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 → γγ in gluon fusion, poor convergence. Such problems have their origins in an interplay between the behaviour of standard experimental cuts at small transverse momenta (pt) 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 pt, 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 pt at low pt, with a variety of consequent advantages.
Highlights
The starting point for almost any analysis at high-energy colliders is a set of requirements, or “cuts”, on the transverse momenta and pseudorapidities of the objects that enter the analysis
It turns out that to obtain the correct N3LO prediction, it is necessary to integrate over Higgs boson transverse momenta that are well below a GeV, which is physically unsettling
To obtain a sense of the behaviour of the perturbative series at high orders, we will consider a simplified approach, where we examine its structure with four models for the series: one based on a double logarithmic (DL) resummation, using eq (2.8); one based on a leading-logarithmic (LL) pt-space resummation dσll = σtot d e−2CALr1(αsLb0), dpt,h pt,h dL
Summary
The starting point for almost any analysis at high-energy colliders is a set of requirements, or “cuts”, on the transverse momenta and pseudorapidities of the objects that enter the analysis. As the calculations have moved forwards, an intriguing situation has arisen in the context of gluon-fusion Higgs production studies, where the calculations are arguably the most advanced For this process, inclusive cross sections and cross sections differential in the Higgs boson rapidity show a perturbative series that converges well at N3LO. One approach to resolving this issue is to give up on the use of fixed-order perturbation theory for Higgs boson fiducial cross sections and other two-body processes, and instead calculate fiducial cross sections using suitably matched resummed plus fixed order calculations (an approach that was explored long ago for dijet calculations [22] and advocated recently for the Higgs case [12]) We believe this to be a valid approach, and it is probably the only robust option available for interpreting fiducial results measured with today’s widespread cut choices.
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