$b\to s\mu^+\mu^-$ tensor operators from $B\to K^*(X_s) \gamma$

Tensor operators are often invoked as specific new physics operators beyond the standard model in an effort to explain anomalies in rare B-decays and CP asymmetries. Specifically, $b \to s \mu^+\mu^-$ tensor operators are invoked in the study of semi-leptonic decays, both inclusive and exclusive. In this note we use the data on $b \to s$ radiative decay modes and CP asymmetries to tightly constrain the tensor operators. It is found that constraints thus obtained are tighter than those from semi-leptonic modes. We also comment on $b \to ss\bar{s}$ tensor operators that help in explaining the $B \to \phi K^*$ polarization puzzle, and $b\to s\tau^+\tau^-$ operators with tensor structure.