https://doi.org/10.1140/epjc/s10052-023-12093-7
Special Article - Tools for Experiment and Theory
Helicity amplitudes without gauge cancellation for electroweak processes
1
Department of Physics, Jinan University, 510632, Guangzhou, Guangdong, China
2
KEK Theory Center and Sokendai, 305-0801, Tsukuba, Ibaraki, Japan
3
Kavli IPMU (WPI), UTIAS, The University of Tokyo, 277-8583, Kashiwa, Chiba, Japan
4
Faculty of Education, Iwate University, 020-8550, Morioka, Iwate, Japan
Received:
30
March
2022
Accepted:
27
September
2023
Published online:
13
October
2023
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 
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.
The original online version of this article was revised: The funding from ’NSFC (National Natural Science Foundation of China)’ no. 12205118 was omitted.
An erratum to this article is available online at https://doi.org/10.1140/epjc/s10052-024-12452-y.
Copyright comment corrected publication 2024
© The Author(s) 2023. corrected publication 2024
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