Helicity amplitudes without gauge cancellation for electroweak processes
Abstract In the 5-component representation of weak bosons, the first four components make a Lorentz four vector, representing the transverse and longitudinal polarizations excluding the scalar component of the weak bosons, whereas its fifth component corresponds to the Goldstone boson. We obtain the...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2023-10-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | https://doi.org/10.1140/epjc/s10052-023-12093-7 |
| _version_ | 1797247072132399104 |
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| author | Junmou Chen Kaoru Hagiwara Junichi Kanzaki Kentarou Mawatari |
| author_facet | Junmou Chen Kaoru Hagiwara Junichi Kanzaki Kentarou Mawatari |
| author_sort | Junmou Chen |
| collection | DOAJ |
| description | Abstract In the 5-component representation of weak bosons, the first four components make a Lorentz four vector, representing the transverse and longitudinal polarizations excluding the scalar component of the weak bosons, whereas its fifth component corresponds to the Goldstone boson. We obtain the $$5\times 5$$ 5 × 5 component propagators of off-shell weak bosons, proposed previously and named after the Goldstone boson equivalence theorem, by starting from the unitary-gauge representation of the tree-level scattering amplitudes, and by applying the BRST (Becchi–Rouet–Stora–Tyutin) identities to the two sub-amplitudes connected by each off-shell weak-boson line. By replacing all weak boson vertices with those among the off-shell 5-component wavefunctions, we arrive at the expression of the electroweak scattering amplitudes, where the magnitude of each Feynman amplitude has the correct on-shell limits for all internal propagators, and hence with no artificial gauge cancellation among diagrams. Although our derivation is limited to the tree-level only, it allows us to study the properties of each Feynman amplitude separately, and then learn how they interfere in the full amplitudes. We implement the 5-component weak boson propagators and their vertices in the numerical helicity amplitude calculation code HELAS (Helicity Amplitude Subroutines), so that an automatic amplitude generation program such as MadGraph can generate the scattering amplitudes without gauge cancellation. We present results for several high-energy scattering processes where subtle gauge-theory cancellation among diagrams takes place in all the other known approaches. |
| first_indexed | 2024-03-07T14:44:47Z |
| format | Article |
| id | doaj.art-77fa81aa7ecf4da2a4e0a5630213f96d |
| institution | Directory Open Access Journal |
| issn | 1434-6052 |
| language | English |
| last_indexed | 2024-04-24T19:52:52Z |
| publishDate | 2023-10-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj.art-77fa81aa7ecf4da2a4e0a5630213f96d2024-03-24T12:30:42ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60522023-10-01831012810.1140/epjc/s10052-023-12093-7Helicity amplitudes without gauge cancellation for electroweak processesJunmou Chen0Kaoru Hagiwara1Junichi Kanzaki2Kentarou Mawatari3Department of Physics, Jinan UniversityKEK Theory Center and SokendaiKavli IPMU (WPI), UTIAS, The University of TokyoFaculty of Education, Iwate UniversityAbstract In the 5-component representation of weak bosons, the first four components make a Lorentz four vector, representing the transverse and longitudinal polarizations excluding the scalar component of the weak bosons, whereas its fifth component corresponds to the Goldstone boson. We obtain the $$5\times 5$$ 5 × 5 component propagators of off-shell weak bosons, proposed previously and named after the Goldstone boson equivalence theorem, by starting from the unitary-gauge representation of the tree-level scattering amplitudes, and by applying the BRST (Becchi–Rouet–Stora–Tyutin) identities to the two sub-amplitudes connected by each off-shell weak-boson line. By replacing all weak boson vertices with those among the off-shell 5-component wavefunctions, we arrive at the expression of the electroweak scattering amplitudes, where the magnitude of each Feynman amplitude has the correct on-shell limits for all internal propagators, and hence with no artificial gauge cancellation among diagrams. Although our derivation is limited to the tree-level only, it allows us to study the properties of each Feynman amplitude separately, and then learn how they interfere in the full amplitudes. We implement the 5-component weak boson propagators and their vertices in the numerical helicity amplitude calculation code HELAS (Helicity Amplitude Subroutines), so that an automatic amplitude generation program such as MadGraph can generate the scattering amplitudes without gauge cancellation. We present results for several high-energy scattering processes where subtle gauge-theory cancellation among diagrams takes place in all the other known approaches.https://doi.org/10.1140/epjc/s10052-023-12093-7 |
| spellingShingle | Junmou Chen Kaoru Hagiwara Junichi Kanzaki Kentarou Mawatari Helicity amplitudes without gauge cancellation for electroweak processes European Physical Journal C: Particles and Fields |
| title | Helicity amplitudes without gauge cancellation for electroweak processes |
| title_full | Helicity amplitudes without gauge cancellation for electroweak processes |
| title_fullStr | Helicity amplitudes without gauge cancellation for electroweak processes |
| title_full_unstemmed | Helicity amplitudes without gauge cancellation for electroweak processes |
| title_short | Helicity amplitudes without gauge cancellation for electroweak processes |
| title_sort | helicity amplitudes without gauge cancellation for electroweak processes |
| url | https://doi.org/10.1140/epjc/s10052-023-12093-7 |
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