Journal of High Energy Physics (Jul 2022)

Vector boson pair production at one loop: analytic results for the process q q ¯ ℓ ℓ ¯ ℓ ′ ℓ ¯ ′ g $$ \mathrm{q}\overline{\mathrm{q}}\ell \overline{\ell}{\ell}^{\prime }{\overline{\ell}}^{\prime}\mathrm{g} $$

  • John M. Campbell,
  • Giuseppe De Laurentis,
  • R. Keith Ellis

DOI
https://doi.org/10.1007/JHEP07(2022)096
Journal volume & issue
Vol. 2022, no. 7
pp. 1 – 44

Abstract

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Abstract We present compact analytic results for the one-loop amplitude for the process 0 → q q ¯ ℓ ℓ ¯ ℓ ′ ℓ ¯ ′ g $$ q\overline{q}\ell \overline{\ell}{\ell}^{\prime }{\overline{\ell}}^{\prime }g $$ , relevant for both the production of a pair of Z and W-bosons in association with a jet. We focus on the gauge-invariant contribution mediated by a loop of quarks. We explicitly include all effects of the loop-quark mass m, appropriate for the production of a pair of Z-bosons. In the limit m → 0, our results are also applicable to the production of W-boson pairs, mediated by a loop of massless quarks. Implemented in a numerical code, the results are fast. The calculation uses novel advancements in spinor-helicity simplification techniques, for the first time applied beyond five-point massless kinematics. We make use of primary decompositions from algebraic-geometry, which now involve non-radical ideals, and p-adic numbers from number theory. We show how to infer whether numerator polynomials belong to symbolic powers of non-radical ideals through numerical evaluations.

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