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     

Diffractive open charm production in deep-inelastic scattering and photoproduction at HERA

Measurements are presented of diffractive open charm production at HERA. The event topology is given by ep→eXY where the system X contains at least one charmed hadron and is well separated by a large rapidity gap from a leading low-mass proton remnant system Y. Two analysis techniques are used for the cross section measurements. In the first, the charm quark is tagged by the reconstruction of a D^*±(2010) meson. This technique is used in deep-inelastic scattering (DIS) and photoproduction (γp). In the second, a method based on the displacement of tracks from the primary vertex is used to measure the open charm contribution to the inclusive diffractive cross section in DIS. The measurements are compared with next-to-leading order QCD predictions based on diffractive parton density functions previously obtained from a QCD analysis of the inclusive diffractive cross section at H1. A good agreement is observed in the full kinematic regime, which supports the validity of QCD factorization for open charm production in diffractive DIS and γp.     

Diffractive parton distributions from perturbative QCD

The asymptotic collinear factorisation theorem, which holds for diffractive deep-inelastic scattering, has important modifications in the sub-asymptotic HERA regime. We use perturbative QCD to quantify these modifications. The diffractive parton distributions are shown to satisfy an inhomogeneous evolution equation. We emphasise that it is necessary to include both the gluonic and sea-quark t-channel components of the perturbative pomeron. The corresponding pomeron-to-parton splitting functions are derived in the appendix.Received: 20 April 2005, Published online: 27 July 2005     

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     

Tests of QCD factorisation in the diffractive production of dijets in deep-inelastic scattering and photoproduction at HERA

Measurements are presented of differential dijet cross sections in diffractive photoproduction (Q²<0.01 GeV²) and deep-inelastic scattering processes (DIS, 4<Q²<80 GeV²). The event topology is given by ep→eXY, in which the system X, containing at least two jets, is separated from a leading low-mass baryonic system Y by a large rapidity gap. The dijet cross sections are compared with NLO QCD predictions based on diffractive parton densities previously obtained from a QCD analysis of inclusive diffractive DIS cross sections by H1. In DIS, the dijet data are well described, supporting the validity of QCD factorisation. The diffractive DIS dijet data are more sensitive to the diffractive gluon density at high fractional parton momentum than the measurements of inclusive diffractive DIS. In photoproduction, the predicted dijet cross section has to be multiplied by a factor of approximately 0.5 for both direct and resolved photon interactions to describe the measurements. The ratio of measured dijet cross section to NLO prediction in photoproduction is a factor 0.5±0.1 smaller than the same ratio in DIS. This suppression is the first clear observation of QCD hard scattering factorisation breaking at HERA. The measurements are also compared to the two soft colour neutralisation models SCI and GAL. The SCI model describes diffractive dijet production in DIS but not in photoproduction. The GAL model fails in both kinematic regions.     

Probing quark-distribution amplitudes through generalized parton distributions at large momentum transfer

In the large momentum transfer limit, generalized parton distributions can be calculated through a QCD factorization theorem which involves perturbatively calculable hard kernels and light-cone parton distribution amplitudes of hadrons. We illustrate this through the H(q)(x,xi,t) distribution for the pion and the proton, presenting the hard kernels at leading order. As a result, experimental data on the generalized parton distributions in this regime can be used to determine the functional form of the parton distribution amplitudes which has thus far been quite challenging to obtain. Our result can also be used as a constraint in phenomenological generalized parton distribution parametrizations.     

