Cuts for two-body decays at colliders

TL;DR

This paper identifies issues in fixed-order calculations of two-body decay processes at colliders caused by experimental cut designs and proposes modifications to improve the convergence and stability of perturbative series.

Contribution

It introduces simple cut modifications that reduce linear acceptance dependence on transverse momentum, enhancing perturbative calculation reliability.

Findings

Linear dependence of acceptance on $p_t$ causes divergence.

Quadratic dependence improves perturbative behavior.

Modified cuts lead to more stable and reliable predictions.

Abstract

Fixed-order perturbative calculations of fiducial cross sections for two-body decay processes at colliders show disturbing sensitivity to unphysically low momentum scales and, in the case of $H\to \gamma \gamma$ in gluon fusion, poor convergence. Such problems have their origins in an interplay between the behaviour of standard experimental cuts at small transverse momenta ($p_t$) and logarithmic perturbative contributions. We illustrate how this interplay leads to a factorially divergent structure in the perturbative series that sets in already from the first orders. We propose simple modifications of fiducial cuts to eliminate their key incriminating characteristic, a linear dependence of the acceptance on the Higgs or $Z$-boson $p_t$, replacing it with quadratic dependence. This brings major improvements in the behaviour of the perturbative expansion. More elaborate cuts can achieve an acceptance that is independent of the Higgs $p_t$ at low $p_t$, with a variety of consequent advantages.