Next-to-leading order jet cross sections in polarized hadronic collisions

TL;DR

This paper presents the first complete next-to-leading order QCD calculation of one- and two-jet cross sections in polarized hadronic collisions, extending the FKS subtraction framework to polarized beams and implementing a Monte Carlo parton generator. It analyzes perturbative stability and dependence on polarized parton distributions, highlighting the large uncertainties in the polarized gluon density Δg and the resulting spread in jet observables. The authors demonstrate that NLO corrections reduce scale dependence and that RHIC jet measurements have potential to constrain Δg, though asymmetries may be small and require substantial luminosity. Overall, the work provides a practical tool for predicting polarized jet observables at RHIC and for exploring Δg through jet data.

Abstract

We present a next-to-leading order computation in QCD of one-jet and two-jet cross sections in polarized hadronic collisions. Our results are obtained in the framework of a general formalism that deals with soft and collinear singularities using the subtraction method. We construct a Monte Carlo program that generates events at the partonic level. We use this code to give phenomenological predictions for $pp$ collisions at $\sqrt{S}=500$ GeV, relevant for the spin physics program at RHIC. The possibility of using jet data to constrain the poorly known polarized parton densities is examined.

Figures (9)

• Figure 1: The polarized gluon (left) and valence quark densities (right), as given by the six NLO parametrizations that will be used in this paper, at the scale $Q^2 = 100\ \mathrm{GeV}^2$. The patterns for the quark densities are the same as those used for the gluon.
• Figure 2: Ratio of NLO to LO polarized gluon densities. We use the same pattern as in fig. \ref{['figPDF']} to distinguish the various lines. Also shown is the ratio for an unpolarized (GRV) set.
• Figure 3: Ratio of the next-to-leading order cross section over (a) the tree-level cross section (i.e. leading order pdf) and (b) the Born cross section (i.e. next-to-leading order pdf) for various parton densities. We use the same pattern as in fig. \ref{['figPDF']} to distinguish the various parton densities.
• Figure 4: Scale dependence of the next-to-leading order and Born $p_{ T}$-distributions for the Ellis--Soper algorithm with $D=1$. (a) Polarized $pp$ scattering and (b) unpolarized $pp$ scattering at $\sqrt{S} =$ 500 GeV. The range of the pseudo-rapidity is restricted to $|\eta| < 1$.
• Figure 5: As in fig. \ref{['figPT']}, for the $x_1$-distribution (see the text for the definition).