Improved Measurements of $D^+ \to \eta e^+\nu_e$ and $D^+ \to \eta \mu^+\nu_\mu$

TL;DR

This paper reports precise measurements of semileptonic $D^+$ decays to $ o ext{eta}$ with electrons and muons, determining form factors and testing lepton flavor universality using BESIII data.

Contribution

The study provides improved measurements of branching fractions, form factors, and tests lepton flavor universality in $D^+$ decays, using a large dataset and simultaneous fitting techniques.

Findings

Branching fractions: $(9.75 ext{ and }9.08) imes10^{-4}$ for electron and muon channels.

Form factor times CKM element: $0.078 ext{ with uncertainties}$.

Lepton flavor universality ratio: $0.93 ext{ within uncertainties}$.

Abstract

Using 20.3 fb$^{-1}$ of $e^+e^-$ collision data collected at the center-of-mass energy of 3.773 GeV with the BESIII detector, we measure the branching fractions of $D^+\to \eta e^+\nu_e$ and $D^+\to \eta\mu^+\nu_\mu$ to be $(9.75\pm0.29\pm0.28)\times10^{-4}$ and $(9.08\pm0.35\pm0.23)\times10^{-4}$, where the first and second uncertainties are statistical and systematic, respectively. From a simultaneous fit to their partial decay rates, we determine the product of the hadronic form factor $f^\eta_+(0)$ and the modulus of the $c\to d$ Cabibbo-Kobayashi-Maskawa matrix element $|V_{cd}|$ to be $f^\eta_+(0)|V_{cd}|=0.078\pm0.002\pm0.001$. Taking the $|V_{cd}|$ value from the Standard Model global fit as input, we obtain $f^\eta_+(0)=0.345\pm0.008\pm0.003$. The ratio between the measured branching fractions of $D^+\to\eta^+\mu^+\nu_{\mu}$ and $D^+\to\eta e^+\nu_e$, is determined to be $0.93\pm0.05_{\rm stat.}\pm0.02_{\rm syst.}$, indicating no violation of lepton flavor universality.