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.
Categories: hep-ex