Vector boson pair production at one loop: analytic results for the process $q\bar{q}$$ℓ\bar{ℓ}$$ℓ'\bar{ℓ}'g$

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

doi:10.1007/jhep07(2022)096

Title: Vector boson pair production at one loop: analytic results for the process $$q\bar{q}$$$$ℓ\bar{ℓ}$$$$ℓ'\bar{ℓ}'g$$

Abstract

We present compact analytic results for the one-loop amplitude for the process 0 → $$q\bar{q}$$$$ℓ\bar{ℓ}$$$$ℓ'\bar{ℓ}'g$$, 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.

Authors:

^[1];

^[2];

^[3]

Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
Albert-Ludwigs-Universität, Freiburg (Germany)
Durham University (United Kingdom)

Publication Date:: Fri Jul 15 00:00:00 EDT 2022

Research Org.:: Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP)

OSTI Identifier:: 1879530

Report Number(s):: FERMILAB-PUB-22-231-T; FR-PHENO-2022-06; IPPP/22/17; arXiv:2203.17170
Journal ID: ISSN 1029-8479; oai:inspirehep.net:2060823; TRN: US2307653

Grant/Contract Number:: AC02-07CH11359

Resource Type:: Accepted Manuscript

Journal Name:: Journal of High Energy Physics (Online)

Additional Journal Information:: Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2022; Journal Issue: 7; Journal ID: ISSN 1029-8479

Publisher:: Springer Nature

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; scattering amplitudes; electroweak precision physics; higher-order perturbative calculations

Citation Formats


                    Campbell, John M., De Laurentis, Giuseppe, and Ellis, R. Keith. Vector boson pair production at one loop: analytic results for the process $q\bar{q}$$ℓ\bar{ℓ}$$ℓ'\bar{ℓ}'g$.  United States: N. p., 2022. 
Web.  doi:10.1007/jhep07(2022)096.

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                    Campbell, John M., De Laurentis, Giuseppe, & Ellis, R. Keith. Vector boson pair production at one loop: analytic results for the process $q\bar{q}$$ℓ\bar{ℓ}$$ℓ'\bar{ℓ}'g$.  United States.  https://doi.org/10.1007/jhep07(2022)096

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                    Campbell, John M., De Laurentis, Giuseppe, and Ellis, R. Keith. Fri .  
"Vector boson pair production at one loop: analytic results for the process $q\bar{q}$$ℓ\bar{ℓ}$$ℓ'\bar{ℓ}'g$".  United States.  https://doi.org/10.1007/jhep07(2022)096.  https://www.osti.gov/servlets/purl/1879530.

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@article{osti_1879530,

  title        = {Vector boson pair production at one loop: analytic results for the process $q\bar{q}$$ℓ\bar{ℓ}$$ℓ'\bar{ℓ}'g$},

  author       = {Campbell, John M. and De Laurentis, Giuseppe and Ellis, R. Keith},

  abstractNote = {We present compact analytic results for the one-loop amplitude for the process 0 → $q\bar{q}$$ℓ\bar{ℓ}$$ℓ'\bar{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.},

  doi          = {10.1007/jhep07(2022)096},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 7,

  volume       = 2022,

  place        = {United States},

  year         = {Fri Jul 15 00:00:00 EDT 2022},

  month        = {Fri Jul 15 00:00:00 EDT 2022}

}

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Title: Vector boson pair production at one loop: analytic results for the process $$q\bar{q}$$$$ℓ\bar{ℓ}$$$$ℓ'\bar{ℓ}'g$$

Abstract

Citation Formats

Vector boson pair production at the LHC journal, July 2011

A Nullstellensatz with nilpotents and Zariski's Main Lemma on holomorphic functions journal, May 1979

Interference effects for Higgs boson mediated Z -pair plus jet production journal, November 2014

OpenLoops 2 journal, October 2019

Weak interactions at very high energies: The role of the Higgs-boson mass journal, September 1977

A Roadmap for HEP Software and Computing R&D for the 2020s journal, November 2019

The one-loop amplitudes for Higgs + 4 partons with full mass effects journal, May 2020

Symbolic powers and the Containment Problem text, January 2018

Scattering Amplitudes with Open Loops journal, March 2012

Extracting analytical one-loop amplitudes from numerical evaluations journal, July 2019

FIRE6: Feynman Integral REduction with modular arithmetic journal, February 2020

RECOLA2: REcursive Computation of One-Loop Amplitudes 2 journal, March 2018

Reconstructing rational functions with FireFly journal, February 2020

A compact expression for the scalar one-loop four-point function journal, December 1991

Double-cut of scattering amplitudes and Stokes' Theorem journal, July 2009

Direct extraction of one loop rational terms journal, January 2009

Higgs boson production at large transverse momentum in hadronic collisions journal, July 1990

A novel approach to integration by parts reduction journal, May 2015

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A fundamental lemma from the theory of holomorphic functions on an algebraic variety journal, December 1949

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Higgs decay to τ+τ−A possible signature of intermediate mass Higgs bosons at high energy hadron colliders journal, February 1988

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Multiple bremsstrahlung in gauge theories at high energies (II). Single bremsstrahlung journal, October 1982

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One-loop corrections for e+e− annihilation into μ+μ− in the Weinberg model journal, November 1979

Helicity amplitudes for O(αs) production of W+W−, W±Z, ZZ, W±γ, or Zγ pairs at hadron colliders journal, October 1998

Kira—A Feynman integral reduction program journal, September 2018

Vector boson pair production at the LHC
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journal, November 2014

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The one-loop amplitudes for Higgs + 4 partons with full mass effects
journal, May 2020

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Scattering Amplitudes with Open Loops
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Extracting analytical one-loop amplitudes from numerical evaluations
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FIRE6: Feynman Integral REduction with modular arithmetic
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RECOLA2: REcursive Computation of One-Loop Amplitudes 2
journal, March 2018

Reconstructing rational functions with FireFly
journal, February 2020

A compact expression for the scalar one-loop four-point function
journal, December 1991

Double-cut of scattering amplitudes and Stokes' Theorem
journal, July 2009

Direct extraction of one loop rational terms
journal, January 2009

Higgs boson production at large transverse momentum in hadronic collisions
journal, July 1990

A novel approach to integration by parts reduction
journal, May 2015

Scalar one-loop integrals
journal, January 1979

Next-to-leading order predictions for WW + jet distributions at the LHC
journal, December 2007

Direct extraction of one-loop integral coefficients
journal, June 2007

Accelerating LHC phenomenology with analytic one-loop amplitudes: A C++ interface to MCFM
journal, December 2021

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A two-loop five-gluon helicity amplitude in QCD
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Automation of one-loop QCD computations
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Reducing full one-loop amplitudes to scalar integrals at the integrand level
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Helicity amplitudes for multiple bremsstrahlung in massless non-abelian gauge theories
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One-loop calculations in quantum field theory: From Feynman diagrams to unitarity cuts
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Generalized unitarity and one-loop amplitudes in super-Yang–Mills
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A fundamental lemma from the theory of holomorphic functions on an algebraic variety
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Top-quark loop corrections in Z+jet and Z + 2 jet production
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Higgs decay to τ+τ−A possible signature of intermediate mass Higgs bosons at high energy hadron colliders
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