Linear power corrections for two-body kinematics in the $q_T$ subtraction formalism

Abstract: Transverse-momentum cuts on undistinguished particles in two-body final states induce an enhanced sensitivity to low momentum scales. This undesirable feature, which ultimately leads to an instability of the fixed-order series, poses additional challenges to non-local subtraction schemes. In this letter, we address this issue for general colour-singlet processes within the $q_T$-subtraction formalism, focussing on neutral-current Drell-Yan production. We present a simple procedure to reduce the dependence on the slicing parameter from linear to quadratic, by accounting for the linear power corrections through an appropriate recoil prescription. We observe a dramatical improvement of the numerical convergence and a reduction of the systematic uncertainties. We also discuss how a linear dependence in $q_T$ can be avoided for Drell-Yan production by using staggered cuts, which, to the best of our understanding, could be used in experimental analyses. We show that our approach can be successfully applied also to on-shell $ZZ$ production. We finally study diphoton production and verify that our approach is insufficient to capture the linear power corrections introduced by the isolation procedure. The recoil prescription is available in version 2.1 of MATRIX.