Model Independent Calculation of $\mathcal{B}({\bar{B}}^0\to D^{(\ast )+}{\tau }^{-}\bar{\nu })/\mathcal{B}({\bar{B}}^0\to D^{(\ast )+}{e}^{-}\bar{\nu })$

Abstract

Using the formulas for the $d\Gamma /d{q}^2$ distribution with non-zero lepton mass and experimentally determined form factors, we calculate the $d\Gamma (D^{(\ast )+}{l}^{-}\bar{\nu })/d{q}^2$ spectra and branching fractions for $l=e$, $\mu$ and $\tau$. We obtain the results $\mathcal{B}({\bar{B}}^0\to D^{+}{\tau }^{-}\bar{\nu })/\mathcal{B}({\bar{B}}^0\to D^{+}{e}^{-}\bar{\nu })=0.278_{-0.035}^{+0.049}$ and $\mathcal{B}({\bar{B}}^0\to D^{\ast +}{\tau }^{-}\bar{\nu })/\mathcal{B}({\bar{B}}^0\to D^{\ast +}{e}^{-}\bar{\nu })=0.256_{-0.013}^{+0.014}$ . Since we used the experimentally measured form factors, these results are independent of theoretical models of form factors.

8 pages, 3 postscript figures. We corrected a mistake in computer program for the numerical calculation, and modified the title and contents