One-loop contributions to decays $e_b\to e_a \gamma$ and $(g-2)_{e_a}$ anomalies, and Ward identity

L. T. Hue; H. N. Long; V. H. Binh; H. L. T. Mai; T. Phong Nguyen

doi:10.1016/j.nuclphysb.2023.116244

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arXiv · 2301.05407

One-loop contributions to decays $e_b\to e_a \gamma$ and $(g-2)_{e_a}$ anomalies, and Ward identity

L. T. Hue·H. N. Long·V. H. Binh·H. L. T. Mai·T. Phong Nguyen

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Abstract

In this paper, we will present analytic formulas to express one-loop contributions to lepton flavor violating decays $e_b\to e_a \gamma$, which are also relevant to the anomalous dipole magnetic moments of charged leptons $e_a$. These formulas were computed in the unitary gauge, using the well-known Passarino-Veltman notations. We also show that our results are consistent with those calculated previously in the 't Hooft-Veltman gauge, or in the limit of zero lepton masses. At the one-loop level, we show that the appearance of fermion-scalar-vector type diagrams in the unitary gauge will violate the Ward Identity relating to an external photon. As a result, the validation of the Ward Identity guarantees that the photon always couples with two identical particles in an arbitrary triple coupling vertex containing a photon.

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L. T. Hue, H. N. Long, V. H. Binh, H. L. T. Mai, T. Phong Nguyen. 2023-01-13. One-loop contributions to decays $e_b\to e_a \gamma$ and $(g-2)_{e_a}$ anomalies, and Ward identity. https://doi.org/10.1016/j.nuclphysb.2023.116244

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