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, $$W^\pm $$ W ± or $$\gamma ^*$$ γ ∗ ) at next-to-next-to-leading order in the strong coupling constant $$\alpha _\mathrm{S}$$ α S . We impose a transverse-momentum cutoff, $$q_{\mathrm{T}}^{\mathrm{cut}}$$ q T 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 $$\alpha _\mathrm{S}^2$$ α 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 $$q_{\mathrm{T}}$$ q T -subtraction method is applied. In addition, the study of the dependence of the cross section on $$q_{\mathrm{T}}^{\mathrm{cut}}$$ q T 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 $$\alpha _\mathrm{S}$$ α 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 $$q_{\mathrm{T}}^{\mathrm{cut}}$$ q T cut .

Non-local slicing approaches for NNLO QCD in MCFM

“…[116], and up to second order for the NNLO qg-initiated channel in Ref. [117]. Therefore a full suite of power corrections at NNLO is not available, even for the simplest processes.…”

Next-to-leading power two-loop soft functions for the Drell-Yan process at threshold

“…However, it should be noted that at NLP accuracy, calculations and studies of the renormalization and evolution properties of the soft function needed for the h → γγ decay process were recently JHEP10(2021)061 presented at O(α s ) in [34,35]. In the context of the q T -subtraction method, calculations at fixed-order accuracy, which required the evaluation of several new integrals, have been recently carried out at NLP in QCD [36] without separating the different regions.…”

Higgs boson production at the LHC: fast and precise predictions in QCD at higher orders

“…However for finite value of q cut T the cross section in Eq. ( 4) contains perturbative power corrections ambiguities O((q cut T /M ) p ) [39][40][41][42], with p > 0 which are particularly severe in the case of fiducial selection cuts which yield an acceptance that has a residual linear dependence on q cut T [40,43,44]. A method to remove such linear fiducial power corrections (FPC) within the q T subtraction formalism has been proposed in Refs.…”