Determination of $$f_+^K(0)$$ f + K ( 0 ) and extraction of $$|V_{cs}|$$ | V c s | from semileptonic $$D$$ D decays

Abstract

By globally analyzing all existing measured branching fractions and partial rates in different four momentum transfer-squared $$q^2$$ bins of $$D\rightarrow Ke^+\nu _e$$ decays, we obtain the product of the form factor and magnitude of Cabibbo–Kobayashi–Maskawa matrix element $$V_{cs}$$ to be $$f_+^K(0)|V_{cs}|=0.717\pm 0.004$$ . With this product, we determine the $$D\rightarrow K$$ semileptonic form factor $$f_+^K(0)=0.737\pm 0.004\pm 0.000$$ in conjunction with the value of $$|V_{cs}|$$ 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 chromodynamics (LQCD) recently, we extract $$|V_{cs}|^{D\rightarrow Ke^+\nu _e}=0.962\pm 0.005\pm 0.014$$ , where the error is still dominated by the uncertainty of the form factor calculated in LQCD. Combining the $$|V_{cs}|^{D_s^+\rightarrow \ell ^+\nu _\ell }=1.012\pm 0.015\pm 0.009$$ extracted from all existing measurements of $$D^+_s\rightarrow \ell ^+\nu _\ell $$ decays and $$|V_{cs}|^{D\rightarrow Ke^+\nu _e}=0.962\pm 0.005\pm 0.014$$ together, we find the most precisely determined $$|V_{cs}|$$ to be $$|V_{cs}|=0.983\pm 0.011$$ , which improves the accuracy of the PDG’2014 value $$|V_{cs}|^\mathrm{PDG'2014}=0.986\pm 0.016$$ by $$45\,\%$$ .