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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:

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Exercise to treat spin-dependent decays

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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.

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=2.2sec.

Positron energies

28 ~191 MeV

GEANT4

8.6MeV positron

B＝3T

50.4MeV positron

102MeV positron

Check basic kinetic values from GEANT4

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!!

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

“Usual” wiggle plot and “Beam-loss free” wiggle plot

4 free parameters

Covariant matrix is OK.

9.5 105 , E> 200 MeV 1.3105e+

“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

• 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

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

Next things….

• 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.)

How many positrons we need for EDM ?

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

EDM sensitivity:

y vs. cos

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