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
In the calculation, the polar angle dependant deflection between the perpendicular direction to the surface of the RICH components (shortest distance through the materials) and particle incident angle (real particle path length through the material) was taken into account.
Small Angle Scattering divided in all RICH components
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
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)
- Properties of SIGRADUR
- Mean thickness = 2.1 mm
- Radiation length X0 = 28 cm
Scattering in the mirror reflective and protection layer
- Properties of Aluminum (reflective layer)
- Thickness = 20 ug/cm**2
- Density = 2.7 g/cm**3
- Radiation length X0 = 24.01 g/cm**2 = 8.9 cm
- Properties of MgF2 (protection layer)
- Thickness = 11 ug/cm**2
- Density = 3.0 g/cm**3
- Radiation length X0 = 29.32 g/cm**2 = 9.77 cm
Scattering in the carbon shell (CFK)
- Properties of CFK
- Thickness = 0.4 mm
- Radiation length X0 = 28 cm
Elliptic (circular) vs rectangular matching cut
Area difference between these two cuts is:
- Rectangular cut: (2*D_phi)*(2*D_theta) = 4*D_theta*D_phi
- Elliptic cut: pi * D_theta * D_phi
- Difference = (4 - pi)/4 = 22%
Conversion / Signal from PLUTO simulation
I have compared the 1D distribution for (theta_rich - theta_RK) (in phi it
looks similar) for electrons coming from conversion and the electrons
coming from all other sources. the conversion signal I have chosen according
to the following condition: "pid.genInfo1==7001 || pid.genInfo1==17001 ||
pid.genInfo1==52001", the "real" signal is negation of the previous
condition. the determination of the mean and sigma of the distribution was
done with the "standard" 2-gaussian fit for momentum bins (0,150>; (150,350>
and (350,1000>
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
==================================================
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
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