All-multiplicity amplitudes with four massive quarks and identical-helicity gluons

TL;DR

This paper derives and compares new analytic formulas for scattering amplitudes involving massive quarks and gluons, demonstrating improved computational efficiency for high-multiplicity processes in QCD.

Contribution

It introduces all-multiplicity formulas for two massive particles with arbitrary spin and identical-helicity gluons, and applies them to QCD with explicit four-quark amplitude solutions.

Findings

New all-multiplicity amplitude formulas for massive quarks and gluons.

Analytic formulas outperform off-shell recursion in computational speed at high multiplicities.

Simpler formula is faster for all external leg counts.

Abstract

We explore the on-shell recursion for tree-level scattering amplitudes with massive spinning particles. Based on the factorization structure encoded in the same way by two different recursion relations, we conjecture an all-multiplicity formula for two gauged massive particles of arbitrary spin and any number of identical-helicity gluons. Specializing to quantum chromodynamics (QCD), we solve the on-shell recursion relations in the presence of two pairs of massive quarks and an arbitrary number of identical-helicity gluons. We find closed-form expressions for the two distinct families of color-ordered four-quark amplitudes, in which all gluons comprise a single color-adjacent set. We compare the efficiency of the numerical evaluation of the two resulting analytic formulae against a numerical implementation of the off-shell Berends-Giele recursion. We find the formulae for both amplitude families to be faster for large multiplicities, while the simpler of the two is actually faster for any number of external legs. Our analytic results are provided in a computer-readable format as two ancillary files.