Peak Shapes in TOF PID histograms
Summary
In TOF PID histograms the peaks of all non-centered particles are deformed due to subtraction of the wrong expected time. We reproduce the deformed peak shapes, first by means of a Monte Carlo simulation, then by a numerical calculation processed into a Spline function. The results of the different methods are compared and proven to be consistent. A convolution with the detector resolution is performed to incorporate detector effects. The Spline is fitted to data from ALICE. A straight forward fit delivered a $\chi^2_{red} = 4333$. To improve the fit crude adjustments, only justified within the scope of further research, were made. A better $\chi^2_{red} = 419$ was found changing the radius of the detector by 10cm. And the best fit with $\chi^2_{red} = 379$ integrated a scaling factor of which the origin is unknown.