DV RunGroupC Moller

need to insert moller shielding into card after moller LUND file is created. (see clas12/beamline)

Simulating the Moller scattering background for EG12

GEANT4 Simulation of Moller Events

Simulation Setup

Use GEANT4 via GEMC to estimate the Moller background for electron scattering experiments in JLab's Hall B. The first step towards this goal is to use GEANT4 without the GEMC infrastructure to create event (LUND) files that will be used as input events for GEMC.

Benchmark GEANT4's Moller scattering prediction with the theoretical cross section using LH2

Comparison of simulation vs. the theoretical Møller differential cross section using 11 GeV electrons impinging LH2

Converting the number of scattered electrons per scattering angle theta to a differential cross-section in barns.

Figure 5c: The experimental and theoretical Moller electron differential cross-section for an incident 11 GeV(Lab) electron in the Center of Mass frame of reference.

Change to a NH3 Target

Replacing the LH2 target with an NH3 target

Comparison of simulation vs. the theoretical Møller differential cross section using 11 GeV electrons impinging NH3

Converting the number of scattered electrons per scattering angle theta to a differential cross-section in barns.

Figure 5c: The theoretical and simulated Moller electron differential cross-section for an incident 11 GeV(Lab) electron in the Center of Mass frame of reference for NH3 target.

Differential Cross-Section Offset

Figure 5c: The theoretical and simulated Moller electron differential cross-section for an incident 11 GeV(Lab) electron in the Center of Mass frame of reference for NH3 target. The theoretical differential cross-section has been adjusted to account for the 10 electrons within NH3.

ROOT Macro to read LUND files and make plots

Run the above theta and E distribution of Mollers through GEMC with and without Solenoid on.  Determine the Theta and E range of Mollers that enter the detector.

Scanning from 2MeV to 5500MeV, and 0 to 36 degrees in Theta.

For Solenoid on with 5T:

<gcard>

        <detector name="../../../../../clas12/fc/forwardCarriage" factory="TEXT" variation="original"/>
        <detector name="../../../../../clas12/dc/dc"            factory="TEXT" variation="original"/>
        <detector name="../../../../../clas12/ec/ec"            factory="TEXT" variation="original"/>
        <detector name="../../../../../clas12/ctof/ctof"            factory="TEXT" variation="original"/>
        <detector name="../../../../../clas12/ftof/ftof"            factory="TEXT" variation="original"/>
        <detector name="../../../../../clas12/htcc/htcc"            factory="TEXT" variation="original"/>
        <detector name="../../../../../clas12/pcal/pcal"            factory="TEXT" variation="original"/>
        <option name="BEAM_P"   value="e-, 2.800*GeV, 18.0*deg, 10*deg"/>
        <option name="SPREAD_P" value="2.798*GeV, 18*deg, 180*deg"/>
        <option name="SCALE_FIELD" value="clas12-torus-big, -1.0"/>
        <option name="HALL_FIELD"  value="clas12-solenoid"/>
        <option name="SCALE_FIELD" value="clas12-solenoid, 1.0"/>
        <option name="OUTPUT" value="evio,eg12.ev"/>

</gcard>

Using the standard commands for gemc

gemc -USE_GUI=0 -N=1000 eg12_sol.gcard
~/src/CLAS/coatjava-1.0/bin/clas12-reconstruction -i eg12.ev -config DCHB::torus=-1.0 -config DCHB::solenoid=1.0 -config DCTB::kalman=true -o eg12_rec.ev -s DCHB:DCTB:EC:FTOF:EB
~/src/CLAS/coatjava-1.0/bin/run-groovy Analysis.groovy eg12_rec.0.evio

Checking for a reconstructed particle that undergoes a phi shift where the 1st column is energy and the 2nd the scattering angle theta:

For Energy:
awk 'NR == 1 {line =$0; min =$2} NR >1 && $2 < min {line =$0; min = $2} END{print line}' Energy_Phi_Shift.dat
289     0.6624017631112946      33.37507824033966       -179.63657653407975     0.7254709       29.696417       -177.79057      473.36051689004984      11.978802748439216      -129.55774724876173


awk 'NR == 1 {line =$0; max =$2} NR >1 && $2 > max {line =$0; max = $2} END{print line}' Energy_Phi_Shift.dat
978     5.584765946130235       24.90893565820338       -170.69784116534063     5.593401        24.90894        -170.65994      472.16552666546283      23.31807917059094       -165.11125601370114

