Rare decay t → cγγ via scalar leptoquark doublets

A calculation of the one-loop contribution to the rare three-body flavor changing neutral current top quark decay t -> c gamma gamma is presented in the framework of models with one or more scalar leptoquark (LQ) SU(2) doublets with hypercharge 7/6. Analytical expressions for the invariant amplitude of the generic decay fi -> fj gamma gamma, with fi;j a lepton or quark, are presented in terms of Passarino-Veltman integral coefficients, from which the amplitudes for the processes t -> c gamma gamma and ei -> ej gamma gamma follow easily. An analysis of the current constraints on the parameter space is presented in the scenario with only one scalar LQ doublet, and bounds on the LQ couplings are obtained from the muon g - 2 anomaly, the lepton flavor violating decay tau -> mu gamma and extra constraints meant to avoid tension between theory predictions and experimental data. For a LQ with a mass in the range of 1-1.5 TeV, the estimate Br(t -> c gamma gamma) similar to 10-11-10-12 is obtained for the largest allowed values of the LQ coupling constants, which means that this decay would be below the reach of future experimental measurements. We also consider a scenario with three scalar doublets, which was recently proposed to explain the lepton flavor universality violation anomalies in B decays as well as the muon g - 2 anomaly. Although this scenario allows large LQ couplings to the tau lepton and the c and t quarks, the branching ratio of the t -> c gamma gamma decay is also of the order of 10-11-10-12 for LQ masses of the order of 1.7 TeV.

Automated summary

In this article, the one-loop contribution to the rare three-body flavor changing neutral current top quark decay t -> c gamma gamma is calculated in the framework of models with scalar leptoquark doublets. Analytical expressions for the invariant amplitude of the decay fi -> fj gamma gamma are obtained in terms of Passarino-Veltman integral coefficients, which allow for the calculation of the amplitudes for t -> c gamma gamma and ei -> ej gamma gamma. The parameter space is constrained using current limits and bounds on the leptoquark couplings are derived. The branching ratio for the t -> c gamma gamma decay is estimated to be on the order of 10-11-10-12 for LQ masses in the range of 1-1.5 TeV, making it difficult to be observed in future experiments.