Exercise to treat spin dependent decays
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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

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.


Exercise to treat spin dependent decays

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 .


Exercise to treat spin dependent decays

  • Expected 2D event yield distribution

  • as functions of y and cmS

Monte Carlo


Exercise to treat spin dependent decays

Monte Carlo


Exercise to treat spin dependent decays

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


Exercise to treat spin dependent decays

GEANT4

8.6MeV positron

B=3T

50.4MeV positron

102MeV positron


Exercise to treat spin dependent decays

Check basic kinetic values from GEANT4


Probing spin dependent decay i nfo

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!!


Exercise to treat spin dependent decays

GEANT4

X axis is always -momentum direction.


Exercise to treat spin dependent decays

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.


Exercise to treat spin dependent decays

Monte Carlo

GEANT4


Exercise to treat spin dependent decays

Wiggle plots made by GEANT4

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


Exercise to treat spin dependent decays

4 free parameters

Covariant matrix is OK.

9.5 105 , E> 200 MeV 1.3105e+


Exercise to treat spin dependent decays

“Beam loss free” wiggle plot by knowing

An angle between + and e+ momentum direction in the center-of-mass system.

Measure!

No exponential term!


Exercise to treat spin dependent decays

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


A big advantage to measure

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


Next things

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.)


How many positrons we need for edm

How many positrons we need for EDM ?

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

EDM sensitivity:


Y vs c os

y vs. cos

cos

y


Exercise to treat spin dependent decays

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


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