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

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

Abstract

We present compact analytic results for the one-loop amplitude for the process 0 → qq¯¯ℓℓ¯ℓ′ℓ¯′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.

Citation

Campbell, J. M., De Laurentis, G., & Ellis, R. K. (2022). Vector boson pair production at one loop: analytic results for the process $$ \mathrm{q}\overline{\mathrm{q}}\ell \overline{\ell}{\ell}^{\prime }{\overline{\ell}}^{\prime}\mathrm{g} $$. Journal of High Energy Physics, 2022(7), Article 96. https://doi.org/10.1007/jhep07%282022%29096

• Journal Article Type: Article
• Acceptance Date: Jun 8, 2022
• Online Publication Date: Jul 15, 2022
• Publication Date: 2022-07
• Deposit Date: Jul 27, 2022
• Publicly Available Date: Jul 27, 2022
• Journal: Journal of High Energy Physics
• Print ISSN: 1126-6708
• Electronic ISSN: 1029-8479
• Publisher: Scuola Internazionale Superiore di Studi Avanzati (SISSA)
• Peer Reviewed: Peer Reviewed
• Volume: 2022
• Issue: 7
• Article Number: 96
• DOI: https://doi.org/10.1007/jhep07%282022%29096
• Public URL: https://durham-repository.worktribe.com/output/1196719