Pervez Hoodbhoy

Spin Structure of the Nucleon in the Asymptotic Limit

In analogy with the Altarelli-Parisi equation for quark and gluon helicity contributions to the nucleon spin, we derive an evolution equation for quark and gluon orbital angular momenta. Solution of the combined equations yields asymptotic fractions of the nucleon spin carried by quarks and gluons: DSy2 1 Lq › 3nf ys16 1 3nf d and Dg 1 Lg › 16ys16 1 3nfd, respectively, with nf the number of active quark flavors. These are identical to the well-known asymptotic partitions of the nucleon momentum between quark and gluon contributions. The axial-anomaly contribution to the quark helicity is canceled with a similar contribution to the quark orbital angular momentum, making the total quark contribution to the nucleon spin anomaly free. PACS numbers: 13.88.+e, 12.38.Bx, 13.60.Hb, 14.20.Dh What is the composition of the nucleon spin in terms of its quark and gluon constituents? In the last few years, the answer has become the holy grail for the nuclear and particle spin community. The motivation is quite clear: given quantum chromodynamics (QCD) is difficult to solve, such information gives us valuable insights into the nonperturbative wave function of the nucleon. A satisfactory understanding of the spin structure would be to know, for instance, how much spin of the nucleon is carried, respectively, by the quark and gluon helicities and orbital angular momenta, in the same way as one now understands how the mass of the nucleon is partitioned among contributions from the quark and gluon kinetic energies, quark masses, and the trace anomaly [1]. The theoretical basis for separating the spin of the nucleon into different contributions begins with the QCD expression for the generators of Lorentz transformations [2],

Helicity-flip off-forward parton distributions of the nucleon

We identify quark and gluon helicity-flip distributions defined between nucleon states of unequal momenta. The evolution of these distributions with a change of renormalization scale is calculated in the leading-logarithmic approximation. The helicity-flip gluon distributions do not mix with any quark distribution and are thus a unique signature of gluons in the nucleon. Their contribution to the generalized virtual Compton process is obtained both in the form of a factorization theorem and an operator product expansion. In deeply virtual Compton scattering, they can be probed through the distinct angular dependence of the cross section. {copyright} {ital 1998} {ital The American Physical Society}

Wave function corrections and off-forward gluon distributions in diffractive J/{psi} electroproduction

Diffractive production of J/{psi} particles by virtual photons on a proton target is studied with a view towards understanding two important corrections to the leading order result. First, the effect of Fermi motion of the heavy quarks is studied by performing a systematic expansion in the relative velocity, and a simple correction factor is derived. This is considerably less than estimated previously. Second, since the kinematics necessarily requires that nonzero momentum be transferred to the proton, off-forward gluon distributions are probed by the scattering process. To estimate the importance of the off-forwardness, we compute, in leading order perturbation theory, the extent of deviation from the usual forward gluon distribution in a quark. {copyright} {ital 1997} {ital The American Physical Society}

Quark fragmentation functions in a diquark model for proton and [Lambda] hyperon production

A simple quark-diquark model for nucleon and [Lambda] structure is used to calculate leading twist light-cone fragmentation functions for a quark to inclusively decay into [ital p] or [Lambda]. The parameters of the model are determined by fitting to the known deep-inelastic structure functions of the nucleon. When evolved from the initial to the final [ital Q][sup 2] scale, the calculated fragmentation functions are in remarkable agreement (for [ital z][gt]0.4) with those extracted from partially inclusive [ital ep] and [ital e][sup +][ital e][sup [minus]] experiments at high energies. Predictions are made, using no additional parameters, for longitudinally and transversely polarized quarks to fragment into [ital p] or [Lambda].

Shadowing of deuteron spin structure functions

Abstract The low x behavior of the twist-two structure functions F2D(x), g1D(x), b1D(x) for the deuteron is examined in the framework of the LPS (Landshoff-Polkinghorne-Short) model for deep inelastic scattering, combined with Glauber theory for quark-nucleon scattering. The quadrupole structure function b1D(x,Q2), which would otherwise vanish for a pure deuteron s-state, turns out to be non-zero once double scattering terms are included. We also observe that, because of nucleon spin correlations in the target, even the unpolarized nuclear structure function requires knowledge of the spin distribution of partons inside individual nucleons. Assuming a simple s-state only in the model of the deuteron, numerical estimates are presented for all twist-two structure functions.

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.

Threshold π0 photoproduction from the Skyrmion

Abstract The Skyrme model for nucleons is used to calculate threshold π 0 photoproduction off a proton. It was found that the anomalous part of the electromagnetic current yields an important contribution to the photoproduction amplitude, roughly of the same magnitude normally ascribed to ω meson exchange. Agreement with the experimental threshold cross section can thus be achieved without invoking ω exchange.

Systematic gauge-invariant approach to heavy quarkonium decays.

We present a method which, starting directly from QCD, permits a systematic gauge-invariant expansion to be made for all hard processes involving quarkonia in powers of the quark relative velocity, a small natural parameter for heavy quark systems. Our treatment automatically introduces soft gluons in the expansion. Corrections arising from the incorporation of gauge symmetry turn out to be important for decay and fragmentation processes involving {ital Q{bar Q}} systems. The contribution of soft gluons is shown to be of higher order in {ital v} and so is neglected for calculations done up to and including {ital O}({ital v}{sup 2}). {copyright} {ital 1996 The American Physical Society.}

The swelling of nucleons and quark antisymmetrization

Abstract Antisymmetrization of the nuclear wavefunction at the quark level implies that quarks belonging to different nucleons are exchanged in proportion to the degree of nucleon overlap. This leads to an additional contribution to the quark-quark correlation beyond that expected in a conventional picture. We first explore this in a simple solvable one-dimensional model. Subsequently an extension is made to a model of nuclear matter for which divergences are encountered in the limit of large N . These are traced to the existence of unlinked quark clusters. After renormalization, the quarkquark correlation is computed. It is concluded that quark antisymmetrization leads to an effective nucleon size which depends on the nuclear density. A simple analytic formula for the effective nucleon radius is obtained.

Explicit proof that electroproduction of transversely polarized mesons vanishes in perturbative QCD

By means of an explicit one-loop calculation, it is shown that the leading twist contribution to the exclusive electroproduction of transversely polarized vector mesons from the nucleon vanishes. This confirms the all-orders proof by Collins and Diehl.