Parametrization of nuclear parton distributions

Optimum nuclear parton distributions are obtained by analysing available experimental data on electron and muon deep inelastic scattering (DIS). The distributions are given at Q ²=1 GeV² with a number of parameters, which are determined by a X ² analysis of the data. Valencequark distributions are relatively well determined at medium x, but they are slightly dependent on the assumed parametrization form particularly at small x. Although antiquark distributions are shadowed at small x, their behavior is not obvious at medium x from the F ₂ data. The gluon distributions could not be restricted well by the inclusive DIS data; however, the analysis tends to support the gluon shadowing at small x. We provide analytical expressions and computer subroutines for calculating the nuclear parton distributions, so that other researchers could use them for applications to other high-energy nuclear reactions.     

Pionic parton distributions

The gluon and sea distributions of the pion are uniquely determined by the requirement of avalence-like structure of the input parton distributions at some low resolution scale. These (dynamical) results are obtained with practically no free parameters, just using the experimentally determined pionic valence distribution combined with the constraints for the pionic gluon distribution provided by direct-γ data. Simple parametrizations of the resulting parton distributions are presented in the range 10^?5?x<1 and 0.3?Q ²?10⁸ GeV² as obtained from the leading-and higher-order evolution equations.     

Spin-dependent parton distributions from polarized structure function data

In the past year, polarized deep inelastic scattering experiments at CERN and SLAC have obtained structure function measurements off proton, neutron and deuteron targets at a level of precision never before achieved. The measurements can be used to test the Bjorken and Ellis-Jaffe sum rules, and also to obtain information on the parton distributions in polarized nucleons. We perform a global leading-order QCD fit to the proton deep inelastic data in order to extract the spin-dependent parton distributions. By using parametric forms which are consistent with theoretical expectations at large and smallx, we find that the quark distributions are now rather well constrained. We assume that there is no significant intrinsic polarization of the strange quark sea. The data are then consistent with a modest amount of the proton's spin carried by the gluon, although the shape of the gluon distribution is not well constrained, and several qualitatively different shapes are suggested. The spin-dependent distributions we obtain can be used as input to phenomenological studies for future polarized hadron-hadron and lepton-hadron colliders.     

Factorization scheme and parton distributions in the polarized virtual photon target

We investigate spin-dependent parton distributions in the polarized virtual photon target in perturbative QCD up to the next-to-leading order (NLO). In the case , where is the mass squared of the probe (target) photon, the parton distributions can be predicted completely up to NLO, but they are factorization-scheme dependent. We analyze the parton distributions in six different factorization schemes and discuss their scheme dependence. We study, in particular, the QCD and QED axial anomaly effects on the first moments of the parton distributions to see the interplay between the axial anomalies and factorization schemes. We also show that the factorization-scheme dependence is characterized by the large-x behaviors of the quark distributions in the virtual photon. The gluon distribution is predicted to be the same up to NLO among the six factorization schemes examined. In particular, the first moment of the gluon distribution is found to be factorization-scheme independent up to NLO. Received: 24 January 2001 / Published online: 18 May 2001     

Polarized parton distribution in the relativistic quark exchange framework

The Spin dependent gluon and sea quark distributions of the proton and the neutron are extracted in the leading order (LO) and the next-to-leading order (NLO) QCD. The relativistic quark exchange model is used to calculate the related valence quark spin dependent structure function. The inverse Mellin transform technique is performed to evaluate the polarized x-dependent distributions of the gluon and the sea quark from the various moments of the valence quarks. It is shown that the calculated spin structure functions (SSF) of the proton and the neutron are in good agreement with the available data, such as E143, SMC, E142, E154 and Hermes experiments. A comparison is also made with the other theoretical models. Finally it is shown that the above calculated parton distributions improve the SSF of the proton and the neutron. Received: 4 January 1999 / Revised version: 12 April 1999     

Higher order QCD corrections to charged-lepton deep-inelastic scattering and global fits of parton distributions

We study the perturbative QCD corrections to the heavy-quark structure functions of charged-lepton deep-inelastic scattering and their impact on global fits of parton distributions. We include the logarithmically enhanced terms near threshold due to soft gluon resummation in the QCD corrections at next-to-next-to-leading order. We demonstrate that this approximation is sufficient to describe the available HERA data in most parts of the kinematic region. The threshold-enhanced next-to-next-to-leading order corrections improve the agreement between predictions based on global fits of the parton distribution functions and the HERA collider data even in the small-x region.     

