Higher-order power corrections in a transverse-momentum cut for colour-singlet production at NLO

We consider the production of a colourless system at next-to-leading order in the strong coupling constant \(\alpha _{{\displaystyle } {\scriptstyle } {\scriptscriptstyle } {\scriptscriptstyle } \mathrm{S}}\). We impose a transverse-momentum cutoff, \(q_{{\displaystyle } {\scriptstyle } {\scriptscriptstyle } {\scriptscriptstyle } \mathrm{T}}^{{\displaystyle } {\scriptstyle } {\scriptscriptstyle } {\scriptscriptstyle } \mathrm{cut}}\), on the colourless final state and we compute the power corrections for the inclusive cross section in the cutoff, up to the fourth power. The study of the dependence of the cross section on \(q_{{\displaystyle } {\scriptstyle } {\scriptscriptstyle } {\scriptscriptstyle } \mathrm{T}}^{{\displaystyle } {\scriptstyle } {\scriptscriptstyle } {\scriptscriptstyle } \mathrm{cut}}\) allows for an understanding of its behaviour at the boundaries of the phase space, giving hints on the structure at all orders in \(\alpha _{{\displaystyle } {\scriptstyle } {\scriptscriptstyle } {\scriptscriptstyle } \mathrm{S}}\) and on the identification of universal patterns. The knowledge of such power corrections is also a required ingredient in order to reduce the dependence on the transverse-momentum cutoff of the QCD cross sections at higher orders, when the \(q_{\mathrm{T}}\)-subtraction method is applied. We present analytic results for both Drell–Yan vector boson and Higgs boson production in gluon fusion and we illustrate a process-independent procedure for the calculation of the all-order power corrections in the cutoff. In order to show the impact of the power-correction terms, we present selected numerical results and discuss how the residual dependence on \(q_{{\displaystyle } {\scriptstyle } {\scriptscriptstyle } {\scriptscriptstyle } \mathrm{T}}^{{\displaystyle } {\scriptstyle } {\scriptscriptstyle } {\scriptscriptstyle } \mathrm{cut}}\) affects the total cross section for Drell–Yan Z production and Higgs boson production via gluon fusion at the LHC.