Determinations of quark mixing matrix elements $\mathrm{\mid }{V}_{cd}\mathrm{\mid }$ and $\mathrm{\mid }{V}_{cs}\mathrm{\mid }$ from leptonic and semileptonic $D$ Decays

With the recent measurements of purely leptonic $D_{(s)}^{+}$ decays and semileptonic $D$ decays in conjunction with decay constants $f_{D_{(s)}^{+}}$ and form factors $f_{+}^{\pi (K)}(0)$ calculated in LQCD, we extract the magnitudes of $V_{cd}$ and $V_{cs}$ to be $\mathrm{\mid }{V}_{cd}\mathrm{\mid }=0.218\pm 0.005$ and $\mathrm{\mid }{V}_{cs}\mathrm{\mid }=0.987\pm 0.016$. Compared to those given in PDG2013, the precisions of these newly extracted $\mathrm{\mid }{V}_{cd}\mathrm{\mid }$ and $\mathrm{\mid }{V}_{cs}\mathrm{\mid }$ are improved by more than 2.0 and 1.5 factors, respectively. With the newly extracted $\mathrm{\mid }{V}_{cd}\mathrm{\mid }$ and $\mathrm{\mid }{V}_{cs}\mathrm{\mid }$ together with other CKM matrix elements given in PDG2013, we check the unitarity of the CKM matrix, which are $\mathrm{\mid }{V}_{ud}{\mathrm{\mid }}^2+\mathrm{\mid }{V}_{cd}{\mathrm{\mid }}^2+\mathrm{\mid }{V}_{td}{\mathrm{\mid }}^2=0.997\pm 0.002$, $\mathrm{\mid }{V}_{us}{\mathrm{\mid }}^2+\mathrm{\mid }{V}_{cs}{\mathrm{\mid }}^2+\mathrm{\mid }{V}_{ts}{\mathrm{\mid }}^2=1.027\pm 0.032$ and $\mathrm{\mid }{V}_{cd}{\mathrm{\mid }}^2+\mathrm{\mid }{V}_{cs}{\mathrm{\mid }}^2+\mathrm{\mid }{V}_{cb}{\mathrm{\mid }}^2=1.023\pm 0.032$.