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Electroweak corrections to the observables of W-boson production at RHIC

V. A. Zykunov

TL;DR

This work analyzes electroweak radiative corrections to inclusive single W production in polarized hadron collisions, aiming to constrain nucleon spin structure through low-$x$ polarized quark densities. It develops a complete $O(\alpha)$ framework combining virtual corrections and real photon bremsstrahlung, with infrared divergences canceled, and expresses results as cross sections and single-spin asymmetries that factorize the second hadron polarization. Numerical studies for RHIC energies using GRV94/GRSV96 PDFs show that $O(\alpha)$ corrections can noticeably modify cross sections and especially single-spin asymmetries, while remaining relatively insensitive to light-quark masses. The results provide a practical, infrared-safe method for precision spin measurements at RHIC (and similar facilities) using W-boson production to extract polarized parton densities at low $x$.

Abstract

The processes of the single W-production in hadron-hadron collisions are suggested for investigation of the nucleon spin. An approach is proposed for the determination of quark spin densities at low x. The lowest order electroweak radiative corrections to the observable quantities are calculated. The numerical calculations of the cross sections and the single spin asymmetries taking into consideration the electroweak corrections at RHIC energies have been made.

Electroweak corrections to the observables of W-boson production at RHIC

TL;DR

This work analyzes electroweak radiative corrections to inclusive single W production in polarized hadron collisions, aiming to constrain nucleon spin structure through low- polarized quark densities. It develops a complete framework combining virtual corrections and real photon bremsstrahlung, with infrared divergences canceled, and expresses results as cross sections and single-spin asymmetries that factorize the second hadron polarization. Numerical studies for RHIC energies using GRV94/GRSV96 PDFs show that corrections can noticeably modify cross sections and especially single-spin asymmetries, while remaining relatively insensitive to light-quark masses. The results provide a practical, infrared-safe method for precision spin measurements at RHIC (and similar facilities) using W-boson production to extract polarized parton densities at low .

Abstract

The processes of the single W-production in hadron-hadron collisions are suggested for investigation of the nucleon spin. An approach is proposed for the determination of quark spin densities at low x. The lowest order electroweak radiative corrections to the observable quantities are calculated. The numerical calculations of the cross sections and the single spin asymmetries taking into consideration the electroweak corrections at RHIC energies have been made.

Paper Structure

This paper contains 10 sections, 94 equations, 10 figures.

Table of Contents

  1. Introduction
  2. Born cross section and single asymmetries
  3. Contribution of additional virtual particles to the cross section
  4. The photon bremsstrahlung $N_1 \stackrel{\rightarrow}{N_2} \rightarrow l^{\pm} \gamma X$
  5. Discussion of numerical results and conclusions
  6. Acknowledgments
  7. Phase space of photon and scalar integrals
  8. Expressions for the $V_j$.
  9. The case of $q \bar{q} \rightarrow l^- \bar{\nu}_l, \bar{q} q \rightarrow l^+ \nu_l$ subprocesses
  10. The case of for $q \bar{q} \rightarrow l^+ \nu_l, \bar{q} q \rightarrow l^- \bar{\nu}_l$ subprocesses

Figures (10)

  • Figure 1: (1) Sketch illustrating the interaction of parton 1 and 2 from incident nucleons $N_1$ and $N_2$, respectively. The partons carry fractional momenta $x_1$ and $x_2$ and interact to produce a charged lepton and antineutrino. (2) The diagram for the lowest order subprocess $q\bar{q}\rightarrow l^- \bar{\nu}$.
  • Figure 2: Physically allowed region of variables $x_1$ and $x_2$. Curves on the plot are $x_2^0$ as a function of $x_1$ at different $\eta$ (kinematics of RHIC experiment STAR: $\sqrt{S}$=500 GeV, ${k_1}_{\perp}$=40 GeV).
  • Figure 3: The virtual one-loop diagrams for $q \bar{q} \rightarrow l^- \bar{\nu}$ process. The contributions to the self-energies and vertex corrections are symbolized by the empty loops, an explicit representation can be found in Ref.BS2.
  • Figure 4: Bremsstrahlung diagrams for $q \bar{q} \rightarrow l^- \bar{\nu} \gamma$ process.
  • Figure 5: Differential cross sections for $p\bar{p} \rightarrow \mu^+X$ at $\sqrt{S}=1.8$ TeV, $-1.2\leq \eta \leq 1.2$, $\Delta \Phi=2\pi$ (Tevatron) as a function of ${k_1}_T$. Shown is the muon transverse momentum spectrum in the Born approximation (dashed line) and taking into account the total EWC (solid line). We use the MRS LO 98 set of parton distribution functions MRS98.
  • ...and 5 more figures