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

Abstract

By globally analyzing all existing measured branching fractions for $D\to \pi e^{+}{\nu }_e$ decays, partial decay rates in different four momentum transfer-squared $q^2$ bins, as well as products of the decay form factor $f_{+}^{\pi }(q^2)$ and the Cabibbo-Kobayashi-Maskawa (CKM) quark-mixing matrix element $|V_{cd}|$, we obtain $f_{+}^{\pi }(0)|V_{cd}|=0.1428\pm 0.0019$. This product, in conjunction with $|V_{cd}|$ from a global Standard Model fit, implies a value for the $D\to \pi$ semileptonic form factor $f_{+}^{\pi }(0)=0.634\pm 0.008\pm 0.002$, which is consistent within error with those calculated in theory based on QCD, but with higher precision than the most accurate $f_{+}^{\pi }(0{)}_{\mathrm{LQCD}}=0.666\pm 0.020\pm 0.021$ calculated in LQCD by a factor of 3.3. Alternately, using this product together with the most accurate form factor calculated in LQCD, we find $|V_{cd}{|}^{D\to \pi e^{+}{\nu }_e}=0.2144\pm 0.0029_{\exp }\pm 0.0093_{\mathrm{LQCD}}$. Combining this $|V_{cd}{|}^{D\to \pi e^{+}{\nu }_e}$ together with $|V_{cd}{|}^{D^{+}\to {\mu }^{+}{\nu }_{\mu }}=0.2160\pm 0.0049\pm 0.0014$ extracted from both the BESIII and CLEO-c measurements of $D^{+}\to {\mu }^{+}{\nu }_{\mu }$ decays, we find the most precisely extracted $|V_{cd}|$ to be $|V_{cd}|=0.2157\pm 0.0045$ up to date, which improves the accuracy of the PDG'2014 value $|V_{cd}{|}_{\mathrm{PD}{\mathrm{G}}^{\prime }2014}=0.225\pm 0.008$ by over $70$. Using this $|V_{cd}|$ together with the PDG'2014 $|V_{ud}|$ and $|V_{td}|$, we check for first column unitarity and find $|V_{ud}{|}^2+|V_{cd}{|}^2+|V_{td}{|}^2-1=-0.004\pm 0.002$, which deviates from unitarity by $2\sigma$. In addition, we find the ratio of $f_{+}^{\pi }(0)$ and $D^{+}$ decay constant $f_{D^{+}}$ to be $f_{+}^{\pi }(0)/f_{D^{+}}=(3.11\pm 0.08)$ GeV${}^{-1}$, which can be used to validate LQCD calculations for these two quantities.

arXiv commentarXiv admin note: substantial text overlap with arXiv:1409.8049

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• Decay $D\to K^{(\ast )}{\ell }^{+}{\nu }_{\ell }$ in covariant quark model
• Recent Experimental Results on Leptonic $D_{(s)}^{+}$ Decays, Semileptonic $D$ Decays and Extraction of $|V_{cd(s)}|$