Abstract
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 (N3LL) 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.
Highlights
Precision and are at the few-percent level even for vector-boson pair production processes
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
We have further checked for these processes that we find full agreement at the level of matched cross sections calculated with Matrix+RadISH and those obtained by matching RadISH distributions with fixed-order predictions from MCFM [124, 125]
Summary
Matrix is a general framework for fixed-order calculations in QCD and EW perturbation theory, covering a large number of primary LHC scattering processes. We make use of the general implementation of fully differential NNLO cross sections in QCD perturbation theory for colour-singlet processes within Matrix. Since the subtraction is not local, a technical cut-off rcut on the dimensionless quantity r = pT /M , where pT is the transverse momentum and M is the invariant mass of the colourless system, is introduced, rendering both terms separately finite This cut-off dσNFL+Ojet and dσNCNTLO are assumed to be identical, which is correct up to power-suppressed terms. To perform the resummation of large logarithmic contributions, we have implemented a general interface to combine the Matrix framework with the RadISH code, which is introduced In this context, Matrix provides all the fixed-order parts of the calculation as well as the Born level phase space points and the hard coefficients needed for the calculation of the resummed component. Present a detailed study of the phenomenological implications for W +W − production only, but our implementation is completely general, and can directly be used for any of the other colour-singlet processes available in Matrix
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