Uncertainties of predictions from parton distributions I: Experimental errors

We determine the uncertainties on observables arising from the errors on the experimental data that are fitted in the global MRST2001 parton analysis. By diagonalizing the error matrix we produce sets of partons suitable for use within the framework of linear propagation of errors, which is the most convenient method for calculating the uncertainties. Despite the potential limitations of this approach we find that it can be made to work well in practice. This is confirmed by our alternative approach of using the more rigorous Lagrange multiplier method to determine the errors on physical quantities directly. As particular examples we determine the uncertainties on the predictions of the charged-current deep-inelastic structure functions, on the cross-sections for W production and for Higgs boson production via gluon-gluon fusion at the Tevatron and the LHC, on the ratio of W^- to W⁺ production at the LHC and on the moments of the non-singlet quark distributions. We discuss the corresponding uncertainties on the parton distributions in the relevant x,Q² domains. Finally, we briefly look at uncertainties related to the fit procedure, stressing their importance and using , and extractions of as examples. As a by-product of this last point we present a slightly updated set of parton distributions, MRST2002. Received: 13 November 2002 / Published online: 5 May 2003 RID="a" ID="a" Royal Society University Research Fellow     

Skewed parton distributions for B\to \pi transitions

We investigate the b-u skewed parton distributions (SPDs) for transitions and determine the contributions from several sources (overlaps of soft light-cone wave functions, quark-antiquark annihilations and meson resonances). The transition form factors, which are relevant in exclusive semi-leptonic and non-leptonic B-decays, are obtained by integrating the b-u SPDs over the momentum fraction x. A phenomenological determination of the relevant parameters allows us to predict the form factors and to obtain the branching ratios for semi-leptonic decays. Received: 18 June 1999 / Revised version: 8 September 1999 / Published online: 3 November 1999     

Extraction of parton distributions and \alpha_{\mathrm{s}} from DIS data within a Bayesian treatment of systematic errors

We have performed a NLO QCD global fit of BCDMS, NMC, H1 and ZEUS data with full account of point-to-point correlations using the Bayesian approach to the treatment of systematic errors. Parton distributions in the proton with their experimental uncertainties, including both statistical and systematic, are obtained. The gluon distribution in a wide region of x is found to be softer than the gluon distribution extracted in standard global analyses which include prompt photon data. We obtain a robust estimate of C.L.) based on Chebyshev's inequality, which is compatible with an earlier determination of from the DIS data, but is less dependent on high-twist effects. Received: 5 May 1997 / Revised version: 12 October 1998 / Published online: 8 September 1999     

Shadowing effects in nuclear parton distributions for small values ofx

The shadowing corrections to gluon and quark distributions in nuclei in the region of small values ofx are discussed. They are related to parton distributions in a pomeron which are in principle measurable in hard diffractive processes on the nucleon target. Multiple scattering corrections to shadowing are considered in a model dependent way. The perturbative QCD evolution of shadowing is also taken into account. Various possibilities of the partonic content of a pomeron are considered. It is shown in particular that the conventional parametrizations of parton distributions in a pomeron which are based on the assumption that it consists mostly of gluons imply substantial nuclear shadowing in gluon distributions in heavy nuclei. Possible phenomenological implications of shadowing corrections in nuclear parton distributions for various semi-hard processes with nuclear targets are briefly discussed.     

Generalized parton distributions from hadronic observables: non-zero skewness

We propose a physically motivated parameterization for the unpolarized generalized parton distributions, H and E, valid at both zero and non-zero values of the skewness variable, ζ. Our approach follows a previous detailed study of the ζ=0 case where H and E were determined using constraints from simultaneous fits of the experimental data on both the nucleon elastic form factors and the deep inelastic structure functions in the non-singlet sector. Additional constraints at ζ≠0 are provided by lattice calculations of the higher moments of generalized parton distributions. We illustrate a method for extracting generalized parton distributions from lattice moments based on a reconstruction using sets of orthogonal polynomials. The inclusion in our fit of data on Deeply Virtual Compton Scattering is also discussed. Our method provides a step towards an extraction of generalized distributions based on a global fit of the available data within the given set of constraints.     

The scale dependent nuclear effects in parton distributions for practical applications

The scale dependence of the ratios of parton distributions in a proton of a nucleus A and in the free proton, , is studied within the framework of the lowest order leading-twist DGLAP evolution. By evolving the initial nuclear distributions obtained with the GRV-LO and CTEQ4L sets at a scale , we show that the ratios are only moderately sensitive to the choice of a specific modern set of free parton distributions. We propose that to a good first approximation, this parton distribution set-dependence of the nuclear ratios can be neglected in practical applications. With this result, we offer a numerical parametrization of for all parton flavours i in any , and at any and any for computing cross sections of hard processes in nuclear collisions. Received: 10 August 1998 / Published online: 27 April 1999     

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     

Radiatively generated parton distributions for high energy collisions

The gluon and antiquark distributions of the nucleon are generated radiatively using the assumption that at some low resolution scale the nucleon consists entirely of valence quarks and valence-like gluons. The agreement between the uniquely predicted gluon and sea distributions and the available data on deep inelastic structure functions (including also recent low-Q ² measurements) and direct-photon production is demonstrated and discussed in detail. Simple parametrizations of the resulting (positive definite!) parton distributions are presented in the range 10^?4?x≦1 and 0.2?Q ²?10⁶ GeV² as obtained according to the leading- and higher-order renormalization group evolution equations.     

