## Example Plot for Separation Power

This histogram visualises how distributions in beta look for kaons and pions, the example being a Time-of-Propagation calculation with perspex radiator, 1000 particle in each peak. One can determine the centroid and second moment (peak width in sigma) of these peaks, the ratio distance over sigma then gives a measure for the separation power. Plotting beta is preferred over plotting the reconstructed mass because it does not introduce a singularity at beta=1, the analysis happily giving values beta>1 sometimes.

• This quantity makes sense as long as the peaks are Gaussian in shape.
• This quantity is independent of the acceptance interval choice for pions and/or kaons.
• Such quantities from several subdetectors can be combined.

For each particle pair (here pion-kaon) this sigma separation power is a function of particle angle (at target vertex) and particle momentum (or energy).

Visualising the full function is a challenge due to the three independent variables. Phi symmetry may reduce this to two, theta and momentum, and (colour coded or contour) 2D plots are possible. The 1D plot above is giving the values for fixed momentum.

Approximate PID momentum limits (3.5 sigma or 4 sigma or some other value) can be derived from the date used for the curve(s) above as the sigma value scales with p^(-2), the assumption being that in the beta histogram (top of this page) only the peak position changes but not the peak width.

-- KlausFoehl - 26 Jun 2006
Topic attachments
I Attachment Action Size Date Who Comment
eps betasigma30port.eps manage 31.9 K 26 Jun 2006 - 14:51 KlausFoehl separation power expressed in sigma
gif betasigma30port.gif manage 5.9 K 26 Jun 2006 - 14:55 KlausFoehl separation power expressed in sigma
gif visualisation1.gif manage 2.6 K 26 Jun 2006 - 15:20 KlausFoehl distributions for kaons and pions
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Topic revision: r1 - 26 Jun 2006, KlausFoehl

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