Use of early data onB→ρπdecays

Abstract

This paper reviews the Dalitz plot analysis for the decays $B^0\left(B^0\right)\to \rho \overrightarrow{\pi }{\pi }^{+}{\pi }^{-}{\pi }^0.$ We discuss what can be learned about the ten parameters in this analysis from untagged and from tagged time-integrated data. We find that, with the important exception of the interesting $\mathrm{CP}$ violating quantity $\alpha ,$ the parameters can be determined from this data sample—and, hence, they can be measured at CLEO as well as at the asymmetric B factories. This observation also suggests that the extraction of $\alpha$ from the time-dependent data sample can be accomplished with a smaller data sample (and, therefore, sooner) than would be required if all ten parameters were to be obtained from the well-tagged time-dependent data sample alone. We also explore bounds on the shift of the true angle $\alpha$ from the angle measured from charged $\rho$ final states alone. These may be obtained prior to measurements of the parameters describing the neutral $\rho$ channel, which are expected to be small.