Observation of $D^+ \to f_0(500) e^+\nu_e$ and Improved Measurements of $D \to\rho e^+\nu_e$

TL;DR

This paper reports the first observation of the S-wave contribution in $D^+ o ho o ho e^+ u_e$ decays, measures branching fractions for several $D$ meson semileptonic decays, and provides form factor ratios, enhancing understanding of charm semileptonic processes.

Contribution

It presents the first observation of the S-wave component in $D^+ o ho o ho e^+ u_e$ decays and provides improved measurements of branching fractions and form factor ratios for $D$ meson semileptonic decays.

Findings

S-wave contribution in $D^+ o ho o ext{pi pi} e^+ u_e$ is (25.7±1.6±1.1)% with >10σ significance.

Branching fractions: $ ext{Br}(D^{0} o ho^- e^+ u_e) = (1.445±0.058±0.039)×10^{-3}$, $ ext{Br}(D^{+} o ho^0 e^+ u_e) = (1.860±0.070±0.061)×10^{-3}$, $ ext{Br}(D^{+} o f_0(500) e^+ u_e) = (6.30±0.43±0.32)×10^{-4}$.

An upper limit for $D^{+} o f_0(980) e^+ u_e$ is set at $<2.8×10^{-5}$ at 90% CL.

Abstract

Using a data sample corresponding to an integrated luminosity of 2.93~fb$^{-1}$ recorded by the BESIII detector at a center-of-mass energy of $3.773$ GeV, we present an analysis of the decays $\bar{D}^0\to\pi^+\pi^0 e^-\bar{\nu}_e$ and $D^+\to\pi^-\pi^+ e^+\nu_e$. By performing a partial wave analysis, the $\pi^+\pi^-$ $S$-wave contribution to $D^+\to\pi^-\pi^+ e^+\nu_e$ is observed to be $(25.7\pm1.6\pm1.1)$% with a statistical significance greater than 10$\sigma$, besides the dominant $P$-wave contribution. This is the first observation of the $S$-wave contribution. We measure the branching fractions $\mathcal{B}(D^{0} \to \rho^- e^+ \nu_e) = (1.445\pm 0.058 \pm 0.039) \times10^{-3}$, $\mathcal{B}(D^{+} \to \rho^0 e^+ \nu_e) = (1.860\pm 0.070 \pm 0.061) \times10^{-3}$, and $\mathcal{B}(D^{+} \to f_0(500) e^+ \nu_e, f_0(500)\to\pi^+\pi^-) = (6.30\pm 0.43 \pm 0.32) \times10^{-4}$. An upper limit of $\mathcal{B}(D^{+} \to f_0(980) e^+ \nu_e, f_0(980)\to\pi^+\pi^-) < 2.8 \times10^{-5}$ is set at the 90% confidence level. We also obtain the hadronic form factor ratios of $D\to \rho e^+\nu_e$ at $q^{2}=0$ assuming the single-pole dominance parameterization: $r_{V}=\frac{V(0)}{A_{1}(0)}=1.695\pm0.083\pm0.051$, $r_{2}=\frac{A_{2}(0)}{A_{1}(0)}=0.845\pm0.056\pm0.039$.