<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:mi>D</mml:mi><mml:mi>l</mml:mi><mml:mi>ν</mml:mi></mml:math>form factors at nonzero recoil and extraction of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mo stretchy="false">|</mml:mo><mml:msub><mml:mrow><mml:mi>V</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi><mml:mi>b</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">|</mml:mo></mml:mrow></mml:math>

Abstract

We present a lattice QCD calculation of the $B\ensuremath{\rightarrow}Dl\ensuremath{\nu}$ semileptonic decay form factors ${f}_{+}({q}^{2})$ and ${f}_{0}({q}^{2})$ for the entire physical ${q}^{2}$ range. Nonrelativistic QCD bottom quarks and highly improved staggered quark charm and light quarks are employed together with ${N}_{f}=2+1$ MILC gauge configurations. A joint fit to our lattice and BABAR experimental data allows an extraction of the Cabibbo-Kobayashi-Maskawa matrix element $|{V}_{cb}|$. We also determine the phenomenologically interesting ratio $R(D)=\mathcal{B}(B\ensuremath{\rightarrow}D\ensuremath{\tau}{\ensuremath{\nu}}_{\ensuremath{\tau}})/\mathcal{B}(B\ensuremath{\rightarrow}Dl{\ensuremath{\nu}}_{l})$ ($l=e,\ensuremath{\mu}$). We find $|{V}_{cb}{|}_{\text{excl}}^{B\ensuremath{\rightarrow}D}=0.0402(17)(13)$, where the first error consists of the lattice simulation errors and the experimental statistical error and the second error is the experimental systematic error. For the branching fraction ratio we find $R(D)=0.300(8)$.

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