New physics upper bound on the branching ratio of [formula omitted] and [formula omitted

Abstract

We consider the most general new physics effective Lagrangian for b → s l + l − . We derive the upper limit on the branching ratio for the processes B s → l + l − where l = e , μ , subject to the current experimental bounds on related processes, B → ( K , K ∗ ) l + l − . If the new physics interactions are of vector/axial-vector form, the present measured rates for B → ( K , K ∗ ) l + l − constrain B ( B s → l + l − ) to be of the same order of magnitude as their respective Standard Model (SM) predictions. On the other hand, if the new physics interactions are of scalar/pseudoscalar form, B → ( K , K ∗ ) l + l − rates do not impose any useful constraint on B ( B s → l + l − ) and the branching ratios of these decays can be as large as present experimental upper bounds. If future experiments measure B ( B s → l + l − ) to be ⩾ 10 −8 then the new physics giving rise to these decays has to be of the scalar/pseudoscalar form. We also consider the effect of new physics on B ( B s → l + l − γ ) subject to the present experimental constraints on B → ( K , K ∗ ) l + l − and B → K ∗ γ . New physics in form scalar/pseudoscalar, which makes a very large contribution to B s → l + l − , makes no contribution at all to B s → l + l − γ due to angular momentum conservation. New Physics in the form of vector/axial-vector operators is constrained by the data on B → ( K , K ∗ ) l + l − and new physics in the form of tensor/pseudo-tensor is constrained by the data on B → K ∗ γ . In both cases, enhancement of B ( B s → l + l − γ ) much beyond the SM expectation is impossible. In conclusion, present data on B → ( K , K ∗ ) transitions allow for large B ( B s → l + l − ) but do not allow B ( B s → l + l − γ ) to be much larger than its SM expectation.