[Halld-physics] Pion/Kaon Separation for gas threshold Cherenkov

[Nathan Sparks]

Hi Paul,

Here is the pion/kaon separation as a function of momentum for the gas threshold Cherenkov currently in the geant simulation. It was obtained in the following manner.

The threshold momentum for producing Cherenkov radiation in a gas of index of refraction n is given by
m/sqrt(n*n-1), where m is the mass of the incident particle.
Using n~1.00153, the threshold momentum is about 2.5 GeV/c for pions and 8.9 GeV/c for kaons. This means that in the kinematic region of interest say momenta less than 8 GeV/c kaons will not radiate, pions do.

Denote the mean number of photoelectrons as a function of momentum resulting from a pion by N(p); the pion/kaon separation in terms of Gaussian sigmas is then 
(N(p) - 0)/sqrt(N(p)) = sqrt(N(p)).

1M pi^+ tracks were thrown in the 2 to 8 GeV/c momentum range, 0 to 20 degrees polar angle range. N was determined for each 50 MeV/c bin by fitting with a Poisson distribution.

The expected mean number of photoelectrons N' can be calculated from
N' ~ N_0*L*sin^2(theta_c) = N_0*L*[1-(1/n^2)*(1+(m^2/p^2))], having the simple momentum dependence
N' ~ A - B/p^2, where A and B are constants.

Finally, N(p) was fit with N', resulting in
A = 38.67 +- 0.02
B = 272.16 +- 0.25 (GeV/c)^2

I have attached plots of N(p) and the separation as function of momentum with the fit function superimposed.
Separation(p) ~ sqrt(38.67 - 272.16/p^2)

3 sigma separation starts at 3.0 GeV/c.
4 sigma separation starts at 3.5 GeV/c.

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Best Regards,
-Nathan