Studies of the decay $$ {\textrm{D}}_{\textrm{s}}^{+}\to {\textrm{K}}^{+}{\textrm{K}}^{-}{\mu}^{+}{\nu}_{\mu } $$
Abstract The$$ {D}_s^{+}\to {K}^{+}{K}^{-}{\mu}^{+}{\nu}_{\mu } $$ D s + → K + K − μ + ν μ decay is studied based on 7.33 fb −1 ofe + 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$$ \mathcal{B}\left({D}_s^{+}\to \phi {\mu}^{+}{\nu}_{\mu}\right)=\left(2.25\pm 0.09\pm 0.07\right)\times {10}^{-2} $$ B D s + → ϕ μ + ν μ = 2.25 ± 0.09 ± 0.07 × 10 − 2 , the most precise measurement to date. Combining with the world average of$$ \mathcal{B}\left({D}_s^{+}\to \phi {e}^{+}{\nu}_e\right) $$ B D s + → ϕ e + ν e , the ratio of the branching fractions obtained is$$ \frac{\mathcal{B}\left({D}_s^{+}\to \phi {\mu}^{+}{\nu}_{\mu}\right)}{\mathcal{B}\left({D}_s^{+}\to \phi {e}^{+}{\nu}_e\right)}=0.94\pm 0.08 $$ B D s + → ϕ μ + ν μ B D s + → ϕ e + ν e = 0.94 ± 0.08 , in agreement with lepton universality. By performing a partial wave analysis, the hadronic form factor ratios atq 2 = 0 are extracted, finding$$ {r}_V=\frac{V(0)}{A_1(0)}=1.58\pm 0.17\pm 0.02 $$ r V = V 0 A 1 0 = 1.58 ± 0.17 ± 0.02 and$$ {r}_2=\frac{A_2(0)}{A_1(0)}=0.71\pm 0.14\pm 0.02 $$ r 2 = A 2 0 A 1 0 = 0.71 ± 0.14 ± 0.02 , where the first uncertainties are statistical and the second are systematic. No significantS-wave contribution fromf 0 (980)→ K + K − is found. The upper limit$$ \mathcal{B}\left({D}_s^{+}\to {f}_0(980){\mu}^{+}{\nu}_{\mu}\right)\cdot \mathcal{B}\left({f}_0(980)\to {K}^{+}{K}^{-}\right)<5.45\times {10}^{-4} $$ B D s + → f 0 980 μ + ν μ ⋅ B f 0 980 → K + K − < 5.45 × 10 − 4 is set at 90% credibility level.