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

Abstract

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