Exercise to treat spin-dependent decays . Tool: GEANT4 . Goal: Study the relationship between momentum p e accuracy/precision and a , Analyzing power <A> . Estimate the required performance of the detector . Today’s contents. Exercise to check basic kinetics:
Direction of decay-positron
Angle between spin-axis and momentum direction of decay-e+ at the center-of-mass system:
We measure .
Tc =7.4nsec, R=333mm,
28 ~191 MeV
Check basic kinetic values from GEANT4
X axis is always -momentum direction.
Monte Carlo vs. GEANT4
y = pcme/pmax
is an angle between spin-axis and momentum direction of decay-e+ at the center-of-mass system.
Wiggle plots made by GEANT4
“Usual” wiggle plot and “Beam-loss free” wiggle plot
4 free parameters
Covariant matrix is OK.
9.5 105 , E> 200 MeV 1.3105e+
“Beam loss free” wiggle plot by knowing
An angle between + and e+ momentum direction in the center-of-mass system.
No exponential term!
9.5 105 , 1.9105 e+
y> 0.6 , LEFT: 1 cos 0.7
RIGHT:1 cos 1 0.7
”Effective Analyzing Power”is smeared by cos cm S
If we can measure cm Sevent-by-event, ”Effective Analyzing Power” is NOT smeared by cos cm S!
We have bigger effective Analyzing Power
Now, I am ready to think about detector performance.
I, also, will play with G4-beamline to think about -beam line. (Need a time to learn it, though.)
“Improved Limit on the Muon Electric Dipole Moment “ 2EAPS/123-QCD
Relationship between a and
I checked with Toy Monte Carlo