First evidence for $D_s^+ \to f_1(1420) e^+ν_e$ and search for $D_s^+ \to f_1(1285) e^+ν_e$

Using $e^+e^-$ collision data corresponding to an integrated luminosity of 7.33~${\rm fb^{-1}}$ recorded by the BESIII detector at center-of-mass energies between 4.128 and 4.226~${\rm GeV}$, we present the first search for the semileptonic decays $D^+_s\to\ f_1(1420)e^+ν_e$ and $D^+_s\to\ f_1(1285)e^+ν_e$. The first evidence for the decay $D^+_s\to\ f_1(1420)e^+ν_e$ is found with a statistical significance of 3.4$σ$, and its product branching fraction $\mathcal{B}(D^+_s\to\ f_1(1420)e^+ν_e)\cdot\mathcal{B}(f_1(1420)\to\ K^+K^-π^0)$ is determined to be $\rm (4.5^{+2.0}_{-1.7}(stat) \pm0.4(syst)) \times 10^{-4} $, corresponding to an upper limit of $7.6 \times10^{-4}$ at the 90% confidence level. No significant signal of the decay $D^+_s\to\ f_1(1285)e^+ν_e$ is observed and the upper limit on the product branching fraction is set to be $\mathcal{B}(D^+_s\to\ f_1(1285)e^+ν_e)\cdot\mathcal{B}(f_1(1285)\to\ π^+π^-η) < 1.7\times10^{-4}$ at the 90% confidence level.