Diffractive production of charm in DIS and gluon nuclear shadowing

We evaluate nuclear shadowing of the total cross section of charm particles production in DIS within the framework of Gribov theory of nuclear shadowing generalized to account for the QCD evolution. We use as an input the recent QCD Pomeron parton density analysis of the HERA diffractive data. Assuming that the QCD factorization theorem is applicable to the charm production off nuclei we also calculate shadowing of the gluon densities in nuclei and find it sufficiently large for heavy nuclei: G_A~200(x,Q²)/AG_N(x,Q²) ~ 0.45 m 0.5 · (A/200)^т.15 for x ~ 10^х1ц, Q² ~ 20 1 40 GeV² to influence significantly the physics of heavy ion collisions at LHC. We evaluate also suppression of minijet and hidden charm production in the central AA collisions. We also discuss some properties of the final states for %^*A processes dominated by the scattering off small x gluons like the high p_t jet and charm production.     

J/\psi +{\mathrm{jet}} diffractive production in the direct photon process at HERA

We present a study of the diffractive production in direct photon processes at HERA based on the factorization theorem for lepton-induced hard diffractive scattering and the factorization formalism of the non-relativistic QCD (NRQCD) for quarkonia production. Using the diffractive gluon distribution function extracted from HERA data on diffractive deep inelastic scattering and diffractive dijet photon production, we demonstrate that this process is measurable at DESY HERA. The experimental study of this process can give valuable insight in the diffractive production mechanism and test the color-octet mechanism for heavy quarkonia production in a new environment. Received: 13 September 1999 / Revised version: 31 December 1999 / Published online: 6 April 2000     

Multiple parton scattering in nuclei: beyond helicity amplitude approximation

Multiple parton scattering and induced parton energy loss in deeply inelastic scattering (DIS) off heavy nuclei is studied within the framework of generalized factorization in perturbative QCD with a complete calculation beyond the helicity amplitude (or soft bremsstrahlung) approximation. Such a calculation gives rise to new corrections to the modified quark fragmentation functions. The effective parton energy loss is found to be reduced by a factor of 5/6 from the result of helicity amplitude approximation.     

A new global analysis of deep inelastic scattering data

A new QCD analysis of deep inelastic scattering (DIS) data is presented. All available neutrino and antineutrino cross sections are reanalyzed and included in the fit, along with charged-lepton DIS and Drell–Yan data. A massive factorization scheme is used to describe the charm component of the structure functions. Next-to-leading-order parton distribution functions are provided. In particular, the strange-sea density is determined with a higher accuracy with respect to other global fits. Received: 16 March 1999 / Published online: 8 December 1999     

Could saturation effects be visible in a future electron–ion collider?

We expect to observe parton saturation in a future electron–ion collider. In this Letter we discuss this expectation in more detail considering two different models which are in good agreement with the existing experimental data on nuclear structure functions. In particular, we study the predictions of saturation effects in electron–ion collisions at high energies, using a generalization for nuclear targets of the b-CGC model, which describes the ep HERA quite well. We estimate the total, longitudinal and charm structure functions in the dipole picture and compare them with the predictions obtained using collinear factorization and modern sets of nuclear parton distributions. Our results show that inclusive observables are not very useful in the search for saturation effects. In the small x region they are very difficult to disentangle from the predictions of the collinear approaches. This happens mainly because of the large uncertainties in the determination of the nuclear parton distribution functions. On the other hand, our results indicate that the contribution of diffractive processes to the total cross section is about 20% at large A   and small Q²$Q^2$, allowing for a detailed study of diffractive observables. The study of diffractive processes becomes essential to observe parton saturation.     

Dynamical parton distributions of the proton and small-x physics

The perturbative properties of parton distributions generated radiatively from a valence-like input at some low resolution scale are discussed with the aim of explaining the physical aspects underlying the reliability of the predicted distributions in the small-x region. Aspects of higher-twist (shadowing) effects as well as small-x resummations are discussed. Utilizing recent improved data atx?10^?2 and a factorization scheme in which the heavy quarksc, b, ..., arenot entailed among the intrinsic (massless) parton distributions, we readjust our valencelike input and provide parametrizations of the slightly modified dynamical LO and NLO $(\overline {MS} ,DIS)$ predictions for parton distributions.     

