Purpose

the DIRC provides

• a positive kaon identification
• a destinction of gammas and relativistic charged particles entering the EMC behind him

Working principle

• Cherenkov Detector
• determination of the mass of the particle by combining his velocity information with momentum information from the tracking detectors

Important values

• Polar angle vs. momentum distribution of the kaons in radiative decays of resonances in formation experiments like J/psi -> K+K- gamma for the search of glue-balls (Ref. TPR):
  

• the barrel DIRC covers the solid angle of 22 to 140 degrees
• the lower momentum threshold for kaons which produce Cherenkov light is for an envisaged refractive index of n=1.47 as low as 460 MeV/c (for single photon producton -- for photon numbers bigger than 4 it is more than 200 MeV/c higher)

FIRST Estimations:

• Single Photon Cherenkov Angle Resolution

• with a DIRC-Bar size of 17x30x2000mm, a distance of l=1.20m of the photomultipiers from the bar exit and a diameter of the photomultiplier cathods of 2cm ( beeing equal to the distance of the centers of the cathods) the geometric contribution of the Single Photon Cherenkov Angle Resulution can be calculated and lies in the order of magnitude of 10mrad

• to this geometric contribution the resolution contribution (comming from the production and the transmission dispersion) has to be added which has a values of similar size

• Correlation of Cherenkov angle Theta c as a function of laboratory momentum in the DIRC detector. The arrows mark a resolution of 10mrad.:
  

• The resolution of the track Cherenkov angle sigma_track scales with the square root of the number of photons detected:

sigma_track(theta) = sigma_single(theta) / sqrt(N_ph)

• Thus we find approximatively the separation of two particle species, i.e. numbers of sigma (N(sigma)), with masses m1 and m2 (Ref. PDG):

N(sigma) ~= |m1*m1 - m2*m2| / (2 * p*p * sigma_track(theta) * sqrt(n*n-1))

• To provide usefull results the DIRC should produce 15 to 20 photons per particle track. The correlation calculated with a photon number of 16 is shown in the figure bellow.

• Correlation between number of sigma's of seperation N(sigma) and the momentum of the particles for 16 photons per track and a single photon angle resolution of 10mrad.:
  

• Identification Efficiency for kaons and pions (Ref. CDR):
  

• It is show the probability to misidentify a pion as a kaon as a function of the particle momentum (red circles) and the efficiency to identify a kaon (open circles)

• Material Budget:

• with 17mm (of thickness) of fused silica the DIRC bars present approximately 14% of a radiation length to normal incident particles. The support structure will add some more percent.

-- GeorgSchepers - 05 May 2006

I	Attachment	Action	Size	Date	Who	Comment
jpg	corr_ang_mom1.jpg	manage	42.0 K	05 May 2006 - 16:10	GeorgSchepers	Correlation of Cherencov angle Theta c as a function of laboratory momentum in the DIRC detector. The arrows mark a resolution of 10mrad.
jpg	corr_ang_mom2.jpg	manage	31.7 K	05 May 2006 - 16:11	GeorgSchepers	NUmber of sigma's of seperation
gif	identification_alone.gif	manage	12.1 K	25 Apr 2006 - 09:31	GeorgSchepers	Identification Efficiency for Kaons and pions
gif	kkgamma.gif	manage	61.4 K	19 Apr 2006 - 13:50	GeorgSchepers	Polar angle vs. momentum distribution of the kaons in radiative decays of resonances in formation experiments like J/psi -> K+K- gamma for the search of glue-balls.