Continuity and Semileptonic $B_{(s)}\rightarrow D_{(s)}$ Form Factors

TL;DR

This paper investigates how small mass variations affect the non-perturbative form factors in semileptonic B and D meson decays, finding that differences are minimal and consistent with lattice results, challenging HQET expectations.

Contribution

The study provides a quantitative analysis of SU(3) breaking effects on form factors, incorporating unitarity and analyticity constraints, and extends understanding beyond zero recoil.

Findings

Form factor differences are within 1% across the entire kinematic range.

Results align with lattice calculations, diverging from HQET predictions.

Small mass changes lead to minor form factor variations, validating the non-perturbative parameterization.

Abstract

Small changes in the masses of massive external scattering states should correspond to small changes in the non-perturbative parameterization of form factors in quantum field theory, as long as the relevant energy range is not near strong deformations. Here, the definition of ``small'' is investigated and applied to $SU(3)$ breaking in semileptonic $B_{(s)}\rightarrow D_{(s)}$ transitions. When unitarity and analyticity are imposed, the differences in the form factors for semileptonic $B\rightarrow D$ versus $B_s\rightarrow D_s$ decays are found to be within $\mathcal{O}(1\%)$ over the entire kinematic range, not just at zero recoil, which is consistent with results from lattice calculations and differs from the expectation using HQET alone.