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

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 $pp\to V(\to \bar{\mathrm{\ell }}\mathrm{\ell })jj$ 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 $\bar{q}Q\bar{Q}q\bar{\mathrm{\ell }}\mathrm{\ell }$ and $\bar{q}ggq\bar{\mathrm{\ell }}\mathrm{\ell }$, 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.