Studies of the decay $D_s^{+}\to K^{+}{K}^{-}{\mu }^{+}{\nu }_{\mu }$

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 $\mathcal{B}(D_s^{+}\to \varphi {\mu }^{+}{\nu }_{\mu })=(2.25\pm 0.09\pm 0.07)\times 10^{-2}$, the most precise measurement to date. Combining with the world average of $\mathcal{B}(D_s^{+}\to \varphi e^{+}{\nu }_e)$, the ratio of the branching fractions obtained is$\frac{\mathcal{B}(D_s^{+}\to \varphi {\mu }^{+}{\nu }_{\mu })}{\mathcal{B}(D_s^{+}\to \varphi e^{+}{\nu }_e)}=0.94\pm 0.08$, in agreement with lepton universality. By performing a partial wave analysis, the hadronic form factor ratios at $q^2=0$ are extracted, finding $r_V=\frac{V(0)}{A_1(0)}=1.58\pm 0.17\pm 0.02$ and $r_2=\frac{A_2(0)}{A_1(0)}=0.71\pm 0.14\pm 0.02$, 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.

27 pages, 4 figures