Abstract
We consider the production of a vector boson (Z, W^pm or gamma ^*) at next-to-next-to-leading order in the strong coupling constant alpha _mathrm{S}. We impose a transverse-momentum cutoff, q_{mathrm{T}}^{mathrm{cut}}, on the vector boson produced in the qg-initiated channel. We then compute the power corrections in the cutoff, up to the second power, of the real-virtual interference contribution to the cumulative cross section at order alpha _mathrm{S}^2. Other terms with the same kinematics, originating from the subtraction method applied to the double-real contribution, have been also considered. The knowledge of such power corrections is a required ingredient in order to reduce the dependence on the transverse-momentum cutoff of the QCD cross sections at next-to-next-to-leading order, when the q_{mathrm{T}}-subtraction method is applied. In addition, the study of the dependence of the cross section on q_{mathrm{T}}^{mathrm{cut}} allows as well for an understanding of its behaviour in the small transverse-momentum limit, giving hints on the structure at all orders in alpha _mathrm{S} and on the identification of universal patterns. Our result are presented in an analytic form, using the process-independent procedure described in a previous paper for the calculation of the all-order power corrections in q_{mathrm{T}}^{mathrm{cut}}.
Highlights
Slicing methods that have been successfully applied at NNLO and N3LO are the transverse-momentum subtraction method [1,2,3,4,5] and N jettiness subtraction [6,7]
By subtracting the lowest powers in the cutoff makes the result less sensitive to the arbitrary cutoff, numerically approaching the theoretical limit of this parameter going to zero. This is valid when the subtraction method is applied to NLO computations, but it is numerically more relevant when applied to higher-order calculations, as pointed out, for example, in the evaluation of NNLO cross sections in Refs. [8,9]
We impose a transverse-momentum cutoff, qTcut, on the vector boson produced in the qg-initiated channel, and we compute, for the first time, the power corrections in the cutoff, up to the second power2, of the real-virtual interference contribution to the cumulative cross section at order αS2, plus other terms with the same kinematics, originating from the application of the subtraction method to the doublereal contribution
Summary
We consider the production of a colourless system F with quadri-momentum q and squared invariant mass Q2, plus a coloured system X at a hadron collider h1 + h2 → F + X. We have made explicit the dependence on z, the ratio between the squared invariant mass of the system F and the partonic center-of-mass energy, and on qT, the transverse momentum of the system F with respect to the hadronic beams. The couplings appearing in the differential cross sections follow this convention: if an electroweak boson F is emitted by a quark with flavour f1 = {u, d, s, c, b} which changes into f2, the vertex is described by the Feynman rule. BB2q3qgg originates from the is the contribution renormalisation from the virtual diagrams with a triangular quark loop, which are present only for Z /γ ∗ production. These contributions are multiplied by a δ(s2) term, since the system recoiling against the. Page 5 of 15 183 and, with a little abuse of notation, when referring to Eq (2.23), we sometimes drop the δ(s2), to ease the notation
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