Observation of $D^+\to\eta^\prime\mu^+\nu_\mu$ and First Study of $D^+\to \eta^\prime \ell^+\nu_\ell$ Decay Dynamics

TL;DR

This paper reports the first observation of the decay $D^+\to \eta'^\mu^+\nu_\mu$, measures its branching fraction, compares muon and electron modes to test lepton flavor universality, and analyzes decay dynamics to extract form factors and mixing angles.

Contribution

It provides the first measurement of the $D^+\to \eta'^\mu^+\nu_\mu$ decay, refines the $D^+\to \eta'^e^+\nu_e$ measurement, and extracts decay form factors and mixing angles from the data.

Findings

First observation of $D^+\to \eta'^\mu^+\nu_\mu$ with 8.6 sigma significance.

Branching fractions measured as $(1.92\pm0.28_{stat}\pm 0.08_{syst})\times 10^{-4}$ and $(1.79\pm0.19_{stat}\pm 0.07_{syst})\times 10^{-4}$.

The ratio of muon to electron branching fractions is $1.07\pm0.19_{stat}\pm0.03_{syst}$, consistent with lepton flavor universality.

Abstract

Using $20.3\,\rm fb^{-1}$ of $e^+e^-$ collision data collected at the center-of-mass energy 3.773\,GeV with the BESIII detector, we report the first observation of the semileptonic decay $D^+\to \eta^\prime \mu^+\nu_\mu$ with significance of $8.6\sigma$ including systematic uncertainties, and an improved measurement of $D^+\to \eta^\prime e^+\nu_e$. The branching fractions of $D^+\to \eta^\prime \mu^+\nu_\mu$ and $D^+\to \eta^\prime e^+\nu_e$ are determined to be $(1.92\pm0.28_{\rm stat}\pm 0.08_{\rm syst})\times 10^{-4}$ and $(1.79\pm0.19_{\rm stat}\pm 0.07_{\rm syst})\times 10^{-4}$, respectively. The ratio of the two branching fractions is determined to be ${\mathcal R}_{\mu/e}=1.07\pm0.19_{\rm stat}\pm 0.03_{\rm syst}$, which agrees with the theoretical expectation of lepton flavor universality within the Standard Model.From an analysis of the $D^+\to \eta^\prime \ell^+\nu_\ell$ decay dynamics, the product of the hadronic form factor $f_+^{\eta^{\prime}}(0)$ and the CKM matrix element $|V_{cd}|$ is measured for the first time, giving $f^{\eta^\prime}_+(0)|V_{cd}| = (5.92\pm0.56_{\rm stat}\pm0.13_{\rm syst})\times 10^{-2}$. The $\eta-\eta^\prime$ mixing angle in the quark flavor basis is determined to be $\phi_{\rm P} =(39.8\pm0.8_{\rm stat}\pm0.3_{\rm syst})^\circ$.