W hadroproduction at large transverse momentum beyond next-to-leading order

TL;DR

This paper analyzes W boson production at large transverse momentum in $p\bar{p}$ collisions and demonstrates that NLO cross sections are dominated by threshold soft-gluon corrections. Building on this, the authors compute NNLO soft-gluon corrections with NNLL and NN NNNLL accuracy for the two leading partonic channels, using $Q_T$ as the hard scale. They find that NNLO soft corrections provide modest enhancements and significantly reduce the factorization/renormalization scale dependence, yielding more stable predictions for Tevatron energies. Overall, the work reinforces the effectiveness of threshold resummation techniques in improving theoretical predictions for electroweak-boson production at high $Q_T$ and provides improved benchmarks for SM tests and new-physics backgrounds.

Abstract

We study the production of W bosons at large transverse momentum in p pbar collisions. We show that the next-to-leading order cross section at large transverse momentum is dominated by threshold soft-gluon corrections. We add next-to-next-to-leading-order soft-gluon corrections to the exact next-to-leading-order differential cross sections. We find that these higher-order corrections provide modest enhancements to the transverse momentum distribution of the W at the Tevatron, and reduce significantly the dependence on the factorization and renormalization scales.

Figures (8)

• Figure 1: The differential cross section, $d\sigma/dQ_T^2$, for $W$ hadroproduction in $p \bar{p}$ collisions at the Tevatron with $\sqrt{S}=1.8$ TeV and $\mu_F=\mu_R=Q_T$. Shown are the Born (solid line), NLO (long-dashed line), NNLO-NNLL (short-dashed line), and NNLO-NNNLL (dotted line) results.
• Figure 2: The differential cross section, $d\sigma/dQ_T^2$, of Fig. 1 at high $Q_T$. The labels are the same as in Fig. 1.
• Figure 3: The $K$-factors for the differential cross section, $d\sigma/dQ_T^2$, for $W$ hadroproduction in $p \bar{p}$ collisions at the Tevatron with $\sqrt{S}=1.8$ TeV and $\mu_F=\mu_R=Q_T$. Shown are the $K$- factors for exact NLO/Born (long-dashed line), NLO-NLL/Born (dash-dotted line), NNLO-NNLL/Born (short-dashed line), and approximate NNLO-NNNLL/Born (dotted line) results. Also shown is the ratio of the exact NLO to the NLO-NLL cross section (solid line).
• Figure 4: The differential cross section, $d\sigma/dQ_T^2$, for $W$ hadroproduction in $p \bar{p}$ collisions at the Tevatron with $\sqrt{S}=1.8$ TeV, $Q_T=80$ GeV, and $\mu \equiv \mu_F=\mu_R$. Shown are the Born (solid line), exact NLO (long-dashed line), and NNLO-NNNLL (dotted line) results.
• Figure 5: The differential cross section, $d\sigma/dQ_T^2$, for $W$ hadroproduction in $p \bar{p}$ collisions at the Tevatron with $\sqrt{S}=1.8$ TeV and $\mu\equiv\mu_F=\mu_R=Q_T/2$ or $2Q_T$. Shown are the Born (solid lines), NLO (long-dashed lines), and NNLO-NNNLL (dotted lines) results. The upper lines are with $\mu=Q_T/2$, the lower lines with $\mu=2 Q_T$.