Transverse-momentum resummation of colorless final states at the NNLL+NNLO

TL;DR

The paper introduces an automated framework within Matrix to compute resummed transverse-momentum distributions for colorless final states at NNLL+NNLO, preserving full differential information and unitarity. By performing resummation in $b$-space with double Mellin moments and combining it with a fixed-order NNLO calculation via $q_T$-subtraction, it delivers accurate predictions for WW and ZZ production, including off-shell effects and spin correlations. The results demonstrate well-behaved small-$p_T$ spectra, reduced theoretical uncertainties, and strong agreement with CMS data for the $ZZ$ spectrum, showcasing the practical impact for precision collider phenomenology. This framework enables precise, fully differential predictions for a broad class of processes and supports future extensions to more complex final states and decay topologies.

Abstract

We present a general framework that allows to compute the resummed transverse-momentum distribution of a system of colorless particles. The implementation is fully differential in the degrees of freedom of the final-state system. As a first application, we consider the transverse-momentum spectrum of ZZ and WW boson pairs produced in hadron collisions, where we resum the logarithmically enhanced contributions due to multiple soft-gluon emission at small transverse momenta to all orders in perturbation theory. We exploit the most advanced perturbative information for the ZZ and WW production processes that is available at present by combining next-to-next-to-leading order QCD corrections with next-to-next-to-leading logarithmic resummation.

Figures (5)

• Figure 1: nameref-fig:matchingNNLO fith LAB: fig:matchingNNLO 1. NNLL1. +1. NNLO $p_T$ spectrum (blue, solid) of the $W^+W^-$ pair at (a) small and (b) large $p_T$ is compared to 1. NNLO (black, dotted) and the finite component of Eq. (\ref{['resplusfin']}) (magenta, dash-double dotted). The lower insets show the 1. NNLL1. +1. NNLO to 1. NNLO ratio.
• Figure 2: nameref-fig:bestpredictionww fith LAB: fig:bestpredictionww $p_T$ spectrum of (a) the $W^+W^-$ pair and (b) the $ZZ$ pair at 1. NLL1. +1. NLO (red, dashed) and 1. NNLL1. +1. NNLO (blue, solid); thick lines: central prediction; bands: $\mu_{F}{}$, $\mu_{R}{}$ and $Q$ uncertainties computed as described in the text; thin lines: borders of bands. The lower insets show the ratio to 1. NNLL1. +1. NNLO.
• Figure 3: nameref-fig:rap fith LAB: fig:rap (a) $W^+W^-$ transverse-momentum shapes at 1. NNLL1. +1. NNLO with cuts on the rapidity of the $W^+W^-$ pair: $|y|<0.5$ (red, solid), $0.5<|y|<1$ (blue, dashed), $1<|y|<2$ (black, dotted), $2<|y|<3$ (magenta, dash-dotted) and $3<|y|$ (orange, double-dash dotted); (b) shape-ratio with respect to the inclusive spectrum.
• Figure 4: nameref-fig:veto fith LAB: fig:veto $p_T$-veto efficiency of the $W^+W^-$ pair at various orders: 1. NLL1. +1. NLO (red, dashed), 1. NNLL1. +1. NNLO (blue, solid), 1. NLO (grey, dash-dotted), 1. NNLO (black, dotted), approximate 1. NNLL1. +1. NLO (magenta, dash-double dotted); thick lines: central prediction; bands: uncertainty due to combined scale variations; thin lines: borders of bands.
• Figure 5: nameref-fig:data fith LAB: fig:data (a) Experimental measurement of the $ZZ$$p_T$ shape in the fiducial region from Ref.CMS:2014xja and (b) comparison of the data with various predictions at higher orders.