Amplitude analysis of the decay $D^+ \to \pi^- \pi^+ \pi^+$ in the LHCb experiment

This thesis is dedicated to the study of the resonant structure of the $D^+ \to \pi^- \pi^+ \pi^+$ decay mode using Dalitz plot analysis in a data sample corresponding to an integrated luminosity of 2.0 fb$^{−1}$ of proton–proton collisions at 8 TeV recorded by the LHCb detector during 2012. The Dalitz Plot Analysis is a unique tool to investigate the spectroscopy of light mesons. In particular for the scalar sector there are a few π−π+ resonances, such as the σ(500), f0(980) and higher mass f0 states which are not well understood, with properties poorly known. The study of the Dalitz plot through and amplitude analysis is performed for about 600 thousand events of D+ → π−π+π+ with two techniques. We first use the so-called Isobar Model, where the final state is described as a coherent sum of quasi two-body states. Within this formalism we find that the Dalitz plot is well represented by a combination of seven quasi-two-body decay channels, which are the σ(500) , ρ(770)0, f0(980), f2(1250), f0(1370), ρ(1450)0 and f0(1500) resonances in the π+π− system as well as a nonresonant (NR) component. Then a Model Independent Partial Wave Analysis (MI-PWA) to measure the S-wave component on the π+π− system is also implemented for the first time on this channel. We show that $D^+ \to \pi^- \pi^+ \pi^+$ decay is dominated by the S-wave structure.