Transverse-momentum spectra of electroweak bosons near threshold at NNLO

Abstract

Abstract:We obtain the next-to-next-to-leading order corrections to transversemomentum 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-toleading 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.

The transverse-momentum spectrum of Higgs bosons near threshold at NNLO

“…The resummation of logarithms should therefore only be a moderate effect. This observation was made earlier in [12,28,29], where it was found that resummation has a small effect on the central value but leads to somewhat reduced scale uncertainties. One sees from the plots that the scales determined from the NLO and NNLO corrections are almost identical, as they should be if there is a natural scale associated with the corrections.…”

“…What is also obvious from the plots is that all of the NNLO corrections to Z-production are small as long as the scales are chosen properly. Indeed, we found in [12] that the two-loop corrections to W and Z production are moderate, of the order of 5%.…”

“…large transverse momentum [12]. At this accuracy, the resummed result includes the full NNLO threshold cross section.…”

“…The jet and soft functions were computed to two-loop order earlier in [13,14] and [15]. In our recent paper [12], we extracted the final ingredient for N 3 LL resummation, namely the two-loop hard function, from the results for the two-loop helicity amplitudes for theses processes [16,17].…”

“…The construction of the hard function from the results for the four-point helicity amplitudes [16,17] is discussed in detail in [12]. It is obtained by squaring renormalized helicity amplitudes,…”