$D_{(s)}-$ mesons semileptonic form factors in the 4-flavor holographic QCD

We investigate semileptonic form factors of $D_{(s)}$ meson from a modified soft-wall 4-flavor holographic model. The model successfully reproduces the masses and decay constants of various mesons, including $\rho$, $K^*$, $D^*$, $D_s^*$, $a_1$, $K_1$, $f_1$, $D_1$,$D_{s1}$, $\pi$, $K$, $\eta$, $D$, and $D_s$. Moreover, we study the semileptonic decay processes $D^{+} \to (\pi, K, \eta) l^{+} \nu_{l}$ and $D_{s}^{+} \to ( K, \eta) l^{+} \nu_{l}$, associated with the vector meson exchange, as well as $D_{(s)}^{+} \to K^{} l^{+} \nu_{l}$, associated with the vector and axial vector meson exchange. The form factors $f_{+}(q^{2})$ for $D \to\pi$ and $D_{(s)}\to K$ decays agree excellently with experimental and lattice data, outperforming other theoretical approaches. The $f_{+}(q^{2})$ form factor for $D^{+} \to \eta $ is compatible with experimental data, while a slight discrepancy is observed for $D_{s}^{+} \to \eta $ at large $q^{2}$. Additionally, we predict the vector form factors $V(q^{2})$ and $A_{1}(q^{2})$ for $D \to K^{}$ and $D_{s} \to K^{}$ decays, respectively. The results agree well with other approaches and lattice data at maximum recoil ($q^{2}=0$).