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

TL;DR

This paper reports a highly precise measurement of the $D^+ o \mu^+ u_\mu$ decay branching fraction, leading to improved determinations of the decay constant and CKM matrix element, enhancing tests of the Standard Model.

Contribution

The study provides the most precise measurement to date of the $D^+ o \\mu^+ u_\\mu$ branching fraction, refining the decay constant and CKM matrix element calculations.

Findings

Branching fraction measured as (4.034 ± 0.080_stat ± 0.040_syst) × 10^{-4}

Decay constant $f_{D^+}$ determined as 213.5 ± 2.1_stat ± 1.1_syst MeV

Extracted $|V_{cd}|$ value consistent with Standard Model expectations

Abstract

Using $20.3~\mathrm{fb}^{-1}$ of $e^+e^-$ collision data collected at a center-of-mass energy of $E_{\rm c.m.}=3.773$ 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 $(4.034\pm0.080_{\rm stat}\pm0.040_{\rm syst})\times10^{-4}$. 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 $f_{D^+}|V_{cd}|=(48.02\pm0.48_{\rm stat}\pm0.24_{\rm syst}\pm0.12_{\rm input}\pm0.15_{\rm EM})~\mathrm{MeV}$ 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 $f_{D^+}=(213.5\pm2.1_{\rm stat}\pm1.1_{\rm syst}\pm0.8_{\rm input}\pm0.7_{\rm EM})$\,MeV. Alternatively, using the value of $f_{D^+}$ from a precise lattice quantum chromodynamics calculation, we extract $|V_{cd}|=0.2265\pm0.0023_{\rm stat}\pm0.0011_{\rm syst}\pm0.0009_{\rm input}\pm0.0007_{\rm EM}$.