Measurements of the Branching Fractions for the Semileptonic Decays D(s)⁺ → φe⁺ν(e), φμ⁺ν(μ), ημ⁺ν(μ) and η′μ⁺ν(μ)

By analyzing 482 pb⁻¹ of e⁺e⁻ collision data collected at the center-of-mass energy √s = 4.009 GeV with the BESIII detector, we measure the branching fractions for the semi-leptonic decays D(s)⁺ → φe⁺ν(e), φμ⁺ν(μ), ημ⁺ν(μ) and η′μ⁺ν(μ) to be ℬ(D(s)⁺ → φe⁺ν(e)) = (2.26 ± 0.45 ± 0.09)%, ℬ(D(s)⁺ → φμ⁺ν(μ)) = (1.94 ± 0.53 ± 0.09)%, ℬ(D(s)⁺ → ημ⁺ν(μ)) = (2.42 ± 0.46 ± 011)% and ℬ(D(s)⁺ → η′μ⁺ν(μ)) = (1.06 ± 0.54 ± 0.07)%, where the first and second uncertainties are statistical and systematic, respectively. The branching fractions for the three semi-muonic decays D(s)⁺ → φμ⁺ν(μ), ημ⁺ν(μ) and η′μ⁺ν(μ) are determined for the first time and that of D(s)⁺ → φe⁺ν(e) is consistent with the world average value within uncertainties.