A symmetry-preserving continuum approach to meson bound states in quantum field theory, employed elsewhere to describe numerous πand K-meson electroweak processes, is used to analyze leptonic and semileptonic decays of D ðsÞ mesons. Each semileptonic transition is conventionally characterized by the value of the dominant form factor at t ¼ 0 and the following results are obtained herein: f D s →K þ ð0Þ ¼ 0.673ð40Þ; f D→π þ ð0Þ ¼ 0.618ð31Þ and f D→K þ ð0Þ ¼ 0.756ð36Þ. Working with the computed t-dependence of these form factors and standard averaged values for jV cd j, jV cs j, one arrives at the following predictions for the associated branching fractions: B D þ s →K 0 e þ ν e ¼ 3.31ð33Þ × 10 −3 , B D 0 →π − e þ ν e ¼ 2.73ð22Þ × 10 −3 , and B D 0 →K − e þ ν e ¼ 3.83ð28Þ%: Alternatively, using the calculated t-dependence, agreement with contemporary empirical results for these branching fractions requires jV cd j ¼ 0.221ð9Þ, jV us j ¼ 0.953ð34Þ. With all D ðsÞ transition form factors in hand, the nature of SU(3)-flavor symmetry breaking in this array of processes can be analysed; and just as in the π-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.
We consider the fidelity of the vector meson dominance (VMD) assumption as an instrument for relating the electromagnetic vector-meson production reaction $$e + p \rightarrow e^\prime + V + p$$
e
+
p
→
e
′
+
V
+
p
to the purely hadronic process $$V + p \rightarrow V+p$$
V
+
p
→
V
+
p
. Analyses of the photon vacuum polarisation and the photon-quark vertex reveal that such a VMD Ansatz might be reasonable for light vector-mesons. However, when the vector-mesons are described by momentum-dependent bound-state amplitudes, VMD fails for heavy vector-mesons: it cannot be used reliably to estimate either a photon-to-vector-meson transition strength or the momentum dependence of those integrands that would arise in calculations of the different reaction amplitudes. Consequently, for processes involving heavy mesons, the veracity of both cross-section estimates and conclusions based on the VMD assumption should be reviewed, e.g., those relating to hidden-charm pentaquark production and the origin of the proton mass.
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