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Exercise to treat spin-dependent decays

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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.

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 .

- Expected 2D event yield distribution
- as functions of y and cmS

Monte Carlo

Monte Carlo

Condition:

GEANT4

B

3 T

P=300MeV/c ,=3,

Tc =7.4nsec, R=333mm,

Ta=2/a=2.2sec.

Positron energies

28 ~191 MeV

GEANT4

8.6MeV positron

B＝3T

50.4MeV positron

102MeV positron

Check basic kinetic values from GEANT4

- 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!!

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.

Monte Carlo

GEANT4

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.

Measure!

No exponential term!

LEFT RIGHT

- No worry about-beam loss!
- But, need to handle left-right detector asymmetry.

9.5 105 , 1.9105 e+

y> 0.6 , LEFT: 1 cos 0.7

RIGHT:1 cos 1 0.7

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

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.)

“Improved Limit on the Muon Electric Dipole Moment “ 2EAPS/123-QCD

EDM sensitivity:

cos

y

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