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

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 $B\left({D}_{s}^{+}\to \varphi {\mu }^{+}{\nu }_{\mu }\right)=\left(2.25±0.09±0.07\right)×{10}^{-2}$ , the most precise measurement to date. Combining with the world average of $B\left({D}_{s}^{+}\to \varphi {e}^{+}{\nu }_{e}\right)$ , the ratio of the branching fractions obtained is $\frac{B\left({D}_{s}^{+}\to \varphi {\mu }^{+}{\nu }_{\mu }\right)}{B\left({D}_{s}^{+}\to \varphi {e}^{+}{\nu }_{e}\right)}=0.94±0.08$ , in agreement with lepton universality. By performing a partial wave analysis, the hadronic form factor ratios at q 2 = 0 are extracted, finding ${r}_{V}=\frac{V\left(0\right)}{{A}_{1}\left(0\right)}=1.58±0.17±0.02$ and ${r}_{2}=\frac{{A}_{2}\left(0\right)}{{A}_{1}\left(0\right)}=0.71±0.14±0.02$ , where the first uncertainties are statistical and the second are systematic. No significant S-wave contribution from f 0(980) → K + K − is found. The upper limit $B\left({D}_{s}^{+}\to {f}_{0}\left(980\right){\mu }^{+}{\nu }_{\mu }\right)\cdot B\left({f}_{0}\left(980\right)\to {K}^{+}{K}^{-}\right)<5.45×{10}^{-4}$ is set at 90% credibility level.