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 → 2 production processes. As an important application we consider W$^{+}$W$^{−}$ production at the LHC, more precisely the full leptonic process pp → $ {\mathrm{\ell}}^{+}\mathrm{\ell}{\prime}^{-}{\nu}_{\mathrm{\ell}}{\overline{\nu}}_{\mathrm{\ell}\prime } $ + X with ℓ′ ≠ ℓ, 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.