Kinematics (momentum) calibration

The well known kinematics and masses of $\Lambda$, $\Sigma$, and the ground state of $^{12}_\Lambda$B can be used to carry out the calibrations for the momentum reconstruction matrices as established in the HNSS experiment.

Events from the peaks of $\Lambda$, $\Sigma$, and the ground state of $^{12}_\Lambda$B will be selected out of the CH$_2$ and C target runs and $\chi^2$'s are defined by the reconstructed missing masses against the well known masses. Using a computerized minimization process for the total $\chi^2$'s, the momentum reconstruction matrices can be optimized. This procedure could be done for one of the spectrometers at a time and will be iterated for the two spectrometers until a consistent result is obtained. Since the natural widths of the peaks are different, proper weights should be taken into account for the $\chi^2$ obtained from different masses. This procedure has been successfully performed for the HNSS experiment to reach the final resolution of 900 keV.