One-loop contributions to decays → And anomalies, and Ward identity
L.T. Hue (Subatomic Physics Research Group, Science and Technology Advanced Institute, Van Lang University, Ho Chi Minh City, Vietnam, Faculty of Applied Technology, School of Technology, Van Lang University, Ho Chi Minh City, Vietnam); H.N. Long (Subatomic Physics Research Group, Science and Technology Advanced Institute, Van Lang University, Ho Chi Minh City, Vietnam, Faculty of Applied Technology, School of Technology, Van Lang University, Ho Chi Minh City, Vietnam); V.H. Binh (Institute of Physics, Vietnam Academy of Science and Technology, Hanoi, Vietnam); H.L.T. Mai (Faculty of Physics Science, Can Tho Medical College, Can Tho, Vietnam); T. Phong Nguyen (Department of Physics, Can Tho University, Can Tho, Vietnam)
In this paper, we will present analytic formulas to express one-loop contributions to lepton flavor violating decays , which are also relevant to the anomalous dipole magnetic moments of charged leptons . 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.
