Semileptonic decays of $D_{(s)}$ mesons

A symmetry-preserving continuum approach to meson bound-states in quantum field theory, employed elsewhere to describe numerous $pi$- and $K$-meson electroweak processes, is used to analyse leptonic and semileptonic decays of $D_{(s)}$ mesons. Each semileptonic transition is conventionally characterised by the value of the dominant form factor at $t=0$ and the following results are obtained herein: $f_+^{D_s o K}(0) = 0.673(40)$; $f_+^{D o pi}(0)=0.618(31)$; and $f_+^{D o K}(0)=0.756(36)$. Working with the computed $t$-dependence of these form factors and standard averaged values for $|V_{cd}|$, $|V_{cs}|$, one arrives at the following predictions for the associated branching fractions: ${cal B}_{D_s^+ o K^0 e^+ u_e} = 3.31(33) imes 10^{-3}$; ${cal B}_{D^0 o pi^- e^+ u_e} = 2.73(22) imes 10^{-3}$; and ${cal B}_{D^0 o K^- e^+ u_e} = 3.83(28)$%. Alternatively, using the calculated $t$-dependence, agreement with contemporary empirical results for these branching fractions requires $|V_{cd}|=0.221(9)$, $|V_{us}|=0.953(34)$. With all $D_{(s)}$ transition form factors in hand, the nature of SU$(3)$-flavour symmetry-breaking in this array of processes can be analysed; and just as in the $pi$-$K$ sector, the magnitude of such effects is found to be determined by the scales associated with emergent mass generation in the Standard Model, not those originating with the Higgs mechanism.