Prospects for Spin Physics at RHIC

Colliding beams of 70% polarized protons at up to $\sqrt{s}$=500 GeV, with high luminosity, L=2$\times10^{{\rm 32}}$ cm$^{-2}$sec$^{-1}$, will represent a new and unique laboratory for studying the proton. RHIC-Spin will be the first polarized-proton collider and will be capable of copious production of jets, directly produced photons, and $W$ and $Z$ bosons. Features will include direct and precise measurements of the polarization of the gluons and of $\bar{u}$, $\bar{d}$, $u$, and $d$ quarks in a polarized proton. Parity violation searches for physics beyond the standard model will be competitive with unpolarized searches at the Fermilab Tevatron. Transverse spin will explore transversity for the first time, as well as quark-gluon correlations in the proton. Spin dependence of the total cross section and in the Coulomb nuclear interference region will be measured at collider energies for the first time. These qualitatively new measurements can be expected to deepen our understanding of the structure of matter and of the strong interaction.Comment: 51 pages, 22 figures. Scheduled to appear in the Annual Review of Nuclear and Particle Science Vol. 50, to be published in December 2000 by Annual Reviews, http://AnnualReviews.or

What two models may teach us about duality violations in QCD

Though the operator product expansion is applicable in the calculation of current correlation functions in the Euclidean region, when approaching the Minkowskian domain, violations of quark-hadron duality are expected to occur, due to the presence of bound-state or resonance poles. In QCD finite-energy sum rules, contour integrals in the complex energy plane down to the Minkowskian axis have to be performed, and thus the question arises what the impact of duality violations may be. The structure and possible relevance of duality violations is investigated on the basis of two models: the Coulomb system and a model for light-quark correlators which has already been studied previously. As might yet be naively expected, duality violations are in some sense "maximal" for zero-width bound states and they become weaker for broader resonances whose poles lie further away from the physical axis. Furthermore, to a certain extent, they can be suppressed by choosing appropriate weight functions in the finite-energy sum rules. A simplified Ansatz for including effects of duality violations in phenomenological QCD sum rule analyses is discussed as well.Comment: 17 pages, 6 figures; version to appear in JHE

Reggeon exchange from gauge/gravity duality

We perform the analysis of quark-antiquark Reggeon exchange in meson-meson scattering, in the framework of the gauge/gravity correspondence in a confining background. On the gauge theory side, Reggeon exchange is described as quark-antiquark exchange in the t channel between fast projectiles. The corresponding amplitude is represented in terms of Wilson loops running along the trajectories of the constituent quarks and antiquarks. The paths of the exchanged fermions are integrated over, while the "spectator" fermions are dealt with in an eikonal approximation. On the gravity side, we follow a previously proposed approach, and we evaluate the Wilson-loop expectation value by making use of gauge/gravity duality for a generic confining gauge theory. The amplitude is obtained in a saddle-point approximation through the determination near the confining horizon of a Euclidean "minimal surface with floating boundaries", i.e., by fixing the trajectories of the exchanged quark and antiquark by means of a minimisation procedure, which involves both area and length terms. After discussing, as a warm-up exercise, a simpler problem on a plane involving a soap film with floating boundaries, we solve the variational problem relevant to Reggeon exchange, in which the basic geometry is that of a helicoid. A compact expression for the Reggeon-exchange amplitude, including the effects of a small fermion mass, is then obtained through analytic continuation from Euclidean to Minkowski space-time. We find in particular a linear Regge trajectory, corresponding to a Regge-pole singularity supplemented by a logarithmic cut induced by the non-zero quark mass. The analytic continuation leads also to companion contributions, corresponding to the convolution of the same Reggeon-exchange amplitude with multiple elastic rescattering interactions between the colliding mesons.Comment: 60+1 pages, 14 figure

Roy-Steiner equations for pion-nucleon scattering

Starting from hyperbolic dispersion relations, we derive a closed system of Roy-Steiner equations for pion-nucleon scattering that respects analyticity, unitarity, and crossing symmetry. We work out analytically all kernel functions and unitarity relations required for the lowest partial waves. In order to suppress the dependence on the high-energy regime we also consider once- and twice-subtracted versions of the equations, where we identify the subtraction constants with subthreshold parameters. Assuming Mandelstam analyticity we determine the maximal range of validity of these equations. As a first step towards the solution of the full system we cast the equations for the $\pi\pi\to\bar NN$ partial waves into the form of a Muskhelishvili-Omn\`es problem with finite matching point, which we solve numerically in the single-channel approximation. We investigate in detail the role of individual contributions to our solutions and discuss some consequences for the spectral functions of the nucleon electromagnetic form factors.Comment: 106 pages, 18 figures; version published in JHE

Wilson-loop formalism for Reggeon exchange in soft high-energy scattering

We derive a nonperturbative expression for the non-vacuum, qqbar-Reggeon-exchange contribution to the meson-meson elastic scattering amplitude at high energy and low momentum transfer, in the framework of QCD. Describing the mesons in terms of colourless qqbar dipoles, the problem is reduced to the two-fermion-exchange contribution to the dipole-dipole scattering amplitudes, which is expressed as a path integral, over the trajectories of the exchanged fermions, of the expectation value of a certain Wilson loop. We also show how the resulting expression can be reconstructed from a corresponding quantity in the Euclidean theory, by means of analytic continuation. Finally, we make contact with previous work on Reggeon exchange in the gauge/gravity duality approach.Comment: A few misprints in the expressions for the relevant Wilson loops have been corrected. 55 pages, 7 figure