Event “zero-time” determination with TOF detector F. Pierella for the TOF-Offline Group INFN & Bologna University PPR Meeting, January 2003

Overview Previous results Present results Summary of algorithms and conclusion Plan

Statistical algorithm By assigning a mass configuration to n selected tracks in a given event, we can require a best fit condition thus deriving the most probable mass configuration for the n tracks, out of the possible N=3n and the corresponding most probable zero-time for the event.

Previous results

Reminder Previous result has been obtained with a smearing on MC momentum in order to take into account the momentum resolution (no reconstructed momentum used); with a gaussian smearing on track length given by GEANT (=30ps); with a gaussian smearing on MC time-of-flight; matching contamination was not included.

Present results Included full simulation Tracks assigned to a “wrong time” are now included in the statistical (combinatorial) method (so contamination is now included); in order to minimize this effect, we select tracks with momentum 1.25GeV/c<p<1.75GeV/c which is the best range for track matching; No (coarse) Gaussian Smearing on MC time-of-flight is used but full TOF detector simulation (edge effect, efficiency, and resolution simulation) is now considered; Reconstructed momenta are now used for zero-time calculation.

Present Results

CPU Timing for the statistical method Considering the combinatorial character of the algorithm, the CPU computing time for the zero-time determination is reported in the following table Number of tracks per set CPU computing time n=10 5 n=15 50

Summary of the algorithms and conclusion Statistical method: no dependence from particle ratios event zero-time resolution of the order of 30ps The pion mass assumption for all tracks has been suggested as an alternative –and faster- method to calculate the event zero-time, but in this case a dependence from particle ratios occurs

Dependence from particle ratio Simplified case with only pions and kaons

Dependence from particle ratio

Plan Plan is to use a GA (Genetic Algorithm) for event “zero-time” determination; The architecture of GA systems allow for a solution to be reached quicker since “better” solutions have a better chance of “surviving” and “procreating”, as opposed to randomly throwing out solutions and seeing which ones work

“Definition” of the problem In the GA dictionary of the “zero-time” problem the “chromosome” corresponds to a mass configuration of the n selected tracks in the event; a “chromosome allele” corresponds to a mass assignment to a given track; the “fitness value” of a given “chromosome” corresponds to the chi-square of the mass configuration; the “parent selection” is done according to the “fitness value”;

Strategy “offspring chromosomes” are obtained “crossing-over” the “father” and “mother” “chromosomes”; generally, the fitness values of the “offspring chromosome” are better than those of the “parent chromosomes”; “mutation” corresponds to a random change of a mass assignment in a given mass configuration; mutations can occur leading to “more performing chromosomes” for systems where the population is larger (say 50) the fitness levels should more steadily and stably approach the desired level.