Precision Measurement of the Branching Fraction of $D^{+}\to {\mu }^{+}{\nu }_{\mu }$

Abstract

Using $20.3{\mathrm{fb}}^{-1}$ of $e^{+}{e}^{-}$ collision data collected at a center-of-mass energy of $E_{c.m.}=3.773$ GeV with the BESIII detector operating at the BEPCII collider, we determine the branching fraction of the leptonic decay $D^{+}\to {\mu }^{+}{\nu }_{\mu }$ to be $(4.034\pm 0.080_{\mathrm{stat}}\pm 0.040_{\mathrm{syst}})\times 10^{-4}$. Interpreting our measurement with knowledge of the Fermi coupling constant $G_F$, the masses of the $D^{+}$ and ${\mu }^{+}$ as well as the lifetime of the $D^{+}$, we determine $f_{D^{+}}|V_{cd}|=(48.02\pm 0.48_{\mathrm{stat}}\pm 0.24_{\mathrm{syst}}\pm 0.12_{\mathrm{input}}\pm 0.15_{\mathrm{EM}})\mathrm{MeV}$ after taking into account necessary radiative corrections. This result is a factor of 2.3 more precise than the previous best measurement. Using the value of the magnitude of the $c\to d$ Cabibbo-Kobayashi-Maskawa matrix element $|V_{cd}|$ given by the global standard model fit, we obtain the $D^{+}$ decay constant $f_{D^{+}}=(213.5\pm 2.1_{\mathrm{stat}}\pm 1.1_{\mathrm{syst}}\pm 0.8_{\mathrm{input}}\pm 0.7_{\mathrm{EM}})$\,MeV. Alternatively, using the value of $f_{D^{+}}$ from a precise lattice quantum chromodynamics calculation, we extract $|V_{cd}|=0.2265\pm 0.0023_{\mathrm{stat}}\pm 0.0011_{\mathrm{syst}}\pm 0.0009_{\mathrm{input}}\pm 0.0007_{\mathrm{EM}}$.

9 pages, 2 figures

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