Improved Measurements of $D^+ \to ηe^+ν_e$ and $D^+ \to ημ^+ν_μ$

TL;DR

This work reports precision measurements of the semileptonic decays $D^+\to \eta e^+\nu_e$ and $D^+\to \eta \mu^+\nu_\mu$ using 20.3 fb$^{-1}$ of $e^+e^-$ data at $\sqrt{s}=3.773$ GeV with the BESIII detector. The analysis employs a double-tag technique to obtain absolute branching fractions and performs a simultaneous fit to partial decay rates across four $q^2$ bins, extracting the product $f_+^{\eta}(0)|V_{cd}|$ and, with a SM input for $|V_{cd}|$, the hadronic form factor $f_+^{\eta}(0)$. The measured branching fractions are $(9.75\pm0.29\pm0.28)\times10^{-4}$ for $D^+\to \eta e^+\nu_e$ and $(9.08\pm0.35\pm0.23)\times10^{-4}$ for $D^+\to \eta \mu^+\nu_\mu$, with a ratio $\mathcal{B}(D^+\to \eta\mu^+\nu_\mu)/\mathcal{B}(D^+\to \eta e^+\nu_e)=0.93\pm0.05_{stat}\pm0.02_{syst}$, showing no LFU violation. The simultaneous fit yields $f_+^{\eta}(0)|V_{cd}|=0.078\pm0.002\pm0.001$ and, using $|V_{cd}|$ from the global SM fit, $f_+^{\eta}(0)=0.345\pm0.008\pm0.003$, representing a substantial (factor ~3.4) improvement in precision over previous measurements. These results provide stringent tests of LCSR/LFQM/CCQM predictions for $f_+^{\eta}(0)$ and reinforce the SM description of charm semileptonic decays and LFU at this energy scale.

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 $D^+\to ηe^+ν_e$ and $D^+\to ημ^+ν_μ$ 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 $f^η_+(0)$ and the modulus of the $c\to d$ Cabibbo-Kobayashi-Maskawa matrix element $|V_{cd}|$ to be $f^η_+(0)|V_{cd}|=0.078\pm0.002\pm0.001$. Taking the $|V_{cd}|$ value from the Standard Model global fit as input, we obtain $f^η_+(0)=0.345\pm0.008\pm0.003$. The ratio between the measured branching fractions of $D^+\toη^+μ^+ν_μ$ and $D^+\toηe^+ν_e$, is determined to be $0.93\pm0.05_{\rm stat.}\pm0.02_{\rm syst.}$, indicating no violation of lepton flavor universality.

Figures (7)

• Figure 1: Fits to the $M_{\rm BC}$ distributions of the ST $D^-$ candidates. The points with error bars are data, the blue curves are the best fits, and the red dashed curves are the fitted combinatorial background shapes. The pairs of red arrows show the $M_{\rm BC}$ signal window.
• Figure 2: Fits to the $U_{\rm miss}$ distributions of the candidates for different signal decays. The dots with error bars are data, The blue solid lines denote the total fit. The black dashed lines denote the fitted peaking backgrounds, and the red dashed lines are the fitted combinatorial background shapes.
• Figure 3: Fits to the $U_{\rm miss}$ distributions of the candidates for the semileptonic decay $D^+\to\eta e^+\nu_e$ in different $q^2$ bins. The dots with error bars are data. The blue solid curves are the fit results, the black solid curves are the signal shapes, and the black dashed curves are the fitted combinatorial background shapes.
• Figure 4: Fits to the $U_{\rm miss}$ distributions of the candidates for the semileptonic decay $D^+\to\eta\mu^+\nu_\mu$ in different $q^2$ bins. The dots with error bars are data. The blue solid curves are the fit results, the black solid curves are the signal shapes, the black dashed curves are the peaking backgrounds stacked to the combinatorial background, and the red dashed curves are the fitted combinatorial background shapes.
• Figure 5: (Left) Separate fits to the partial decay rates of the four semileptonic decays $D^+\to\eta\ell^+\nu_\ell$ and (Right) projections of the hadronic form factor as a function of $q^2$. The dots with error bars are the measured partial decay rates and the solid curves are the fits.