Exercise to treat spin-dependent decays

1. Exercise to treat spin-dependent decays Tool: GEANT4 • Goal: • Study the relationship between momentum pe accuracy/precision and a, Analyzing power <A>. • Estimate the required performance of the detector. Today’s contents • Exercise to check basic kinetics: • Energy and momentum conservation, • 2D event yield distribution as functions of y and cmS • y = pcme/pmax • cmS is an angle between spin-axis and momentum direction of decay-e+ at the center-of-mass system. ( see next page) • Check wiggle plots: • “usual” wiggle plot, • “Beam-loss free” wiggle plot.

2. Center-of-Mass system Magnetic field Z Y Spin-direction Direction of decay-positron X, Momentum Angle between spin-axis and momentum direction of decay-e+ at the center-of-mass system: Lorentz boost  We measure .

3. Expected 2D event yield distribution • as functions of y and cmS Monte Carlo

4. Monte Carlo

5. Condition: GEANT4 B 3 T P=300MeV/c ,=3, Tc =7.4nsec, R=333mm, Ta=2/a=2.2sec. Positron energies 28 ~191 MeV

6. GEANT4 8.6MeV positron B＝3T 50.4MeV positron 102MeV positron

7. Check basic kinetic values from GEANT4

8. Probing Spin-dependent Decay Info. • To be more simple, I set 100% ! • Probe “decay process” information in the lab frame directly. (I use “UserSteppingAction”.) • Spin vector, momentum of  at previous step of decay process. • Momentum and energies of daughters. • Check momentum/energy conservation. • Within few eV at =1, within few keV at =3.  why? • Apply Lorentz transformation to get values in the center-of-mass system. • Cook values as I want!!

9. GEANT4 X axis is always -momentum direction.

10. 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.

11. Monte Carlo GEANT4

12. Wiggle plots made by GEANT4 “Usual” wiggle plot and “Beam-loss free” wiggle plot

13. 4 free parameters Covariant matrix is OK. 9.5 105 , E> 200 MeV 1.3105e+

14. “Beam loss free” wiggle plot by knowing An angle between + and e+ momentum direction in the center-of-mass system. Measure! No exponential term!

15. LEFT RIGHT • No worry about-beam loss! • But, need to handle left-right detector asymmetry. 9.5 105 , 1.9105 e+ y> 0.6 , LEFT: 1  cos   0.7 RIGHT:1 cos  1  0.7

16. A big advantage to measure Lab-frame ”Effective Analyzing Power”is smeared by cos cm S Center-of-mass frame If we can measure cm Sevent-by-event, ”Effective Analyzing Power” is NOT smeared by cos cm S! We have bigger effective Analyzing Power

17. Next things…. Now, I am ready to think about detector performance. • Study the relationship between measured momentum accuracy/precision and a, Analyzing power <A>. • Estimate the required performance of the detector. I, also, will play with G4-beamline to think about -beam line. (Need a time to learn it, though.)

18. How many positrons we need for EDM ? “Improved Limit on the Muon Electric Dipole Moment “ 2EAPS/123-QCD EDM sensitivity:

19. y vs. cos cos y

20. Relationship between a and  ミュービーム強度はによらず、一定だとし、(Ntotal=const.) I checked with Toy Monte Carlo