Transverse-momentum spectra of electroweak bosons near threshold at NNLO

TL;DR

This paper calculates NNLO corrections to the transverse-momentum spectra of electroweak bosons near threshold, improving theoretical precision and reducing uncertainties in predictions for W, Z, and Higgs boson production.

Contribution

It provides the first NNLO threshold corrections for electroweak boson spectra, combining two-loop amplitudes with soft-collinear functions in SCET, and implements results in a public code.

Findings

Moderate increase in W and Z cross sections due to two-loop corrections.

Reduction of scale uncertainty by about a factor of two.

Significantly larger corrections observed for Higgs production.

Abstract

We obtain the next-to-next-to-leading order corrections to transverse-momentum spectra of W, Z and Higgs bosons near the partonic threshold. In the threshold limit, the electroweak boson recoils against a low-mass jet and all radiation is either soft, or collinear to the jet or the beam directions. We extract the virtual corrections from known results for the relevant two-loop four-point amplitudes and combine them with the soft and collinear two-loop functions as defined in Soft-Collinear Effective Theory. We have implemented these results in a public code PeTeR and present numerical results for the threshold resummed cross section of W and Z bosons at next-to-next-to-next-to-leading logarithmic accuracy, matched to next-to-leading fixed-order perturbation theory. The two-loop corrections lead to a moderate increase in the cross section and reduce the scale uncertainty by about a factor of two. The corrections are significantly larger for Higgs production.