lectures deals with longitudinally polarized parton distributions related to the structure functiong ₁, in particular with various scenarios to explain the total spin structure of nucleons, including the gluon anomaly as well. Specific (realistic) tests for discriminating between these alternatives are discussed as well asx-dependent expectations, in particular for neutron targets in connection with the Bjorken sum rule. Furthermore, various theoretical expectations and sum rules for the transverse (chiral-even) structure functiong ₂ are presented and very recent developments of transverse chiral-odd (‘transversity’) distributions are briefly discussed.