First Observation and Dynamical Study of the $D_s^{+}\to f_0(980){\mu }^{+}{\nu }_{\mu }$ Decay

Abstract

Using 7.33 fb${}^{-1}$ of $e^{+}{e}^{-}$ annihilation data recorded with the BESIII detector at center-of-mass energies from 4.128 to 4.226 GeV, we report the first observation and dynamical study of the semileptonic decay $D_s^{+}\to f_0(980){\mu }^{+}{\nu }_{\mu }$. The absolute branching fraction of $D_s^{+}\to f_0(980){\mu }^{+}{\nu }_{\mu }$ with $f_0(980)\to {\pi }^{+}{\pi }^{-}$ is $(1.59\pm 0.18_{\mathrm{stat}}\pm 0.11_{\mathrm{syst}})\times 10^{-3}$. Combining this result with our earlier BESIII measurement of $\mathcal{B}(D_s^{+}\to f_0(980)e^{+}{\nu }_e)$, their ratio is found to be $\frac{\mathcal{B}(D_s^{+}\to f_0(980){\mu }^{+}{\nu }_{\mu })}{\mathcal{B}(D_s^{+}\to f_0(980)e^{+}{\nu }_e)}=0.92\pm 0.13_{\mathrm{stat}}\pm 0.08_{\mathrm{syst}}$, in agreement with the Standard Model expectation of lepton flavor universality. From a dynamical analysis of the $D_s^{+}\to f_0(980){\mu }^{+}{\nu }_{\mu }$ decay with a simple pole parametrization for the hadronic transition form factor, the product of the form factor $f_{+}^{f_0(980)}(0)$ and the $c\to s$ Cabibbo-Kobayashi-Maskawa matrix element $|V_{cs}|$ is determined to be $f_{+}^{f_0(980)}(0)|V_{cs}|=0.490\pm 0.059_{\mathrm{stat}}\pm 0.025_{\mathrm{syst}}$. Averaging with our previously reported result for the $D_s^{+}\to f_0(980)e^{+}{\nu }_e$ decay, we obtain $f_{+}^{f_0(980)}(0)|V_{cs}|=0.500\pm 0.016_{\mathrm{stat}}\pm 0.020_{\mathrm{syst}}$. Using $|V_{cs}|$ from the CKMfitter group, we extract $f_{+}^{f_0(980)}(0)=0.514\pm 0.017_{\mathrm{stat}}\pm 0.021_{\mathrm{syst}}$. This represents the most precise determination of the $D_s\to f_0(980)$ transition form factor to date, and provides stringent tests of various theoretical models.

12 pages, 3 figures