Determinations of quark mixing matrix elements $|V_{cd}|$ and $|V_{cs}|$ from leptonic and semileptonic $D$ Decays

Abstract

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 $|V_{cd}|=0.218\pm0.005$ and $|V_{cs}|=0.987\pm0.016$. Compared to those given in PDG2013, the precisions of these newly extracted $|V_{cd}|$ and $|V_{cs}|$ are improved by more than 2.0 and 1.5 factors, respectively. With the newly extracted $|V_{cd}|$ and $|V_{cs}|$ together with other CKM matrix elements given in PDG2013, we check the unitarity of the CKM matrix, which are $|V_{ud}|^2+|V_{cd}|^2+|V_{td}|^2=0.997\pm0.002$, $|V_{us}|^2+|V_{cs}|^2+|V_{ts}|^2=1.027\pm0.032$ and $|V_{cd}|^2+|V_{cs}|^2+|V_{cb}|^2=1.023\pm0.032$.