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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
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.
slide2

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 .

slide3

Expected 2D event yield distribution

  • as functions of y and cmS

Monte Carlo

slide5

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

slide6

GEANT4

8.6MeV positron

B=3T

50.4MeV positron

102MeV positron

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!!
slide9

GEANT4

X axis is always -momentum direction.

slide10

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.

slide12

Wiggle plots made by GEANT4

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

slide13

4 free parameters

Covariant matrix is OK.

9.5 105 , E> 200 MeV 1.3105e+

slide14

“Beam loss free” wiggle plot by knowing

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

Measure!

No exponential term!

slide15

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:

slide20

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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