A New Look at the Scalar Meson \(f_0(500)\) via \(D^+\to \pi^+\pi^-\ell^+\nu_\ell\) Decays

• Published in: arXiv.org
• Main Authors: Ablikim, M, Begzsuren, K, Boyko, I, Chen, G, Chen, Z J, Cui, J J, Deng, Z Y, Denysenko, I, Ding, X X, Dong, M Y, Feldbauer, F, Garzia, I, Gersabeck, E M, Gong, L, Guan, C Y, Heinz, C H, Herold, C, Holtmann, T, Hou, X T, Hu, B Y, Hu, S L, Huang, Y P, Hüsken, N, W Ji, Ji, X L, Jiang, X S, Jiao, J K, Jiao, Z, Jing, M Q, Ke, B C, Kui, X, Kumar, N, Lellmann, M, Li, C H, G Li, Li, X Y, Li, Z J, Liang, Y T, Lin, C C, Liu, C, Liu, H B, Liu, Huihui, Liu, J B, Liu, J Y, Liu, L C, Liu, P L, Liu, Q, Liu, W M, Liu, Z A, Lou, X C, H Ma, Mao, Y J, Marcello, S, Miao, H, Mo, X H, Nefedov, Y, Niu, Q L, Ouyang, Q, Ping, J L, Qian, S, Qin, J J, Qin, L Q, Qiu, J F, Qu, Z H, Redmer, C F, Schelhaas, Y, Shen, C P, Shi, B A, Shi, H, Shi, J Y, Song, T Z, Song, Y J, Sosio, S, Spataro, S, Sun, Y C, Tang, G Y, Tang, M, Teng, J X, Wang, H J, Wang, L L, Wang, M, Wang, X F, Wang, X J, Wang, Z, Wu, Y J, Xiao, H, Xu, C J, Yuan, C Z, Yuan, H, Yuan, S C, Zeng, S H, Zeng, X, Zhang, J J, Zhang, J S, Zhang, Y, Zhang, Y H, Zhang, Yan, Zhou, J Y, Zhu, L, Zhu, L X
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 05.02.2024
• Subjects: Decay rate; Flavor (particle physics); Form factors; Leptons; Momentum transfer; Standard model (particle physics)
• ISSN: 2331-8422

Using \(2.93~\mathrm{fb}^{-1}\) of \(e^+e^-\) collision data collected with the BESIII detector at the center-of-mass energy of 3.773 GeV, we investigate the semileptonic decays \(D^+\to \pi^+\pi^- \ell^+\nu_\ell\) (\(\ell=e\) and \(\mu\)). The \(D^+\to f_0(500)\mu^+\nu_\mu\) decay is observed for the first time. By analyzing simultaneously the differential decay rates of \(D^+\to f_0(500) \mu^+\nu_\mu\) and \(D^+\to f_0(500) e^+\nu_e\) in different \(\ell^+\nu_\ell\) four-momentum transfer intervals, the product of the relevant hadronic form factor \(f^{f_0}_{+}(0)\) and the magnitude of the \(c\to d\) Cabibbo-Kobayashi-Maskawa matrix element \(|V_{cd}|\) is determined to be \(f_{+}^{f_0} (0)|V_{cd}|=0.0787\pm0.0060_{\rm stat}\pm0.0033_{\rm syst}\) for the first time. With the input of \(|V_{cd}|\) from the global fit in the standard model, we determine \(f_{+}^{f_0} (0)=0.350\pm0.027_{\rm stat}\pm0.015_{\rm syst}\). The absolute branching fractions of \(D^+\to f_0(500)_{(\pi^+\pi^-)}\mu^+\nu_\mu\) and \(D^+\to \rho^0_{(\pi^+\pi^-)} \mu^+\nu_\mu\) are determined as \((0.72\pm0.13_{\rm stat}\pm0.10_{\rm syst})\times10^{-3}\) and \((1.64\pm0.13_{\rm stat}\pm0.11_{\rm syst})\times 10^{-3}\). Combining these results with those of previous BESIII measurements on their semielectronic counterparts from the same data sample, we test lepton flavor universality by measuring the branching fraction ratios \({\mathcal B}_{D^+\to \rho^0 \mu^+\nu_\mu}/{\mathcal B}_{D^+\to \rho^0 e^+\nu_e}=0.88\pm0.10\) and \({\mathcal B}_{D^+\to f_0(500) \mu^+\nu_\mu}/{\mathcal B}_{D^+\to f_0(500) e^+\nu_e}=1.14\pm0.28\), which are compatible with the standard model expectation.