Isospin asymmetries in $B\to (K^*,\rho) \gamma/ l^+ l^-$ and $B \to K l^+ l^-$ in and beyond the Standard Model

Understand

We compute the isospin asymmetries in $B \to (K^*,\rho) \gamma$ and $B\to (K,K^*,\rho) l^+l^-$ for low lepton pair invariant mass $q^2$, 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 $B \to (K,K^*,\rho) ll$, between $1{\rm GeV}^2 \leq q^2 \leq 4m_c^2$, are predicted to be small (below 1.5%) though with significant cancellation.
• In the SM the non-CP averaged asymmetries for $B \to \rho ll$ deviate by $\approx \pm 5%$ 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).