Isospin asymmetries in B → (K*,ρ) γ/l+l- and B → K l+l- in and beyond the Standard Model

Preprint number: CP3-Origins-2013-7 DNRF90 and DIAS-2013-7
Authors: James Lyon (Edinburgh University) and Roman Zwicky (CP3-Origins & DIAS)
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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 (BSM) 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 ≤ 4mc2, 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 (UV) isospin violation due to differences between operators coupling to up and down quarks, and infrared (IR) 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 (QLSS) 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 ninety degrees allows us to construct a (quasi) null test for the SM out of the respective isospin symmetries. We provide an update on B(B0 → K*0γ)/B(Bs → ϕγ) which is sensitive to WA.