$\Lambda_b^0 \rightarrow J/\psi \Sigma^+ \pi^-$ Reconstruction Studies

The $\Sigma^+ \rightarrow n \pi^+$ decay is unobserved at LHCb and in this report the first steps are described regarding the possibilities of reconstructing this decay by studying the $\Sigma^+$ baryon. For the production of the $\Sigma^+$ baryons, the $\Lambda_b^0 \rightarrow J/\psi \Sigma^+ \pi^-$ decay has been used. The scenario is studied in which the $\Sigma^+$ baryon decays after the vertex detector, such that the trajectory of the $\Sigma^+$ baryon can be reconstructed directly in this detector. The main idea presented in this report are the analytical ways to assign momenta to the $\Sigma^+$ tracks decaying from the $\Lambda_b^0$. This is evaluated using kinematic constraints based on the invariant mass and the impact parameter of the $\Lambda_b^0$ system. A consideration is given mentioning the next steps in the reconstruction study of the $\Sigma^+ \rightarrow n \pi^+$ decay using information from the hadronic calorimeter.