Multiple parton scattering in nuclei: twist-four nuclear matrix elements and off-forward parton distributions

Multiple parton scatterings inside a large nucleus generally involve higher-twist nuclear parton matrix elements. The gluon bremsstrahlung induced by multiple scattering depends not only on direct parton matrix elements but also on momentum-crossed ones, due to the Landau–Pomeranchuk–Migdal interference effect. We show that both types of twist-four nuclear parton matrix elements can be factorized approximately into the product of twist-two nucleon matrix elements in the limit of extremely large nuclei, A→∞, as assumed in previous studies. Due to the correlative nature of the twist-four matrix elements under consideration, it is actually the off-forward parton distributions that appear naturally in this decomposition, rather than the ordinary diagonal distributions probed in deeply-inelastic scattering. However, we argue that the difference between these two distribution classes is small in certain kinematic regimes. In these regions, the twist-four nuclear parton matrix elements are evaluated numerically and compared to the factorized form for different nuclear sizes within a schematic model of the two-nucleon correlation function. The nuclear size dependence is found to be A^4/3 in the limit of large A, as expected. We find that the factorization is reasonably good when the momentum fraction carried by the gluon field is moderate. The deviation can be more than a factor of 2, however, for small gluon momentum fractions, where the gluon distribution is very large.     

Improved calculation of distributions sensitive to the three gluon vertex ine + e −→4-jets using a coherent parton shower simulator

The calculation of hadron distributions ine ⁺ e ^?→4-jets using the 4-parton matrix element diverges unless cuts are imposed on the parton phase space. Experimentally cuts can be applied only on the hadron spectrum and not at the 4-parton level. Test observables for the three gluon vertex relying on jet-jet angular correlations are found to be particularly sensitive to these parton cuts. The contribution from the parton phase space below the cut region is calculated to modified logarithmic approximation accuracy using a Monte Carlo simulator HERWIG and is found to be of order 45%. This modifies the predictions of the tests so that differences between QCD and ‘QED’ are diminished significantly. A tagging method based on the average energy of particles in a jet is found to be best at identifying both gluon jets with a possible 9:1 success to failure ratio and it allows the presence of the three gluon vertex to be verified.     

Study of parton spin-dependent distributions in hard proton-proton collisions through measurement of handedness

Polarization of partons emitted in hard scattering of an unpolarized proton beam from a polarized hydrogen target can be found through a measurement of jet handedness. Two definitions of handedness are suggested with zero and essentially nonzero contributions of gluon jets. A sensitivity of the handedness to the valence, sea quark and gluon distributions is considered. Handedness properties under the charge conjugation and flavorSU (2) transformations are investigated. An option to study the spin-dependent parton distributions in hard scattering of the unpolarized HERA proton beam from the polarized internal hydrogen target is discussed.     

MRST2001: partons and $\alpha_S$ from precise deep inelastic scattering and Tevatron jet data

We use all the available new precise data for deep inelastic and related hard scattering processes to perform NLO global parton analyses. These new data allow an improved determination of partons and, in particular, the inclusion of the recent measurements of the structure functions at HERA and of the inclusive jets at the Tevatron help to determine the gluon distribution and better than ever before. We find a somewhat smaller gluon at low x than previous determinations and that . Received: 17 October 2001 / Revised version: 29 October 2001 / Published online: 20 December 2001     

Dynamical parton distributions revisited

Dynamical parton densities, generated radiatively from valence-like inputs at some low resolution scale, are confronted with recent small-x data on deep inelastic and other hard scattering processes. It is shown that within theoretical uncertainties our previous (1994) dynamical/radiative parton distributions are compatible with most recent data and still applicable within the restricted accuracy margins of the presently available next-to-leading order calculations. Due to recent high precision measurements we also present an updated, more accurate, version of our (valence-like) dynamical input distributions. Furthermore, our perturbatively stable parameter-free dynamical predictions are extended to the extremely small-x region, , relevant to questions concerning ultra-high-energy cosmic ray and neutrino astronomy. Received: 22 June 1998 / Published online: 21 August 1998