DV RunGroupC Moller
Simulating the Moller scattering background for EG1
Step 1
Determine the Moller background using an LH2 target to check the physics in GEANT4
Incident electron energy varies from 1-11 GeV.
LH2 target is a cylinder with a 1.5 cm diameter and 1 cm thickness.
(Following dimensions listed on page 8 of File:PHY02-33.pdf)
Numbers Moller electrons per incident electron.
While 2nd and 3rd generations are created, only 2 2nd generation daughter particles are created for 1E6 incident particles. All knock on electrons are not counted.
Momentum distributions.
In the collision of two particles of mass m_1 and m_2, the total energy in the center of mass frame can be written
where θ is the angle between the particles. In the frame where one particle (m2) is at rest
The velocity of the center of mass in the lab frame is
where plab≡p1 lab and
This gives the momenta of the particles in the center of mass to have equal magnitude, but opposite directions
For an incoming electron with momentum of 11GeV, we should find the momentum in the center of mass to be around 50 MeV which is not confirmed in the the plots.
Sample output from GEANT4 simulation:
KEi | Pxi | Pyi | Pzi | xi | yi | zi | KEf | Pxf | Pyf | Pzf | xf | yf | zf | KEm | Pxm | Pym | Pzm | xm | ym | zm |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
11000 | 0 | 0 | 11000.5 | 0 | 0 | -510 | 10999.1 | 0.433025 | -0.858867 | 10999.6 | 0 | 0 | -509.276 | 0.905324 | -0.433025 | 0.858867 | 0.905366 | 0 | 0 | -509.276 |
Running a GEANT simulation just to put this set into a .dat file, then using the .dat file through the Moller_OG.C file in ROOT, we find in the Lab Frame:
Fnl4Mom.P 10999.599651 Fnl4Mom.E 10999.599621 Mol4Mom.P 1.320928 Mol4Mom.E 1.039583 Fnl4Mom.Theta(degrees) 0.005013 Fnl4Mom.Theta(radians) 0.000087 Mol4Mom.Theta(degrees) 46.756514 Mol4Mom.Theta(radians) 0.815641
And we find in the Center of Mass Frame:
Fnl4Mom.P 27.183827 Fnl4Mom.E 27.171610 Mol4Mom.P 27.183827 Mol4Mom.E 27.171609 Fnl4Mom.Theta(degrees) 2.028767 Fnl4Mom.Theta(radians) 0.035391 Mol4Mom.Theta(degrees) 178.062532 Mol4Mom.Theta(radians) 3.106202
THE MOMENTUM IS HIGHER THAN THE ENERGY
We had been using the relationship that the Energy was approximately equal to the (pz^2+m^2)^.5, the real relationship should have been EKE+m=E. Once that change was made:
Fnl4Mom.P 10999.599651 Fnl4Mom.E 10999.610609 Mol4Mom.P 1.320928 Mol4Mom.E 1.416324 Fnl4Mom.Theta(degrees) 0.005013 Fnl4Mom.Theta(radians) 0.000087 Mol4Mom.Theta(degrees) 46.756514 Mol4Mom.Theta(radians) 0.815641
Fnl4Mom.P 52.455386 Fnl4Mom.E 54.704969 Mol4Mom.P 52.455386 Mol4Mom.E 52.457875 Fnl4Mom.Theta(degrees) 1.051202 Fnl4Mom.Theta(radians) 0.018338 Mol4Mom.Theta(degrees) 179.040096 Mol4Mom.Theta(radians) 3.123255
Rerunning the simulation, after changing the molar mass of LH2 to 2.02g/mole, for 1e7 electrons at 11GeV.
File:FnlMomCM.jpgFile:MolMomCM.jpg
File:FnlTheta.jpgFile:MolTheta.jpg
File:FnlThetaCM.jpgFile:MolThetaCM.jpg
Comparing experimental vs. theoretical for Møller differential cross section 11GeV
Using the equation from Halzen and Martin (p121) to approximate Moller scattering
where
and
Converting the number of electrons to nano-barns,
where ρtarget is the density of the target material, ltarget is the length of the target, and iscattered is the
Step 2
Replace the LH2 target with an NH3 target and compare with LH2 target.
Step 3
Determine impact of Solenoid magnet on Moller events
Papers used
A polarized target for the CLAS detectorFile:PHY02-33.pdf
An investigation of the spin structure of the proton in deep inelastic scattering of polarized muons on polarized protons File:1819.pdf