$|V_{cs(d)}|$ measurements and LFU tests in charm leptonic decays

BESIII collected 2.93 fb$^{−1}$, 0.482 fb$^{−1}$, 3.19 fb$^{−1}$, and 0.567 fb$^{−1}$ of data samples at the center of-mass energies $\sqrt{s}$ = 3.773, 4.009, 4.178, and 4.6 GeV, respectively. Herein, we report the improved measurements of the quark mixing matrix elements $|V_{cs(d)}|$ by using $D$$^{+}_{(s)}$ → $\ell$$^{+}$$\nu$$_{\ell}$, $D$$^{0}$$^{(+)}$ → $\bar{K}$$\ell$$^{+}$$\nu$$_{\ell}$, $D$$^{0}$$^{(+)}$ → $\pi$$\ell$$^{+}$$\nu$$_{\ell}$, and $D$$_{s}^{+}$ → η$^{(')}$$\ell$$^{+}$$\nu$$_{\ell}$ and . We also report tests of lepton flavor universality with the (semi-)leptonic decays $D$$^{+}_{(s)}$ → $\ell$$^{+}$$\nu$$_{\ell}$, $D$$^{0}$$^{(+)}$ → $\bar{K}$$\ell$$^{+}$$\nu$$_{\ell}$, $D$$^{0}$$^{(+)}$ → $\pi$$\ell$$^{+}$$\nu$$_{\ell}$, and $D$$_{s}^{+}$ → $\phi $η$^{(')}$$\ell$$^{+}$$\nu$$_{\ell}$ and $\Lambda$$_{c}^{+}$ → $\Lambda$$\ell$$^{+}$$\nu$$_{\ell}$. Also, we present the improved measurements of the decay constants $f$$_{D}$$_{(s)}^{+}$ and the hadronic form factors of some semi-leptonic $D$ decays.