Unified worldline treatment of Yukawa and axial couplings

Abstract We provide a worldline representation of the one-loop effective action for a Dirac particle coupled to external scalar, pseudoscalar, vector and axialvector fields. Extending previous work by two of the authors on the pure vector-axialvector case to all four couplings, it allows one to trea...

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Main Authors: F. Bastianelli, O. Corradini, J. P. Edwards, D. G. C. McKeon, C. Schubert
Format: Article
Language:English
Published: SpringerOpen 2024-11-01
Series:Journal of High Energy Physics
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Online Access:https://doi.org/10.1007/JHEP11(2024)152
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author F. Bastianelli
O. Corradini
J. P. Edwards
D. G. C. McKeon
C. Schubert
author_facet F. Bastianelli
O. Corradini
J. P. Edwards
D. G. C. McKeon
C. Schubert
author_sort F. Bastianelli
collection DOAJ
description Abstract We provide a worldline representation of the one-loop effective action for a Dirac particle coupled to external scalar, pseudoscalar, vector and axialvector fields. Extending previous work by two of the authors on the pure vector-axialvector case to all four couplings, it allows one to treat the real and the imaginary parts of the effective action in a unified manner, at the price of having a non-Hermitian Hamiltonian. Unlike existing worldline representations, our new worldline action contains terms with an odd number of Grassmann fields, leading to ordering problems that in the worldline formalism are usually encountered only in curved space. Drawing on the highly developed technology for worldline path-integrals in gravity, we employ the Time Slicing regularisation of the path integral which comes about with a specific “counterterm Lagrangian”, which we calculate once and for all and non-perturbatively, to provide unambiguous rules to treat products of distributions occurring in some diagrams of the one-dimensional worldline theory. We then employ the usual worldline machinery to lay out the rules for the calculation of the effective action itself as well as the corresponding one-loop amplitudes. We test the formalism on the calculation of various heat-kernel coefficients, self energies and scattering amplitudes, including the Higgs decay into two photons or gluons and the PCAC relation. In all cases we find perfect agreement with more established approaches.
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spelling doaj-art-ada7580c789242ba8d16df9dcc8c8d1e2024-12-08T12:08:28ZengSpringerOpenJournal of High Energy Physics1029-84792024-11-0120241113210.1007/JHEP11(2024)152Unified worldline treatment of Yukawa and axial couplingsF. Bastianelli0O. Corradini1J. P. Edwards2D. G. C. McKeon3C. Schubert4Dipartimento di Fisica e Astronomia “Augusto Righi”, Università di BolognaDipartimento di Scienze Fisiche, Informatiche e Matematiche, Università degli Studi di Modena e Reggio EmiliaDipartimento di Scienze Fisiche, Informatiche e Matematiche, Università degli Studi di Modena e Reggio EmiliaDepartment of Applied Mathematics, The University of Western OntarioFacultad de Ciencias Físico-Matemáticas, Universidad Michoacana de San Nicolás de HidalgoAbstract We provide a worldline representation of the one-loop effective action for a Dirac particle coupled to external scalar, pseudoscalar, vector and axialvector fields. Extending previous work by two of the authors on the pure vector-axialvector case to all four couplings, it allows one to treat the real and the imaginary parts of the effective action in a unified manner, at the price of having a non-Hermitian Hamiltonian. Unlike existing worldline representations, our new worldline action contains terms with an odd number of Grassmann fields, leading to ordering problems that in the worldline formalism are usually encountered only in curved space. Drawing on the highly developed technology for worldline path-integrals in gravity, we employ the Time Slicing regularisation of the path integral which comes about with a specific “counterterm Lagrangian”, which we calculate once and for all and non-perturbatively, to provide unambiguous rules to treat products of distributions occurring in some diagrams of the one-dimensional worldline theory. We then employ the usual worldline machinery to lay out the rules for the calculation of the effective action itself as well as the corresponding one-loop amplitudes. We test the formalism on the calculation of various heat-kernel coefficients, self energies and scattering amplitudes, including the Higgs decay into two photons or gluons and the PCAC relation. In all cases we find perfect agreement with more established approaches.https://doi.org/10.1007/JHEP11(2024)152Scattering AmplitudesGauge Symmetry
spellingShingle F. Bastianelli
O. Corradini
J. P. Edwards
D. G. C. McKeon
C. Schubert
Unified worldline treatment of Yukawa and axial couplings
Journal of High Energy Physics
Scattering Amplitudes
Gauge Symmetry
title Unified worldline treatment of Yukawa and axial couplings
title_full Unified worldline treatment of Yukawa and axial couplings
title_fullStr Unified worldline treatment of Yukawa and axial couplings
title_full_unstemmed Unified worldline treatment of Yukawa and axial couplings
title_short Unified worldline treatment of Yukawa and axial couplings
title_sort unified worldline treatment of yukawa and axial couplings
topic Scattering Amplitudes
Gauge Symmetry
url https://doi.org/10.1007/JHEP11(2024)152
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AT ocorradini unifiedworldlinetreatmentofyukawaandaxialcouplings
AT jpedwards unifiedworldlinetreatmentofyukawaandaxialcouplings
AT dgcmckeon unifiedworldlinetreatmentofyukawaandaxialcouplings
AT cschubert unifiedworldlinetreatmentofyukawaandaxialcouplings