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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

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


Authors

John M. Campbell

Giuseppe De Laurentis



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
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

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Publisher Licence URL
http://creativecommons.org/licenses/by/4.0/

Copyright Statement
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.





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