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 and angular distributions. 11GeV

In the collision of two particles of mass m₁ and m₂, the total energy in the center of mass frame can be written

E_cm=[(E₁+E₂)²-(p₁+p₂)²]^1/2 E_cm=[m₁²+m₂²+2E₁E₂(1-β₁β₂cosθ)]^1/2

where θ is the angle between the particles. In the frame where one particle (m₂) is at rest

E_cm=(m₁²+m₂²+2E_{1 lab}m₂)^1/2

The velocity of the center of mass in the lab frame is

β_cm=p_lab/(E_{1 lab}+m₂),

where p_lab≡p_{1 lab} and

γ_cm(E_{1 lab}+m₂)/E_cm

This gives the momenta of the particles in the center of mass to have equal magnitude, but opposite directions

p_cm=p_labm₂/E_cm

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 confirmed in the the plots.

Comparing experimental vs. theoretical for Møller differential cross section 11GeV

Using the equation from Halzen and Martin (p121) to approximate Moller scattering

[math]\frac{d\sigma}{d\Omega}=\frac{m^2 \alpha^2}{16 p^2}\left(\frac{1}{\sin^4 \frac{\theta}{2}}+\frac{1}{\cos^4 \frac{\theta}{2}}-\frac{1}{\sin^2 \frac{\theta}{2}\cos^2 \frac{\theta}{2}}\right)[/math]

where [math]\alpha = \frac{e^2}{4\pi}[/math]

and [math]e^2 = 1.43299764 MeV - fm[/math]

Converting the number of electrons to nano-barns, \begin{center} [math]L=\frac{i_{scattered}}{\sigma} \approx i_{scattered}\times \rho_{target}\times l_{target}[/math]

[math]L=\frac{70.85 kg}{1 m^3}\times \frac{1 mole}{2.02 g} \times \frac{1000g}{1 kg} \times \frac{6\times10^{23} atoms}{1 mole} \times \frac{1cm}{100 cm} \times \frac{1 m}{ } \times \frac{10^{-23} m^2}{barn} =2.10\times 10^{-2} barns[/math]

[math]\frac{1}{L \times 10^7}=4.75\times 10^{-6} barns[/math] \end{center}

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

EG12