Parton distributions in the virtual photon target up to NNLO in QCD

Parton distributions in the virtual photon target are investigated in perturbative QCD up to the next-to-next-to-leading order (NNLO). In the case Λ ²≪P ²≪Q ², where −Q ² (−P ²) is the mass squared of the probe (target) photon, parton distributions can be predicted completely up to the NNLO, but they are factorisation-scheme dependent. We analyse parton distributions in two different factorisation schemes, namely the and DIS _γ schemes, and we discuss their scheme dependence. We show that the factorisation-scheme dependence is characterised by the large-x behaviours of the quark distributions. The gluon distribution is predicted to be very small in absolute value except in the small-x region.     

One-loop factorization for inclusive hadron production in p-A collisions in the saturation formalism

We demonstrate the QCD factorization for inclusive hadron production in p-A collisions in the saturation formalism at one-loop order, with explicit calculation of both real and virtual gluon radiation diagrams. In particular, we find that the cross section can be written into a factorization form in the coordinate space at the next-to-leading order, while the naive form of the convolution in the transverse momentum space does not hold. The collinear divergences associated with the incoming parton distribution of the nucleon and the outgoing fragmentation function of the final-state hadron, as well as the rapidity divergence with small-x dipole gluon distribution of the nucleus are factorized into the splittings of the associated parton distribution and fragmentation functions and the energy evolution of the dipole gluon distribution function. The hard coefficient function is evaluated at one-loop order, and contains no divergence.     

The thermal width of heavy quarkonia moving in quark–gluon plasma

The velocity dependence of the thermal width of heavy quarkonia traveling with respect to the quark–gluon plasma is calculated up to the NLO in perturbative QCD. At the LO, the width decreases with increasing speed, whereas at the NLO it increases with a magnitude approximately proportional to the expectation value of the relative velocity between the quarkonium and a parton in thermal equilibrium. Such an asymptotic behavior is due to the NLO dissociation cross section converging to a nonvanishing value in the high energy limit.     

On nuclear dependence of direct photon production

We have calculated the impact on theA dependence of direct photon production at large transverse momenta (p _T ) of models that were used successfully to explain the EMC effect. We find that, for energies andp _T 's typical of present direct photon measurements, the change in the photon yield due to nuclear modification of parton distributions can be expected to be about 15–20% on Fe. The effect is quite sensitive to the gluon distribution. In particular, for the models used in our calculations, theA dependence is affected more by the gluon distribution than by the quark distributions.     

Spin-dependent structure functions of real and virtual photons

The implications of the positivity constraint, , on the presently unknown spin–dependent structure function of real and virtual photons are studied at scales where longitudinally polarized photons dominate physically relevant cross sections. In particular it is shown how to implement the physical constraints of positivity and continuity at in NLO calculations which afford a nontrivial choice of suitable (DIS) factorization schemes related to and and appropriate boundary conditions for the polarized parton distributions of real and virtual photons. The predictions of two extreme ‘maximal’ and ‘minimal’ saturation scenarios are presented and compared with results obtained within the framework of a simple quark ‘box’ calculation expected to yield reasonable estimates in the not too small regions of x and . Received: 16 March 2001 / Published online: 18 May 2001     

Virtual photon structure

The structure functions of a real photon are calculable in QCD. The leading contribution is proportional to 1n Q², with a coefficient reflecting the gluon flux in a real photon. We investigate this leading term for non-zero target photon mass. In an appropriate limit the gluon content in a virtual photon is found to vanish. The gluon radiative corrections of QCD can thus be turned off by tuning the target photon mass.     

Evolution of the helicity and transversity. Transverse-momentum-dependent parton distributions

We examine the QCD evolution of the helicity and transversity parton distribution functions when including also their dependence on transverse momentum. Using an appropriate definition of these polarized transverse momentum distributions (TMDs), we describe their dependence on the factorization scale and rapidity cutoff, which is essential for phenomenological applications.     

Gluon distributions in real and virtual photon and the photon structure function

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 ₀ ² ∼1GeV²; (2) it is assumed that gluonic content of the photon at lowQ ₀ ² 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.     

Quarkonium plus prompt-photon associated hadroproduction and nuclear shadowing

Quarkonium hadroproduction in association with a photon at high energies provides a probe of the dynamics of the strong interactions as it is dependent on the nuclear gluon distribution. Therefore, it could be used to constrain the behavior of the nuclear gluon distribution in proton–nucleus and nucleus–nucleus collisions. Such processes are useful to single out the magnitude of the shadowing/antishadowing effects in the nuclear parton densities. In this work we investigate the influence of nuclear effects in the production of J/ψ+γ and ?+γ and estimate the transverse momentum dependence of the nuclear modification factors. The theoretical framework considered in the J/ψ (?) production associated with a direct photon at the hadron collider is the non-relativistic QCD (NRQCD) factorization formalism.     