Factorization and infrared properties of non-perturbative contributions to DIS structure functions

In this paper we present a new derivation of QCD factorization. We deduce the k _T and collinear factorizations for the DIS structure functions by consecutive reductions of a more general theoretical construction. We begin by studying the amplitude of forward Compton scattering off a hadron target, representing this amplitude as a set of convolutions of two blobs connected by the simplest, two-parton intermediate states. Each blob in the convolutions can contain both the perturbative and non-perturbative contributions. We formulate conditions for separating the perturbative and non-perturbative contributions and attributing them to the different blobs. After that the convolutions correspond to QCD factorization. Then we reduce this totally unintegrated (basic) factorization first to k _T -factorization and finally to collinear factorization. In order to yield a finite expression for the Compton amplitude, the integration over the loop momentum in the basic factorization must be free of both ultraviolet and infrared singularities. This obvious mathematical requirement leads to theoretical restrictions on the non-perturbative contributions (parton distributions) to the Compton amplitude and the DIS structure functions related to the Compton amplitude through the Optical Theorem. In particular, our analysis excludes the use of the singular factors x ^−a (with a>0) in the fits for the quark and gluon distributions because such factors contradict the integrability of the basic convolutions for the Compton amplitude. This restriction is valid for all DIS structure functions in the framework of both k _T -factorization and collinear factorization if we attribute the perturbative contributions only to the upper blob. The restrictions on the non-perturbative contributions obtained in the present paper can easily be extended to other QCD processes where the factorization is exploited.     

Key Features of the TMD Soft-Factor Structure

We show that the geometry of the Wilson lines, entering the operator definition of the transverse-momentum dependent parton distributions and that of the soft factor, follows from the kinematics of the underlying physical process in conjunction with the gauge invariance of the QCD Lagrangian. We demonstrate our method in terms of concrete examples and determine the paths of the associated Wilson lines. The validation of the factorization theorem in our approach is postponed to future work.     

Weak interactions in polarized semi-inclusive DIS

We calculate, within the pQCD parton model at leading orders, the expression of the polarization P of spin 1/2 hadrons (typically baryons), produced in polarized semi-inclusive DIS in all possible cases in which weak interactions are involved. We discuss how to gather new information on fragmentation and distribution functions and give numerical estimates in the cases for which data are or will soon be available. Received: 7 June 2001 / Published online: 10 August 2001     

Evidence for factorization breaking in diffractive low-Q2 dijet production

We calculate diffractive dijet production in deep-inelastic scattering at next-to-leading order of perturbative QCD, including contributions from direct and resolved photons, and compare our predictions to preliminary data from the H1 Collaboration at DESY HERA. In contrast to recent experimental claims, evidence for factorization breaking is found only for resolved, and not direct, photon contributions. No evidence is found for large normalization uncertainties in diffractive parton densities. The results confirm theoretical expectations for the (non)cancellation of soft singularities in diffractive scattering as well as previous results for (almost) real photoproduction.     

Generalized parton distributions with helicity flip

We show that for both quarks and gluons there are eight generalized parton distributions in the proton: four which conserve parton helicity and four which do not. We explain why time reversal invariance does not reduce this number from eight to six, as previously assumed in the literature. Received: 7 February 2001 / Published online: 23 March 2001     

Fragmentation functions from semi-inclusive DIS pion production and implications for the polarized parton densities

By combining recent HERMES data on semi-inclusive DIS (SIDIS) -production with the singlet fragmentation function , which is well determined from data, we are able to extract, for the first time, the flavoured fragmentation functions , and without making any assumptions about favoured and unfavoured transitions. Whereas and are very well determined, the accuracy of is limited by the uncertainty in evolving from the pole down to the SIDIS scale of a few . We discuss how the precision on could be improved. Knowledge of the will permit the extraction of the polarized parton densities from future polarized SIDIS asymmetry measurements. We study the precision that can be expected in such an extraction. Received: 6 August 2001 / Revised version: 3 October 2001 / Published online: 12 November 2001