Three-body decay as a baryon polarizer

Abstract: According to the standard model, the size of CP violation in the weak decay Λ → pπ- is predicted to be ∼ 10-5. This means that a very high precision is needed if we want to be able to measure it. It turns out that the precision mainly depends on three factors: if the decay already has a large parity-breaking effect, if we take more measurements, or if the Lambda baryon has a large polarization. The uncertainty is inversely proportional to the root mean square of the polarization, √⟨P2⟩, of Λ. Polarization is a measurement of the fraction of particles with parallel spin. In this project, we simulated the kinematic properties of the three-body decay of the charmed lambda baryon Λc+  → Λπ+ π0 by assuming that Λ+ c decays 100% of the times via the ρ+-resonance, i.e. Λc+ decays like Λc+ → Λρ+ , and ρ+ subsequently decays ρ+ → π+π0. The invariant masses of the daughter particles were then plotted in a so-called Dalitz plot. The fact that the ρ+-meson is a vector meson is exploited to compute the helicity amplitudes HλΛ,λρ, where λ is the helicity of respective particle, meaning the projection of the spin in the direction of the ρ+-mesons momentum. The helicity amplitudes describe the helicities of the particles involved before and after the decay. These are then used to compute the polarization of Λ. After doing the simulation, the invariant masses are plotted in the Dalitz plot and the polarization in each point is computed. The root mean square polarization of Λ was √⟨P2⟩ = 0.81 ± 0.08. This result gives a large polarization and points to this process being a good baryon polarizer. When conducting more research into the three-body decay of Λc+ as a potential source of Λ with large polarization, the contributions of other resonances should be taken into account. In light of these results, it would also be interesting to investigate if three-body decays could work as a baryon polarizer for other baryons.