For Theta:
awk 'NR == 1 {line =$0; min =$3} NR >1 && $3 < min {line =$0; min = $3} END{print line}' Energy_Phi_Shift.dat
12      4.83485521395583        10.577021312967325      -50.86708775351051      4.8205996       10.617784       -50.895683      491.627055439108        5.9032309421001985      -43.82964507576243

awk 'NR == 1 {line =$0; max =$3} NR >1 && $3 > max {line =$0; max = $3} END{print line}' Energy_Phi_Shift.dat
187     1.3382869250001856      35.63598792463312       29.887530073265214      1.3481133       35.449417       30.009071       472.455052447561        19.034043420497742      55.20328358414997

Similarly for 0T:

For Energy:
awk 'NR == 1 {line =$0; min =$2} NR >1 && $2 < min {line =$0; min = $2} END{print line}' Energy_Phi_Shift.dat
148     0.36418038435234207     33.68296595663359       -175.89942431595827     0.35383263      51.743824       -39.45801       469.5694572319308       24.353383233947522      -176.27025218702502


awk 'NR == 1 {line =$0; max =$2} NR >1 && $2 > max {line =$0; max = $2} END{print line}' Energy_Phi_Shift.dat
818     5.5278794590742235      12.937136966282836      -43.35663621477178      5.539351        12.95216        -49.09295       484.8800252169308       8.27731670021694        -43.245753766203364

For Theta:
awk 'NR == 1 {line =$0; min =$3} NR >1 && $3 < min {line =$0; min = $3} END{print line}' Energy_Phi_Shift.dat
559     4.909449160222199       9.918634647646794       0.06548256930681198     4.914272        9.938521        -5.861595       492.1448533455858       7.501204563534799       -0.006721611135017764

awk 'NR == 1 {line =$0; max =$3} NR >1 && $3 > max {line =$0; max = $3} END{print line}' Energy_Phi_Shift.dat
326     1.272966353429713       35.731680814303196      85.3173707349696        1.2830343       38.27654        58.368687       483.4835073848272       3.950855595379657       83.87603767806992

Cover Full Solid Angle of Detector

Using Isotropic spread in Theta and Energy for Set Angle Phi

Since the Differential Cross-Section for Moller scattering is well known in the center of mass frame of reference, a conversion to the detector's lab frame of reference will need to occur. To ensure that the GEMC detector is fed a Moller LUND file for the differential cross section, the center of mass frame LUND information must be converted to the lab frame equivalent. Using the expression for the differntial cross-section:

[math]\frac{d\sigma}{d\Omega}=\frac{ \alpha^2 }{4E^2}\frac{ (3+cos^2\theta)^2}{sin^4\theta}[/math]

where,

[math]\alpha ^2=5.3279\times 10^{-5}[/math]

[math]E\approx 53 MeV[/math]

A beam of electrons with a constant energy impinging on a stationary electron in the lab frame can be converted to the center of mass frame energies which by definition must be equal. Since the Energy in the CM frame is constant in so long as the incoming electron energy is constant, we should be able to cycle through only the scattering angle theta to obtain the differential cross-section.

For the GEMC detector to simulate a given distribution, a LUND file must be created. LUND files can pass information about position and momentum, but not angle, in the lab frame. Assuming a constant position at the vertex, this implies that we will need to cycle through the momentum components for the scattered and Moller electrons in the CM frame to vary angle theta in the lab frame. The CM frame also implies that the total momentum for the scattered and Moller electron be equal but opposite.

From the definition of the differential cross-section:

[math]\frac{d\sigma}{d\Omega} =\frac{dN}{\mathcal L d\Omega}=\frac{dN}{\Phi \rho \ell d\Omega}[/math]

where

[math]\Phi \equiv [/math]flux, or incoming particles per second

[math]\rho \equiv [/math]target density

[math]\ell \equiv [/math]length of target

[math]dN=\frac{dR}{dt}=\mathcal L \times \sigma_p[/math]

Detector Occupancy

clas12->Draw("Detector.wire:Detector.layer>>(7,1,7,120,0,120)","Detector.superlayer<3","colz")

Papers used

[1]Farrukh Azfar's Derivation of Moller Scattering

File:FarrukAzfarMollerScatter.pdf

A polarized target for the CLAS detector

File: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

QED Radiative Corrections to Low-Energy Moller and Bhabha Scattering

http://arxiv.org/abs/1602.07609

EG12