Studies of the decay $D^+_s\to K^+K^- \mu^+ \nu_{\mu}$

TL;DR

This paper presents a precise measurement of the decay $D^+_s o K^+K^- u_ ext{mu}$, tests lepton universality, and extracts hadronic form factors using data from the BESIII detector, with implications for understanding charm semileptonic decays.

Contribution

It provides the most precise measurement to date of the branching fraction and form factors for $D^+_s o ext{phi} u_ ext{mu}$ decay, confirming lepton universality and analyzing the decay dynamics.

Findings

Branching fraction ${ m B}(D_s^+ o ext{phi} u_ ext{mu})$ measured as (2.25 ± 0.09 ± 0.07)%

Branching ratio ${ m B}(D_s^+ o ext{phi} u_ ext{mu})/{ m B}(D_s^+ o ext{phi}e^+ u_e)$ is 0.94 ± 0.08, consistent with lepton universality

Hadronic form factor ratios at $q^2=0$ are $r_V=1.58±0.17±0.02$ and $r_2=0.71±0.14±0.02$

Abstract

The $D^+_s\to K^+K^-\mu^+\nu_\mu$ decay is studied based on 7.33 fb$^{-1}$ of $e^+e^-$ collision data collected with the BESIII detector at center-of-mass energies in the range from 4.128 to 4.226 GeV. The absolute branching fraction is measured as ${\mathcal B}(D^+_s\to \phi \mu^+\nu_\mu) = (2.25\pm 0.09 \pm 0.07) \times10^{-2}$, the most precise measurement to date. Combining with the world average of ${\mathcal B}(D^+_s\to \phi e^+\nu_e)$, the ratio of the branching fractions obtained is$\frac{{\mathcal B}(D^+_s\to \phi \mu^+\nu_\mu)}{{\mathcal B}(D^+_s\to \phi e^+\nu_e)} = 0.94\pm0.08$, in agreement with lepton universality. By performing a partial wave analysis, the hadronic form factor ratios at $q^{2}=0$ are extracted, finding $r_{V}=\frac{V(0)}{A_{1}(0)}=1.58\pm0.17\pm0.02$ and $r_{2}=\frac{A_{2}(0)}{A_{1}(0)}=0.71\pm0.14\pm0.02$, where the first uncertainties are statistical and the second are systematic. No significant $S$-wave contribution from $f_0(980)\to K^+K^-$ is found. The upper limit $\mathcal{B}(D_s^+\to f_0(980)\mu^{+}{\nu}_{\mu}) \cdot{\mathcal B}(f_0(980)\to K^+K^-) < 5.45 \times 10^{-4}$ is set at 90\% confidence level.