Power corrections in a transverse-momentum cut for vector-boson production at NNLO: the $qg$-initiated real-virtual contribution

Abstract

We consider the production of a vector boson ($Z$, $W^{\pm }$ or ${\gamma }^{\ast }$) 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 $q_{\mathrm{T}}^{\mathrm{cut}}$.

28 pages. arXiv admin note: text overlap with arXiv:1906.09044

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