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: $f_{+}^{D_s\to K}(0)=0.673(40)$; $f_+^{D\to \pi}(0)=0.618(31)$;and$f_+^{D\to K}(0)=0.756(36)$\mathrm{.}Workingwiththecomputed$t$-dependenceoftheseformfactorsandstandardaveragedvaluesfor$|V_{cd}|$,$|V_{cs}|$, one arrives at the following predictions for the associated branching fractions: ${\cal B}{D_s^+\to K^0 e^+ \nu_e} = 3.31(33)\times 10^{-3}$;${\cal B}{D^0\to \pi^- e^+ \nu_e} = 2.73(22)\times 10^{-3}$;and${\cal B}_{D^0\to K^- e^+ \nu_e} = 3.83(28)$%. Alternatively, using the calculated $t$-dependence, agreement with contemporary empirical results for these branching fractions requires $\mathrm{\mid }{V}_{cd}\mathrm{\mid }=0.221(9)$, $\mathrm{\mid }{V}_{us}\mathrm{\mid }=0.953(34)$. 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.