Semileptonic decays of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>D</mml:mi><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mi>s</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msub></mml:math> mesons

Abstract

A symmetry-preserving continuum approach to meson bound states in quantum field theory, employed elsewhere to describe numerous $\ensuremath{\pi}$- and $K$-meson electroweak processes, is used to analyze leptonic and semileptonic decays of ${D}_{(s)}$ mesons. Each semileptonic transition is conventionally characterized by the value of the dominant form factor at $t=0$ and the following results are obtained herein: ${f}_{+}^{{D}_{s}\ensuremath{\rightarrow}K}(0)=0.673(40)$; ${f}_{+}^{D\ensuremath{\rightarrow}\ensuremath{\pi}}(0)=0.618(31)$ and ${f}_{+}^{D\ensuremath{\rightarrow}K}(0)=0.756(36)$. 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: ${\mathcal{B}}_{{D}_{s}^{+}\ensuremath{\rightarrow}{K}^{0}{e}^{+}{\ensuremath{\nu}}_{e}}=3.31(33)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, ${\mathcal{B}}_{{D}^{0}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{\ensuremath{-}}{e}^{+}{\ensuremath{\nu}}_{e}}=2.73(22)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, and ${\mathcal{B}}_{{D}^{0}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{e}^{+}{\ensuremath{\nu}}_{e}}=3.83(28)%.$ 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)-flavor symmetry breaking in this array of processes can be analysed; and just as in the $\ensuremath{\pi}\text{\ensuremath{-}}K$ 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.

Topics & Concepts