QCD Parton Model Research Articles

AGK CUTTING RULES AND PERTURBATIVE QCD

The purpose of this article is to describe a few features of semihard interactions, in high energy nuclear collisions, that are better understood with the help of the AGK cutting rules, and of the probabilistic picture of the interaction which follows. In the first part of the article the cutting rules are discussed for the simplest component of the forward three-body parton amplitude in the large s fixed t limit. The case considered corresponds to the term — at the lowest order in the coupling constant and with vacuum quantum number exchange in both t channels — of the amplitude which describes the interaction of a high energy quark with the two target quarks. The different leading cuts of the amplitude are shown to be proportional to one another with the same weights of the cutting rules derived in the context of multi-Pomeron exchange. The probabilistic picture of the multiple interactions, which originates from the cutting rules, and the self-shadowing cross sections are then discussed. The second part of the article deals with the semihard interactions. The semihard cross section in high energy nucleus–nucleus collisions is represented as a self-shadowing cross section, and a feature which is pointed out is that the single scattering factorized expression of the perturbative QCD parton model holds at any order in the multiparton correlations, the relation being the analog of the AGK cancellation for the average number of soft interactions in high energy hadron–nucleus collisions. Finally, an infrared problem which finds a solution within the self-shadowing representation of the semihard cross section is discussed.

Trends in Polarized Lepton Nucleon Scattering

The thoery of scattering between polarized leptons and polarized nucleons is reviewed in a comprehensive and pedagogical way. The polarized structure functions are introduced and their interpretation in the framework of the QCD parton model is discussed, including the gluon contribution. Sum rules ( = relations between moments of the structure functions) are derived and critically considered. They are then contrasted to recent experimental results.

The sigma term and the quark number operator in QCD

We discuss the relationship of the forward matrix element of the operator $\bar\psi\psi$, related to the so-called sigma term, to the quark number. We show that in the naive quark model in the canonical formalism these quantities coincide in the limit of small average quark momenta. In the QCD parton model defined through light-front quantization this result is preserved at leading perturbative order but it receives radiative corrections. We analyze the theoretical and phenomenological consequences of this result, which provides a bridge between a current algebra quantity, the sigma term, and a deep-inelastic quantity, the parton number.

Partons and the EMC spin effect

We focus on the parton model and the role of the axial anomaly in polarised deep inelastic scattering. We show that the axial anomaly is relevant to each of the higher moments of the spin dependent structure functiong 1 (x) and not just the first moment. This result implies that the factorisation of mass singularities is not sufficient to define the parton model in spin dependent QCD. (It is certainly a necessary condition.) We also need to consider the locality of the photon parton interaction. The anomaly is observed over allx in the EMCg 1 (x) data.

Average fraction of jet momentum carried by highP ? leading hadrons

The average fraction, , of jet momentum carried by the associated charged leading hadron has been determined in the reactionp+N→h 1+h 2+X whereN is the target nucleon;h 1,h 2 are the leading particles of two jets produced at highP ⊥. An 800 GeV/c proton beam and 4 nuclear targets: Be, Al, Fe and W were used. The distributions agree with the QCD-parton model predictions for single independent protonnucleon scattering and independent fragmentation process.

The U (1) Goldberger-Treiman relation and the two components of the proton “spin”

We present a simple and rigorous derivation of a recently proposed generalisation of the Goldberger-Treiman relation, and discuss its renormalisation group properties. We then show how to define separately isospin-conserving quark and gluon components of the proton “spin”, which evolve precisely as in the QCD parton model.

Small- x behavior of parton distribution functions in the next-to-leading order QCD parton model

The systematic application of the QCD-based parton model to the quantitative analysis of high energy processes requires reliable parton distributions including second-order QCD evolution effects — both for consistency and for accuracy, especially in exceptional kinematic regimes such as the small- x region. We discuss qualitative expectations and present quantitative results on the behavior of second-order evolved parton distribution in this region which is particularly important for studying physical processes at future accelerators. Direct comparisons with recently available second-order parton distributions are made in order to check consistency for future studies of high energy processes. Also presented are quantitative results on the scheme-dependence of parton distributions in the next-to-loading order approximation.

Determination of quark distributions in ep collisions

A method is presented for extracting various interesting quark distributions from measurements of differential cross sections for neutral and charged current processes at an ep collider such as HERA. The complete structure of ep interactions as described by the parton model in leading-order QCD and lowest-order electroweak theory is taken into account. Using Monte Carlo data we illustrate the experimental feasibility of the proposed unfolding procedure.

Degenerate states and the Kinoshita-Lee-Nauenberg theorem in deep-inelastic scattering.

