Accurate single- and double-differential resummation of colour-singlet processes with MATRIX+RadISH: $W^+W^-$ production at the LHC

We present the combination of fully differential cross sections for colour-singlet production processes at next-to-next-to-leading order (NNLO) QCD obtained with MATRIX and all-order resummation through RadISH. This interface allows us to achieve unprecedented accuracy for various transverse observables in $2 \rightarrow 2$ production processes. As an important application we consider $W^+ W^-$ production at the LHC, more precisely the full leptonic process $pp\to \ell^+\ell^{\prime\, -}\nu_{\ell}{\bar\nu}_{\ell^\prime}+X$ with $\ell'\neq\ell$, and we present resummed predictions for differential distributions in presence of fiducial selection cuts. In particular, we resum the transverse-momentum spectrum of the $W^+ W^-$ pair at next-to-next-to-next-to-leading logarithmic (N$^3$LL) accuracy and match it to the integrated NNLO cross section. The transverse-momentum spectrum of the leading jet in $W^+ W^-$ production is calculated at NNLO+NNLL accuracy. Finally, the joint resummation for the transverse-momentum spectrum of the $W^+ W^-$ pair in the presence of a jet veto is performed at NNLO+NNLL. Our phenomenological study highlights the importance of higher-order perturbative and logarithmic corrections for precision phenomenology at the LHC.