Impact of Isolation and Fiducial Cuts on $q_T$ and N-Jettiness Subtractions

TL;DR

This paper investigates how experimental cuts and isolation criteria impact the effectiveness of $q_T$ and N-jettiness subtraction methods in fixed-order calculations, revealing enhanced power corrections and proposing differential subtraction techniques.

Contribution

It provides analytic and numerical analysis of cut-induced power corrections in subtraction methods and suggests differential implementation to mitigate these effects.

Findings

Kinematic cuts induce parametrically enhanced power corrections.

Power corrections are more severe for $q_T$ than N-jettiness.

Differential subtraction methods can incorporate cuts without additional power corrections.

Abstract

Kinematic selection cuts and isolation requirements are a necessity in experimental measurements for identifying prompt leptons and photons that originate from the hard-interaction process of interest. We analyze how such cuts affect the application of the $q_T$ and $N$-jettiness subtraction methods for fixed-order calculations. We consider both fixed-cone and smooth-cone isolation methods. We find that kinematic selection and isolation cuts both induce parametrically enhanced power corrections with considerably slower convergence compared to the standard power corrections that are already present in inclusive cross sections without additional cuts. Using analytic arguments at next-to-leading order we derive their general scaling behavior as a function of the subtraction cutoff. We also study their numerical impact for the case of gluon-fusion Higgs production in the $H\to\gamma\gamma$ decay mode and for $pp\to\gamma\gamma$ direct diphoton production. We find that the relative enhancement of the additional cut-induced power corrections tends to be more severe for $q_T$, where it can reach an order of magnitude or more, depending on the choice of parameters and subtraction cutoffs. We discuss how all such cuts can be incorporated without causing additional power corrections by implementing the subtractions differentially rather than through a global slicing method. We also highlight the close relation of this formulation of the subtractions to the projection-to-Born method.