Determination of $f_+^\pi(0)$ and Extraction of $|V_{cd}|$ from Semileptonic $D$ Decays

By globally analyzing all existing measured branching fractions and partial rates in different four momentum transfer-squared q(2) bins of D -> Ke+v(e) decays, we obtain the product of the form factor and magnitude of Cabibbo-Kobayashi-Maskawa matrix element V-cs to be f(+)(K) (0)vertical bar V-cs vertical bar = 0.717 +/- 0.004. With this product, we determine the D -> K semileptonic form factor f(+)(K) (0) = 0.737 +/- 0.004 +/- 0.000 in conjunction with the value of vertical bar V-cs vertical bar determined from the standard model global fit. Alternately, with the product together with the input of the form factor f(+)(K) (0) calculated in lattice quantum chromo-dynamics (LQCD) recently, we extract vertical bar V-cs vertical bar (D -> Ke+ve) = 0.962 +/- 0.005 +/- 0.014, where the error is still dominated by the uncertainty of the form factor calculated in LQCD. Combining the vertical bar V-cs vertical bar(Ds+-> l+vl) = 1.012 +/- 0.015 +/- 0.009 extracted from all existing measurements of D-s(+) -> l(+)v(e) decays and vertical bar V-cs vertical bar(D -> Ke+ve) = 0.962 +/- 0.005 +/- 0.014 together, we find the most precisely determined vertical bar V-cs vertical bar to be vertical bar V-cs vertical bar = 0.983 +/- 0.011, which improves the accuracy of the PDG'2014 value vertical bar V-cs vertical bar(PDG/2014) = 0.986 +/- 0.016 by 45 %.