On the Determination of $a_1$ and $a_2$ from Hadronic Two Body $B$ Decays

Abstract

{}From Class I decays : $B^o\text{ra}{\pi }^{+}({\rho }^{+})+D^{-}({D^{\ast }}^{-})$, we determine $a_1$, and from Class III decays : $B^{+}\text{ra}{\pi }^{+}({\rho }^{+})+\text{ol}{D}^o({\text{ol}{D}^{\ast }}^o)$, we determine an allowed domain in the $(a_1,a_2)$ plane. We find that within one standard deviation errors, the allowed band of $a_1$ from Class I decays is at least three standard deviations removed from the allowed domain $(a_1,a_2)$ from Class III decays.If we expand the experimental errors to two standard deviations we do find a small intersection between the $a_1$ band and the allowed $(a_1,a_2)$ domain. The results usually quoted in the literature lie in this intersection. We suggest : (1) an independent measurement of the branching ratio for the Class III decay, $B^{+}\text{ra}{\rho }^{+}\text{ol}{D}^o$, (2) a high-statistics measurement of the branching ratio of the Class I decay, $B\text{ra}\text{ol}D(\text{ol}{D}^{\ast })+D_s(D_s^{\ast })$ in both charged states, and (3) a measurement of the longitudinal polarization fraction in the Class III decay $B^{+}\text{ra}{\rho }^{+}{\text{ol}{D}^{\ast }}^o$ to shed more light on the questions involved .

Comments: 9pages(Latex)+4 figures(PS file appended), PAR/LPTHE/94-22