Isospin asymmetries in B→(K ∗ ,ρ)γ/l + l − and B→Kl + l − in and beyond the standard model

We compute the isospin asymmetries in B -> (K*, rho)gamma and B -> (K, K*, rho)l(+)l(-) for low lepton pair invariant mass q(2), within the Standard Model (SM) and beyond the SM in a generic dimension six operator basis. Within the SM the CP-averaged isospin asymmetries for B -> (K, K*, rho)ll, between 1 GeV2 <= q(2) <= 4m(c)(2), are predicted to be small (below 1.5%) though with significant cancellation. In the SM the non-CP-averaged asymmetries for B -> rho ll deviate by approximate to +/-5% from the CP-averaged ones. We provide physical arguments, based on resonances, of why isospin asymmetries have to decrease for large q(2) (towards the endpoint). Two types of isospin violating effects are computed: ultraviolet isospin violation due to differences between operators coupling to up and down quarks, and infrared isospin violation where a photon is emitted from the spectator quark and is hence proportional to the difference between the up-and down-quark charges. These isospin violating processes may be subdivided into weak annihilation (WA), quark loop spectator scattering, and a chromomagnetic contribution. Furthermore we discuss generic selection rules based on parity and angular momentum for the B -> Kll transition as well as specific selection rules valid for WA at leading order in the strong coupling constant. We clarify that the relation between the K and the longitudinal part of the K* only holds for leading twist and for left-handed currents. In general the B -> rho ll and B -> K* ll isospin asymmetries are structurally different yet the closeness of alpha(CKM) to 90 degrees allows us to construct a (quasi) null test for the SM out of the respective isospin symmetries. We provide and discuss an update on B(B-0 -> K*(0)gamma)/B(B-s -> phi gamma) which is sensitive to WA.