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

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.