New physics upper bound on the branching ratio of B_s--> l+ l- and B_s--> l+ l- gamma

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, mu, 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_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_s--> l+ l- and the branching ratios of these decays can be as large as present experimental upper bounds. If future experiments measure 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_s--> l+ l- gamma subject to the present experimental constraints on B--> (K,K*) l+ l- and B--> K* gamma. 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- gamma 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* gamma. In both cases, enhancement of B_s--> l+ l- gamma 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- gamma) to be much larger than its SM expectation.