Improved Bounds for the Slope and Curvature of $\bar{B}\to D^{(\ast )}\ell \bar{\nu }$ Form Factors

Abstract

We derive a theoretically allowed domain for the slope ${\hat{\varrho }}^2$ and curvature $\hat{c}$ of the physical form factor appearing in the decay $\bar{B}\to D^{\ast }\ell \bar{\nu }$. Using heavy-quark symmetry, we relate this function to a particular $\bar{B}\to D$ form factor free of ground-state $B_c$ poles below the threshold for $BD$ production, for which almost model-independent constraints are derived from QCD using unitarity and analyticity. Our results are of interest for the extraction of $|V_{cb}|$ from the recoil spectrum in exclusive semileptonic $B$ decays. Making conservative estimates of the theoretical uncertainties, we find (up to $1/m_Q$ corrections) ${\hat{\varrho }}^2<1.11$ and $\hat{c}\simeq 0.66{\hat{\varrho }}^2-0.11$. We also derive the corresponding bounds for the form factor in the decay $\bar{B}\to D\ell \bar{\nu }$.

Comments: 13 pages LaTeX, 2 figures appended