Threshold Resummation for W-Boson Production at RHIC

TL;DR

The paper addresses large threshold logarithms in W boson production in singly polarized proton-proton collisions at RHIC and develops a next-to-leading logarithmic threshold resummation for the rapidity-differential cross section using Mellin-Fourier techniques. Resummation is matched to the fixed-order NLO result to preserve accuracy and include qg channels. Numerical results show modest corrections at RHIC's 500 GeV energy but significantly larger corrections near threshold at 200 GeV, with improved scale stability and little impact on the rapidity shape or spin asymmetry. These findings enhance the theoretical precision for extracting polarized quark and anti-quark distributions from RHIC data.

Abstract

We study the resummation of large logarithmic perturbative corrections to the partonic cross sections relevant for the process pp -> W^+- X at the BNL Relativistic Heavy Ion Collider (RHIC). At RHIC, polarized protons are available, and spin asymmetries for this process will be used for precise measurements of the up and down quark and anti-quark distributions in the proton. The corrections arise near the threshold for the partonic reaction and are associated with soft-gluon emission. We perform the resummation to next-to-leading logarithmic accuracy, for the rapidity-differential cross section. We find that resummation leads to relatively moderate effects on the cross sections and spin asymmetries.

Figures (5)

• Figure 1: (a) Differential cross section for $W^+$-production in unpolarized $pp$ collision at RHIC for ${\sqrt S}=500$ GeV as a function of the rapidity of the produced boson. (b) Same, but when one of the proton beams is longitudinally polarized. (c) The corresponding single-spin asymmetry ${\mathrm A}_L$. For all three plots, "resummed(1)" denotes the threshold-resummed cross section without including subleading $\ln(\bar{N})/N$ terms and without the $\cos\left( M\ln\frac{1}{\sqrt{z}}\right)$ term, while for "resummed(2)" the Cosine term is included. "Resummed(3)" is with the $\ln(\bar{N})/N$ terms. The curve labelled "NNLO exp." gives the NNLO expansion of the "resummed(1)" result. We also display the LO and NLO cross sections.
• Figure 2: Same as Fig. \ref{['fig1']}, but for $W^-$ production.
• Figure 3: Same as Fig. \ref{['fig1']}, but for $\sqrt{S}=200$ GeV.
• Figure 4: Same as Fig. \ref{['fig2']}, but for $\sqrt{S}=200$ GeV.
• Figure 5: (a) Scale dependence of the NLO and the "resummed(1)" differential cross sections for $W^+$ production in unpolarized $pp$ collisions at RHIC at ${\sqrt S}=500$ GeV. We have varied the factorization/renormalization scale $\mu$ between $M_W/2$ and $2 M_W$. Note that we have multiplied the NLO cross section by 0.8 for better visibility. The uppermost curves in each case are for the scale $M_W/2$. (b) Same for the singly-polarized cross section. (c) Scale dependence of the single-spin asymmetry ${\mathrm A}_L$, calculated from the resummed cross sections.