A variation of the QCD parton model is proposed in which the partons are identified with nearly degenerate quark-gluon states. This relies only on the Kinoshita-Lee-Nauenberg theorem to cancel infrared singularities. In deep-inelastic scattering, incoming quark states are replaced by degenerate ``jet'' states and the Bjorken x variable is reinterpreted to be the momentum fraction of a ``jet'' in a hadron. Calculations of the full O(${\ensuremath{\alpha}}_{s}$) corrections are then done for the nonsinglet structure functions and for the associated nonsinglet operator matrix elements. In both quantities, the soft infrared singularities cancel and the collinear singularities cancel. Thus the proposal has been implemented. By the operator-product expansion the associated coefficient function is obtained and it is the usual one.

POLARIZATION IN LARGE PT PHOTOPRODUCTION OF VECTOR MESONS

QCD hard scattering model predictions for the vector meson (V) spin density matrix elements in the large pT process γp → VX are discussed. These results can be a test of both the underlying probabilistic scheme of the QCD parton model and of the elementary interactions, as well as a way of learning about the spin dependence of the fragmentation process of quarks and gluons. The process e+e- → VX in the γ-Z interference region is also discussed.

Polarization in large-pT photoproduction of vector mesons

We compute the QCD hard-scattering-model predictions for the vector-meson ($V$) spin-density-matrix elements in the large-${p}_{T}$ process $\ensuremath{\gamma}p\ensuremath{\rightarrow}\mathrm{VX}$. These results can be a test of both the underlying probabilistic scheme of the QCD parton model and of the elementary interactions, as well as a way of learning about the spin dependence of the fragmentation process of quarks and gluons.

On the determination of sin 2θw in semileptonic neutrino interactions

It is shown that if sin 2 θ w is measured in semileptonic neutrino interactions then, contrary to a claim in the literature, the error due to unknown dynamical (higher-twist) corrections to the QCD parton model is small provided an isoscalar target is used. The largest contributions to σ nc and σ cc are related by isospin invariance alone. Neglecting heavy quarks and Kobayashi-Maskawa (KM) mixing, the parton model is only needed for very small terms and introduces an uncertainty in sin 2 θ w which is probably less than 1%. There is a much larger theoretical error due to uncertainties in the element U cs of the KM matrix and in the strange quark distribution. With the full range 0.80 ⩽ | U cs | 0.98 which is allowed phenomenologically, these uncetainties give δsin 2 θ w = ± 0.008. There is also an error of ±0.004 due to uncertainties in | U dc| and | U du|.

Nuclear effects at large transverse momentum in a QCD parton model

Production of single mesons and opposite side pairs of mesons in hadron-nucleus and nucleusnucleus collisions are calculated in the framework of the QCD parton model, with the assumption that quarks and gluons undergo multiple scattering in the nucleus. A comparison with all available data is made. It is also shown that the anomalous nuclear enhancement, especially its dependence on the flavour, can be quantitatively described within the model. Furthermore, we predict no enhancement for symmetric pairs as it seems to be indicated by the data. Predictions for largep T production in α−α scattering at ISR are made.

Power corrections to the parton model in QCD

We calculate the power corrections to deep inelastic lepton-hadron scattering in QCD in terms of Feynman graphs, introducing a “transverse basis” of parton correlation functions as a useful language which, although unrelated to observable transverse momenta effects, may help physical intuition. The method is applicable to other hand scattering processes. In that framework we stress the relationship to the naïve parton model with intrinsic transverse momentum and show how the average intrinsic transverse momentum squared of that model is modified in the interacting theory.

The naive parton model and large pT scattering data

We attempt to fit FNAL data on large p T scattering beam and trigger particle ratio using a naive QCD parton model constrained as much as possible by existing experimental input. We find that, in the context of a model with canonical gluon distributions, recent data on the production of large p T pions by pion beams gives evidence for the presence of the three-gluon vertex. We argue, however, that there is no set of gluon distributions which is consistent with all the existing data.

Parton models of high momentum transfer electron-nuclear scattering

High-energy electron-nuclear scattering processes are discussed from the point of view of a parton model description. The light-cone formalism is introduced in a schematic presentation emphasizing: (i) the connection to relativistic dynamics, (ii) the phenomenological construction of the far off-shell components of wave functions, and (iii) asymptotic scaling laws. A survey is made of some of the recent calculations based on a nucleon constituent parton model and their comparison with data for momentum transfers Q 2 ≲ 6(GeV/ c) 2. A prospective discussion is also made on multiquark nuclear components and the quark parton model in QCD.

Target mass corrections in the QCD parton model

We show how target mass corrections can be incorporated to all orders of the QCD parton model, for leading and non-leading logarithms. This algorithm reproduces the ξ scaling analysis of totally inclusive leptoproduction. Target mass corrections to semi-inclusive leptoproduction are computed. We show that the simplest final-state variable to use is ωH = −2P′·q/Q2, where P′ is the observed hadron's momentum. We define double moments for this process for which scaling violations and factorization breaking are target-mass independent.

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.

Factorization and the parton model in QCD

We argue that mass-singularities of inclusive cross sections in QCD factor to all orders in perturbation theory as required for a parton model interpretation.