Projection-to-Born-improved Subtractions at NNLO

Abstract

While the current frontier in fixed-order precision for collider observables is N$^3$LO, important steps are necessary to consolidate NNLO cross-section predictions with improved stability and efficiency. Slicing methods have been successfully applied to obtain NNLO and N$^3$LO predictions, but have shown poor performance in the presence of fiducial cuts due to large kinematical power corrections. In this paper we implement Projection-to-Born-improved $q_T$ (P2B $q_T$) and jettiness (P2B $τ_0$) subtractions for a large class of color singlet processes in MCFM. This method allows for the efficient evaluation of \emph{fiducial} power corrections in any non-local subtraction scheme using a Projection-to-Born subtraction. We demonstrate the significant numerical improvements of this method based on fiducial Drell-Yan and Higgs cross-sections. Moreover, with fiducial power corrections removed via this method, the leading-logarithmic power corrections that have only been calculated without fiducial cuts can be included, further improving the calculations. For di-photon production with photon isolation, we devise a novel method in combination with P2B-improved subtractions, which we name $P2B_γ$ $τ_0$, and $P2B_γ$ $q_T$ for the two subtraction schemes, respectively. This method allows the inclusion of both fiducial power corrections due to kinematic cuts on the photons and a set of isolation power corrections in the fragmentation channel where a quark may enter the isolation cone. We find significant improvements in the convergence of NNLO di-photon cross-sections with photon isolation cuts, demonstrating that it is possible to achieve a stable and efficient calculation of di-photon cross-sections using slicing methods.