Towards a new approximation for pair-production and associated-production of the Higgs boson

TL;DR

The paper introduces a new approximation method for evaluating loop integrals with heavy particles, improving accuracy across phase space, especially at high energies, and demonstrates its effectiveness in Higgs boson pair production calculations.

Contribution

A systematically improvable approximation method for loop integrals with heavy particles applicable across the entire phase space, including high-energy tails.

Findings

Accurately approximates one-loop and two-loop integrals in Higgs pair production.

Outperforms existing expansion methods outside specific phase space regions.

Facilitates fast and reliable differential cross section calculations for Higgs processes.

Abstract

We propose that loop integrals with internal heavy particles can be evaluated by expanding in the limit of small external masses. This provides a systematically improvable approximation to the integrals in the entire phase space, and works particularly well for the high energy tails of kinematic distributions (where the usual $1/M$ expansions cease to be valid). We demonstrate our method using Higgs boson pair production as an example. We find that at both one-loop and two-loop, our method provides good approximations to the integrals appearing in the scattering amplitudes. Comparing to existing expansion methods, our method are not restricted to a special phase space region. Combining our efficient method to compute the two-loop amplitude with an infrared subtraction method for the real emission corrections, we expect to have a fast and reliable tool to calculate the differential cross sections for Higgs boson pair production. This will be useful for phenomenological studies and for the extraction of the Higgs self-coupling from future experimental data. Our method can also be applied to other processes, such as the associated production of the Higgs boson with a jet or a $Z$ boson.