Total scattering in RICH

Total scattering was calculated using the formula:

Theta_0 = 13.6 MeV/(beta*c*p) * Z * sqrt(SUM) * {1 + 0.038 * ln(SUM)}
where SUM = sum(x_i / X0_i)
Taking into account electrons, than beta = Z = 1

Total scattering angle as a function of polar angle and momenta.

Total scattering angle as a function of momenta for different polar angles.

Dependance of the deflection angle on the polar angle.

Scattering in the radiator gas C4F10

• Properties of C4F10
  • Density: 24.61 g/cm**3 (at 20deg Celsius, 2.28bar, gas phase)
  • Density: 1516 g/cm**3 (at 20deg Celsius, liquid phase)
  • Radiation Length X0 = 34.52 g/cm**2 = 3200 cm in the gas phase at atmospheric pressure

Small angle scattering in RICH radiator as a function of polar angle and momenta.

Dependance of the particle trajectory length in the RICH radiator on the polar angle.

Scattering angle in RICH radiator as a function of momenta for different polar angles.	Scattering angle in RICH radiator as a function of momenta for polar angle Theta = 50deg.

In the following, only the mean deflection to the perpendicular direction of 22.25deg was taken into account to make the pictures simple

Scattering in SIGRADUR (mirror substrate material)

Scattering angle in RICH mirror substrate material SIGRADUR as a function of momenta for mean deflection angle 22.25deg

Scattering in the mirror reflective and protection layer

Scattering in Aluminium.	Scattering in MgF2.

Scattering in the carbon shell (CFK)

• Properties of CFK
  • Thickness = 0.4 mm
  • Radiation length X0 = 28 cm

Scattering in CFK

Area difference between these two cuts is:

Conversion / Signal from PLUTO simulation

in the picture "compareSim.png" you can see mean and sigma of the delta_theta distributions for the 3 momenta bins. the upper two pictures are done for electrons and positrons separately (red color "real" signal, blue conversion signal). in the lowest picture the comparision between electrons and positrons for the "real" signal is done.

as one can see, the differences in the simulation are only minor. the yields for signal and conversion are comparable (almost 1:1) for momenta (0,150>, it drops to 2:1 for momenta (350,1000> (see thetaNeg.jpg)

The sigma of the delta_theta distributions for negative tracks is:

• Signal: 0.96, 0.74, 0.54
• Conversion: 1.01, 0.81, 0.62

The sigma of the delta_theta distributions for positive tracks is:

• Signal: 1.18, 0.79, 0.60
• Conversion: 1.12, 0.88, 0.60

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in phi are the distributions much more narrower:

The sigma of the delta_phi distributions for negative tracks is:

• Signal: 0.55, 0.47, 0.47
• Conversion: 0.40, 0.53, 0.56

The sigma of the delta_phi distributions for positive tracks is:

• Signal: 0.57, 0.49, 0.50
• Conversion: 0.46, 0.51, 0.40

At this point i have to add, that i set following limits for the fit parameters: for signal is sigma in the range (0.4; 2.0) and for the background (2.0; infinity), which you can see in the fits not very well describing the distributions. in the most cases, the background had sigma of 2.0 in few cases just a touch higher than 2.0! (not a very good model :-(...), since for experimental data this limits worked very well, i decided not to introduce new limits for the fits.

I hope, the selection of the conversion was done properly (according to the documentation i hope i have not overseen something...)

• Comparision delta theta (RICH - MDC) distribution of signal and conversion leptons:
  

• Phi correlation for positive leptons (signal left, conversion right):
  

• Theta correlation for positive leptons (signal left, conversion right):
  

-- MartinJurkovic - 29 May 2007

I	Attachment	Action	Size	Date	Who	Comment
txt	scattering50.txt	manage	3.3 K	12 Jun 2007 - 12:32	MartinJurkovic	Total scattering and scattering in radiator as a function of momenta at polar angle 50deg
txt	theta2length.txt	manage	1.3 K	12 Jun 2007 - 12:31	MartinJurkovic	Path length and deflection angle as a function of polar angle