Abstract
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 $f_+^{D\to K}(0)=0.756(36)$. 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: ${\cal B}_{D_s^+\to K^0 e^+ \nu_e} = 3.31(33)\times 10^{-3}$; ${\cal B}_{D^0\to \pi^- e^+ \nu_e} = 2.73(22)\times 10^{-3}$; 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 $|V_{cd}|=0.221(9)$, $|V_{us}|=0.953(34)$. 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.
Highlights
Working with a large sample of eþe− collision data that was acquired using the Beijing Electron Positron Collider (BEPC), the BES III Detector Collaboration has released precise results on the semileptonic decays of DðsÞ mesons [1,2,3]
With all DðsÞ 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
Light quark values are listed in Eq (A9).] using the Schlessinger point method (SPM) [22,23], strengthened by the statistical sampling technique introduced in Refs. [24,25,26], we built interpolations: mPðm QÞ, fPðm QÞ
Summary
Working with a large sample of eþe− collision data that was acquired using the Beijing Electron Positron Collider (BEPC), the BES III Detector Collaboration has released precise results on the semileptonic decays of DðsÞ mesons [1,2,3] When these results are combined with those obtained using the BABAR detector at the Stanford Linear Accelerator Center [4], the Belle detector in Japan [5], and the CLEO detector at Cornell University [6], science is shown a new window into the Standard Model and beyond. F−ðtÞ overlaps with both channels. (These properties have been exemplified in studies of Kl3 transitions [13,14].)
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