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

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.

arXiv commentThe version accepted to Nuclear Physics B

References in corpus (33)

• Automatized One-Loop Calculations in 4 and D dimensions
• Measurement of the Positive Muon Anomalous Magnetic Moment to 0.46 ppm
• The anomalous magnetic moment of the muon in the Standard Model
• Reevaluation of the Hadronic Contributions to the Muon g-2 and to alpha(MZ)
• Collier: a fortran-based Complex One-Loop LIbrary in Extended Regularizations
• The muon $g-2$ and $\alpha (M_Z^2)$: a new data-based analysis
• Refinements in electroweak contributions to the muon anomalous magnetic moment
• Reevaluation of the hadronic vacuum polarisation contributions to the Standard Model predictions of the muon g-2 and alpha(mZ) using newest hadronic cross-section data
• The $g-2$ of charged leptons, $\alpha (M_Z^2)$ and the hyperfine splitting of muonium
• Hadronic contribution to the muon anomalous magnetic moment to next-to-next-to-leading order
• A new evaluation of the hadronic vacuum polarisation contributions to the muon anomalous magnetic moment and to $\mathbf{\alpha }({\mathbf{m}}_{\mathbf{Z}}^2)$
• The electroweak contributions to (g-2)_μ after the Higgs boson mass measurement
• Remarks on higher-order hadronic corrections to the muon g-2
• The hadronic light-by-light scattering contribution to the muon anomalous magnetic moment from lattice QCD
• Pseudoscalar-pole contribution to the $(g_{\mu }-2)$: a rational approach
• Short-distance constraints for the HLbL contribution to the muon anomalous magnetic moment
• Lattice calculation of the pion transition form factor with $N_f=2+1$ Wilson quarks
• Anomalies in $B$-decays and $U(2)$ flavour symmetry
• Combined explanations of $(g-2{)}_{\mu ,e}$ and implications for a large muon EDM
• The Muon Magnetic Moment and Supersymmetry
• General formulae for f1 --> f2 gamma
• Axion-like particles, lepton-flavor violation and a new explanation of $a_{\mu }$ and $a_e$
• The Higgs - photon - Z boson coupling revisited
• Improved Bounds on the Electromagnetic Dipole Moments of the Tau Lepton
• $\mu \to e\gamma$ selecting scalar leptoquark solutions for the $(g-2{)}_{e,\mu }$ puzzles
• Lepton flavor violating decays of Standard-Model-like Higgs in 3-3-1 model with neutral lepton
• Exact one-loop results for $l_i\to l_j\gamma$ in 3-3-1 models
• General one-loop formulas for decay $h\to Z\gamma$
• Large $(g-2{)}_{\mu }$ and signals of decays $e_b\to e_a\gamma$ in a 3-3-1 model with inverse seesaw neutrinos
• Explanation of electron and muon $g-2$ anomalies in AMSB
• General Remarks on the One-loop Contributions to the Muon Anomalous Magnetic Moment
• Heavy singly charged Higgs bosons and inverse seesaw neutrinos as origins of large $(g-2{)}_{e,\mu }$ in two higgs doublet models
• Higgs Decays in Gauge Extensions of the Standard Model

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• The Muon Magnetic Moment and Physics Beyond the Standard Model
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