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     

Perturbation theory and the parton model in QCD

We prove that for any process which admits a parton-model interpretation, the naive parton model can be modified to include the effects of QCD interactions to all orders in perturbation theory. This requires that the mass singularities in quark and gluon inclusive cross sections factor into universal functions which renormalize the naive parton model distribution and decay functions. We prove that this factorization takes place for all leading and non-leading logs and thus check consistency of the parton model to all orders in perturbation theory.     

QCD resummation for jet substructures

We provide a novel development in jet physics by predicting the energy profiles of light-quark and gluon jets in the framework of perturbative QCD. Resumming large logarithmic contributions to all orders in the coupling constant, our predictions are shown to agree well with Tevatron CDF and Large Hadron Collider CMS data. We also extend our resummation formalism to the invariant mass distributions of light-quark and gluon jets produced in hadron collisions. The predicted peak positions and heights in jet mass distributions are consistent with CDF data within uncertainties induced by parton distribution functions.     

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.     

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.     

Probing gluonic spin-orbit correlations in photon pair production

We consider photon pair production in hadronic collisions at large mass and small transverse momentum of the pair, assuming that factorization in terms of transverse-momentum dependent parton distributions applies. The unpolarized cross section is found to have azimuthal angular dependencies that are generated by a gluonic version of the Boer-Mulders function. In addition, the single transversely polarized cross section is sensitive to the gluon Sivers function. We present simple numerical estimates for the Boer-Mulders and Sivers effects in diphoton production at RHIC and find that the process would offer unique opportunities for exploring transverse-momentum dependent gluon distributions.     

Inclusive Single- and Dijet Rates in Next-to-Leading Order QCD for γ*p and γ*γ Collisions

We present one- and two-jet inclusive cross sections for γ*γ scattering and virtual photoproduction in ep collisions. The hard cross sections are calculated in next-to-leading order QCD. Soft and collinear singularities are extracted using the phase-space-slicing method. The initial state singularity of the virtual photon depends logarithmically its’ virtuality. This logarithm is large and has to be absorbed into the parton distribution function of the virtual photon. We define for this purpose an factorization scheme similar to the real photon case. We numerically study the dependence of the inclusive cross sections on the transverse energies and rapidities of the outgoing jets and on the photon virtuality. The ratio of the resolved to the direct cross section in ep collisions is compared to ZEUS data.     

Global analysis of helicity parton densities and their uncertainties

We present a new analysis of the helicity parton distributions of the nucleon. The analysis takes into account the available data from inclusive and semi-inclusive polarized deep inelastic scattering, as well as from polarized proton-proton (p-p) scattering at RHIC. For the first time, all theoretical calculations are performed fully at next-to-leading order (NLO) of perturbative QCD, using a method that allows incorporation of the NLO corrections in a very fast and efficient way in the analysis. We find evidence for a rather small gluon polarization in the nucleon, over a limited region of momentum fraction, and for interesting flavor patterns in the polarized sea.     

Measurement of inclusive D^{\ast\pm} and associated dijet cross sections in photoproduction at HERA

Inclusive photoproduction of mesons has been measured for photon-proton centre-of-mass energies in the range GeV and photon virtuality 1 GeV. The data sample used corresponds to an integrated luminosity of 37 pb. Total and differential cross sections as functions of the transverse momentum and pseudorapidity are presented in restricted kinematical regions and the data are compared with next-to-leading order (NLO) perturbative QCD calculations using the “massive charm” and “massless charm” schemes. The measured cross sections are generally above the NLO calculations, in particular in the forward (proton) direction. The large data sample also allows the study of dijet production associated with charm. A significant resolved as well as a direct photon component contribute to the cross section. Leading order QCD Monte Carlo calculations indicate that the resolved contribution arises from a significant charm component in the photon. A massive charm NLO parton level calculation yields lower cross sections compared to the measured results in a kinematic region where the resolved photon contribution is significant. Received: 9 July 1998 / Published online: 22 October 1998     

Dependence of Jet Photoproduction on Scales in Higher Order QCD Corrections at HERA

The dependencies of two-jet cross section on renormalization scale and factorization scales of resolved photon and proton are investigated up to next-to-leading order (NLO) QCD. It is shown that the NLO cross section is quite sensitive to the choice of the renormalization scale and the factorization scales of resolved photon and proton in large invariant mass and large negative. rapidity of the two-jet system.     

PDF and scale uncertainties of various DY distributions in ADD and RS models at hadron colliders

In the extra dimension models of ADD and RS we study the dependence of the various parton distribution functions on observables of Drell–Yan processes to NLO in QCD at LHC and Tevatron energies. Uncertainties at LHC due to factorisation scales in going from leading to next-to-leading order in QCD for the various distributions get reduced by about 2.75 times for a μ_F range 0.5Q<μ_F<1.5Q. Further uncertainties arising from the error on the experimental data are estimated using the MRST parton distribution functions.