Setup tuning using Lambda and anti-Lambda particles

In order to check the general geometry of the DIRAC experiment, we use the $\Lambda$ and $\bar{\Lambda}$ particles that decay in our setup into $p\pi^-$ and $\pi^+\bar{p}$. The Lambda mass is very well determined [1] and comparing the value reconstructed in our data with the published one we can be condent that our geometrical description is correct. The main factors that can influence the value of the Lambda mass are: the position of the Aluminum membrane and the opening angle of the two downstream arms, they will be discussed in this note in section 3. The width of the Lambda mass distribution is another tool that we use to evaluate the resolution of the momentum reconstruction of the particles. There are several factors that can contribute to the momentum reconstruction resolution. The most important are: the multiple scattering in the Aluminum membrane and in the Drift Chambers (DC), the resolution of the DC planes, the alignment of the DC downstream and the multiple scattering in the upstream detectors. In order to evaluate the last one we have used the $\pi\pi$ data. Using the $\pi^+\pi^-$ vertex distribution at the target for experimental data and simulated data [2] the upstream multiple scattering has been quantified, and, since then, all the simulated data were generated taking into account these new measurements. Once fixed the upstream multiple scattering we attribute the remaining difference between experimental and simulated data to the DC "effect" on the track reconstruction. Once corrected for this effect, we obtain an evaluation of the momentum resolution in a momentum range larger that the one used with the $\pi^+\pi^-$ pair analysis. This study has been already performed in the past on the previous experimental setup and many notes were published on the subject.