Heavy + light pseudoscalar meson semileptonic transitions

Abstract

A symmetry-preserving regularisation of a vector $\times$ vector contact interaction (SCI) is used to deliver a unified treatment of semileptonic transitions involving $\pi$, K, $D_{(s)}$, $B_{(s,c)}$ initial states. The framework is characterised by algebraic simplicity, few parameters, and the ability to simultaneously treat systems from Nambu–Goldstone modes to heavy+heavy mesons. Although the SCI form factors are typically somewhat stiff, the results are comparable with experiment and rigorous theory results. Hence, predictions for the five unmeasured $B_{s,c}$ branching fractions should be a reasonable guide. The analysis provides insights into the effects of Higgs boson couplings via current-quark masses on the transition form factors; and results on $B_{(s)}\to D_{(s)}$ transitions yield a prediction for the Isgur–Wise function in fair agreement with contemporary data.