The decay $b\to s\gamma$ in the presence of a constant antisymmetric tensor field

A constant antisymmetric 2-tensor can arise in general relativity with spontaneous symmetry breaking or in field theories formulated in a noncommutative space-time. In this work, the one-loop contribution of a nonstandard $WW\gamma$ vertex on the flavor violating quark transition $q_i\to q_j\gamma$ is studied in the context of the electroweak Yang-Mills sector extended with a Lorentz-violating constant 2-tensor. An exact analytical expression for the on shell case is presented. It is found that the loop amplitude is gauge independent, electromagnetic gauge invariant, and free of ultraviolet divergences. The dipolar contribution to the $b\to s\gamma$ transition together with the experimental data on the $B\to X_s\gamma$ decay is used to derive the constraint ${\mathrm{\Lambda }}_{LV}>1.96$ TeV on the Lorentz-violating scale.