Analysis method for double-$\Lambda$ hypernulear events

To study hyperon-hyperon interaction, the experiment E373 was carried out at KEK-PS. $\Xi^-$ hyperons are produced via the $p(K^-, K^+)\Xi^-$ reaction, and double-$\Lambda$ hypernucleus were produced at a $\Xi^-$ stopping point as a fragment in the nuclear emulsion. Double-$\Lambda$ hypernucleus sequentially decays via non-mesonic or mesonic weak interaction. So that, double-$\Lambda$ hypernuclear event has three vertices. Until now, we succesfully found 7 double-$\Lambda$ hypernuclear events. The recoiled hyperfragments had only few $\mu$m track lengths in the emulsion, then we need the high precision measurement. In this paper, we report detailed method of analysis and those results for two double-$\Lambda$ hypernuclear events which were successfully reconstructed as those ones. To reconstruct events we took pictures all tracks related the event every 0.1 $\mu$m depth, and obtained the brightness and position information. Using central values of brightness along the tracks, straight-line fitting fas been made. Thus, production and decay vertices have been measured as intersection of the lines. Accoding to the above analysis, one event was found to be as a $^{11}_{\Lambda \Lambda}$Be, and another one was uniquely identfied as a $^{6}_{\Lambda \Lambda}$He.