Two-Loop Five-Point One-Mass Amplitudes in the Spinor-Helicity Formalism

TL;DR

This paper presents the first expression of two-loop five-point one-mass amplitudes in the spinor-helicity formalism, significantly simplifying complex calculations crucial for precision Standard Model predictions at the LHC.

Contribution

It introduces a novel spinor-helicity formalism representation for two-loop five-point one-mass amplitudes, reducing expression size and aiding phenomenological analysis.

Findings

Achieved three orders of magnitude smaller amplitude expressions.

Provided results for specific partonic processes relevant to collider physics.

Facilitated future phenomenological studies and mathematical analysis.

Abstract

Processes involving electroweak vector bosons in association with jets are crucial for precision studies of the Standard Model at the Large Hadron Collider. Accurate predictions for the process $pp\rightarrow V(\rightarrow\bar\ell\ell)jj$ at next-to-next-to-leading order (NNLO), as well as N$^3$LO ones for the process with one fewer jet, require two-loop five-point one-mass amplitudes. These exhibit a significant increase in complexity compared to their massless counterparts. We present results for the partonic processes $\bar qQ\bar Qq\bar\ell\ell$ and $\bar qggq\bar\ell\ell$, with a forthcoming package for phenomenology. The present recalculation is based on the previous analytic results from ref. [1]. For the first time, we express two-loop five-point one-mass amplitudes in the spinor-helicity formalism. We achieve three orders of magnitude smaller expressions compared to previous results. This will facilitate phenomenological studies and help clarify mathematical properties of the amplitude.