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# ThreeDseparationplot

part of the DircPlayground

## Calculation of the Separationpower in dependence of momentum and angle

The dependence of N(sigma) from the momentum p and the angle theta is calculated and displayed with Mathematia:

1. Momentum Dependence

Plot Number of sigma in dependence of momentum p:
• Number of sigma:

The plot represents the Numbers of sigmas two particles are separated depending on the mometum with
• "sigma" = 0.01 is the resolution of a single photon track
• "sigma/sqrt(nph)" gives the resolution of a track with
• nph = 16 is a typical number of produced photons
• Kaon = 493.68 MeV
• pionn = 139.57
• refractiv index n=1.47

## 2. Angle Dependence

The number of produced photons denpends on the pathlength in the radiator which depends again on the incident angle.
http://www.gae.ucm.es/~emma/docs/tesina/node4.html

## Pathlength:

(see PathLength, Aida Galoyan))with: Angle psi:

Pathlength of a partice in the radiator of the barrel:

## Number of measured Cherenkov photons:

Detected Cherenkov photons:

## Number of sigma in dependence of momentum and theta angle:

Number of sigma in dependence of momentum p (500-5000MeV/c) and angle theta:

Number of sigma in dependence of momentum p (2000-4000MeV/c) and angle theta:

## Example on the treatment on the Phase Space Plots

(Presented in the PidtagMeeting07). On the Example pbar p to phi phi (find the full set of Phasespaceplots on VrvsMeeting11) it is shown which fraction of produced kaons can be separated from pions with the help of the Barrel Dirc. First one sees all the kaons produced, secondly the kaons in the solid angle and the lower threshold (of the Kaon detection) of the Cherenkov detector and last but not least all the kaons over the limit of numbers of sigma separation beeing 4. The latter conditions is done for the two track resolutions "sigma" (track) = 10 mrad and 30 mrad. It shows that we loose with a bad track resolution for higher monenta a not minor amount of kaons (meaning having a not sufficient resolution to separate them from pions) in the angular region of the Barel DIRC. Remark: The calculations are peliminary and the separation limit arbitrary.

Cut momentum and theta angle:

Cut momentum and theta angle and number of sigma larger 4:

With a track resulution of 10 mrad:

With a track resolution of 30 mrad:

-- GeorgSchepers - 29 Nov 2007
I Attachment Action Size Date Who Comment
jpeg goodtrackresolution.jpeg manage 30 K 2008-01-14 - 17:47 GeorgSchepers traqck resulution 10 mrad
gif separationpower.gif manage 3 K 2007-11-29 - 17:17 GeorgSchepers Separation power versus momentum
jpeg ppbartophiphi.jpeg manage 63 K 2007-12-11 - 14:54 GeorgSchepers pbar p to phi phi
gif l.gif manage 1 K 2007-12-06 - 17:18 GeorgSchepers Pathlength of a partice in the radiator of the barrel
gif pathlength_thetapsi_plot.gif manage 12 K 2007-12-07 - 15:27 GeorgSchepers Pathlength
gif Full.gif manage 6 K 2007-12-06 - 17:21 GeorgSchepers Number of sigma in depndence of momentum and theta angle
gif nsigma_p_theta_500-5000.gif manage 21 K 2007-12-07 - 18:39 GeorgSchepers Number of sigma in dependence of momentum p (500-5000MeV/c) and angle theta
gif nsigma_p_theta_2000-4000.gif manage 21 K 2007-12-07 - 18:40 GeorgSchepers Number of sigma in dependence of momentum p (2000-4000MeV/c) and angle theta
gif nsigma_p_plot.gif manage 3 K 2007-12-07 - 18:38 GeorgSchepers Number of sigma in dependence of momentum p
gif nsigma.gif manage 2 K 2007-12-06 - 17:12 GeorgSchepers Number of sigma
gif nphotonp.gif manage 4 K 2007-12-06 - 17:13 GeorgSchepers Number of measured Cherenkov photons
gif nphotonsdetected_plot.gif manage 16 K 2007-12-07 - 18:35 GeorgSchepers Detected Cherenkov photons
jpeg pbarptophiphi_cutns.jpeg manage 48 K 2007-12-11 - 14:56 GeorgSchepers Cut momentum and theta angle and number of sigma larger 4
jpeg pbarptophiphi_cutptheta.jpeg manage 52 K 2007-12-11 - 14:55 GeorgSchepers Cut momentum and theta angle
gif psi.gif manage 2 K 2007-12-06 - 17:20 GeorgSchepers Angle psi
Topic revision: r12 - 2008-02-15, LarsSchmitt
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