Procedure for direct measurement of the Cabibbo-Kobayashi-Maskawa angle $γ$

A natural procedure is presented to measure the angle $\gamma$ from the decay $B^{\pm} \to \pi^{\pm}\pi^+\pi^-$. It is based in the Dalitz plot fitting analysis. Neither amplitudes nor strong phases have to be known a priori. We present simulations of this decay computing both statistical and theoretical uncertainties and analyze the experimental feasibility. We found that $\gamma$ could be measured with a combined error of the order of 20$^o$ with 90% of CL after about a couple of years of running of the first generation of B factories.