Observation of $D^+\to K^0_Sπ^0μ^+ν_μ$, Test of Lepton Flavor Universality and First Angular Analysis of $D^+\to \bar{K}^\ast(892)^0\ell^+ν_\ell$

TL;DR

This study reports the first observation of the semileptonic decay $D^+ \to K_S^0\pi^0\mu^+\nu_\mu$ and an improved measurement of $D^+ \to K_S^0\pi^0 e^+\nu_e$ using BESIII data. By performing a comprehensive angular analysis of $D^+ \to \bar{K}^{*0}\ell^+\nu_\ell$ with $\bar{K}^{*0}\to K_S^0\pi^0$, the authors extract hadronic form-factor ratios $r_V=V(0)/A_1(0)$ and $r_2=A_2(0)/A_1(0)$, quantify the $S$-wave admixture, and determine the resonance parameters and $S$-wave phase via a SM helicity-amplitude framework with a single-pole dominance for the FFs. They measure the full set of angular observables and CP asymmetries, including ${\cal R}_{\mu/e}$ across the full and binned $q^2$ ranges, and find results consistent with the Standard Model and no lepton-flavor universality violation. The analysis leverages a double-tag technique at the $\psi(3770)$ and an amplitude analysis that incorporates $S$-wave interference via a LASS-inspired parameterization, providing stringent constraints on new-physics scenarios affecting $c\to s\ell\nu$ transitions.

Abstract

We report a study of the semileptonic decays $D^+\to K_S^0π^0\ell^+ν_\ell$ ($\ell = e, μ$) based on $20.3\,\mathrm{fb}^{-1}$ of $e^+e^-$ collision data collected at the center-of-mass energy of 3.773 GeV with the BESIII detector. The $D^+\to K_S^0π^0μ^+ν_μ$ decay is observed for the first time, with a branching fraction of $(0.896\pm0.017_{\rm stat}\pm0.008_{\rm syst})\%$, and the branching fraction of $D^+\to K_S^0π^0e^+ν_e$ is determined with the improved precision as $(0.943\pm0.012_{\rm stat}\pm0.010_{\rm syst})\%$. From the analysis of the dynamics, we observe that the dominant $\bar{K}^\ast(892)^0$ component is accompanied by an $S$-wave contribution, which accounts for $(7.10 \pm 0.68_{\rm stat} \pm 0.41_{\rm syst})\%$ of the total decay rate of the $μ^+$ channel and $(6.39 \pm 0.17_{\rm stat} \pm 0.14_{\rm syst})\%$ of the $e^+$ channel. Assuming a single-pole dominance parameterization, the hadronic form factor ratios are extracted to be $r_V=V(0)/A_1(0)=1.42 \pm\, 0.03_{\rm stat} \pm\, 0.02_{\rm syst}$ and $r_2=A_2(0)/A_1(0)=0.75 \pm\, 0.03_{\rm stat} \pm\, 0.01_{\rm syst}$. Based on the first comprehensive angular and the decay-rate $CP$ asymmetry analysis, the full set of averaged angular and $CP$ asymmetry observables are measured as a function of the momentum-transfer squared; they are consistent with expectations from the Standard Model. No evidence for violation of $μ-e$ lepton-flavor universality is observed in either the full range or the five chosen bins of momentum-transfer squared.

Figures (5)

• Figure 1: Fits to the $U_{\rm miss}$ distributions of the accepted candidates.
• Figure 2: Projections of the data and amplitude analysis fits for the (top) $\mu^+$ and (bottom) $e^+$ channels.
• Figure 3: Measured observables $\langle A_i \rangle$, $\langle S_i \rangle$, $\mathcal{R}_{\mu/e}$ and the $CP$ asymmetry for $D^+ \to \bar{K}^{*0}\ell^+\nu_\ell$ in different $q^2$ regions with $0.8<m_{\bar{K}^{*0}}<1.0$ GeV$^2/c^4$. The $e^+$ ($\mu^+$) results are shown in blue (red). The horizontal lines and shaded bands represent the mean value and 1 standard deviation across full $q^2$ range.
• Figure 4: Definition of the angular variables in the $D^+\to \bar{K} \pi \ell^+\nu_\ell$ decay.
• Figure 5: Fits to the $M_{\rm BC}$ distributions of tag channels. The dots with error bars are data, the blue solid curves are the total fits, the red dashed lines indicate the background contributions. The pair of red arrows indicate the $M_{\rm BC}$ signal window.