We compute the isospin asymmetries in B→(K∗,ρ)γ and B→(K,K∗,ρ)l+l− for low lepton pair invariant mass q2, 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∗,ρ)ll, between 1 GeV2≤q2≤4m2c, are predicted to be small (below 1.5%) though with significant cancellation. In the SM the non-CP-averaged asymmetries for B→ρll deviate by ≈±5% from the CP-averaged ones. We provide physical arguments, based on resonances, of why isospin asymmetries have to decrease for large q2 (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→ρll and B→K∗ll isospin asymmetries are structurally different yet the closeness of αCKM to 90° 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(B0→K*0γ)/B(Bs→ϕγ) which is sensitive to WA.
|Journal||Physical Review D - Particles, Fields, Gravitation and Cosmology|
|Publication status||Published - 11 Nov 2013|