First evidence for $D_s^{+}\to f_1(1420)e^{+}{\nu }_e$ and search for $D_s^{+}\to f_1(1285)e^{+}{\nu }_e$

Using $e^{+}{e}^{-}$ collision data corresponding to an integrated luminosity of 7.33~$\mathrm{f}{\mathrm{b}}^{-1}$ recorded by the BESIII detector at center-of-mass energies between 4.128 and 4.226~$\mathrm{G}\mathrm{e}\mathrm{V}$, we present the first search for the semileptonic decays $D_s^{+}\to f_1(1420)e^{+}{\nu }_e$ and $D_s^{+}\to f_1(1285)e^{+}{\nu }_e$. The first evidence for the decay $D_s^{+}\to f_1(1420)e^{+}{\nu }_e$ is found with a statistical significance of 3.4$\sigma$, and its product branching fraction $\mathcal{B}(D_s^{+}\to f_1(1420)e^{+}{\nu }_e)\cdot \mathcal{B}(f_1(1420)\to K^{+}{K}^{-}{\pi }^0)$ is determined to be $(4.5_{-1.7}^{+2.0}(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})\pm 0.4(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t}))\times {10}^{-4}$, corresponding to an upper limit of $7.6\times {10}^{-4}$ at the 90% confidence level. No significant signal of the decay $D_s^{+}\to f_1(1285)e^{+}{\nu }_e$ is observed and the upper limit on the product branching fraction is set to be $\mathcal{B}(D_s^{+}\to f_1(1285)e^{+}{\nu }_e)\cdot \mathcal{B}(f_1(1285)\to {\pi }^{+}{\pi }^{-}\eta )<1.7\times {10}^{-4}$ at the 90% confidence level.