The sensitivity on $\alpha$ of LHCb using a time dependent Dalitz plot analysis of the $B_{d} \to 3\pi$ channel

Under a small number of theoretical assumptions, a time-dependent Dalitz plot analysis of the three-body decay B->3pi allows to perform a clean extraction of the CKM angle alpha. Compared to a two-body approach, ambiguities are theoretically removed and such a method gives access to an independent measurement of tree and penguin parameters. The purpose of this note is to transpose the method proposed by Snyder-Quinn to the LHCb experimental framework. Resolutions, acceptances and tagging dilution are taken into account and we investigate various effects of background contamination by using Monte-Carlo toy simulations. The alpha sensitivity study is presented by considering systematic effects originating from phenomenological hypotheses and experimental uncertainties. We show that, with these effects under control, a resolution such that sigma_alpha/alpha < 0.1 can be reached after one year of data taking (2fb-1).