1. Exercise to treat spin-dependent decays I.Goal: – Study the relationship between momentum p e accuracy/precision and  a, Analyzing power. – Estimate the required performance of the detector. 1 II.Exercise to check basic kinetics: 1.Energy and momentum conservation, 2.2D event yield distribution as functions of y and  cm S y = p cm e /p max  cm S is an angle between spin-axis and momentum direction of decay-e + at the center-of-mass system. (  see next page) III.Check wiggle plots: “usual” wiggle plot, “Beam-loss free” wiggle plot. Today’s contents

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

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

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

7. II.Check basic kinetic values from GEANT4 7

8. Probing Spin-dependent Decay Info. I.To be more simple, I set 100% ! II.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. III.Check momentum/energy conservation. Within few eV at   =1, within few keV at   =3.  why? IV.Apply Lorentz transformation to get values in the center-of-mass system. V.Cook values as I want!! 8

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

10. y = p cm e /p max  is an angle between spin-axis and momentum direction of decay-e + at the center-of-mass system. 10

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

13. 4 free parameters Covariant matrix is OK. 9.5  10 5 , E> 200 MeV 1.3  10 5 e + 13

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

15. LEFT RIGHT  No worry about  -beam loss!  But, need to handle left-right detector asymmetry. 9.5  10 5 , 1.9  10 5 e + y> 0.6, LEFT: 1  cos   0.7 RIGHT:  1  cos  1   0.7 15

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

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

18. 18 How many positrons we need for EDM ? Value [e  cm] statisticscomment Exp. results ( 3.7  3.4 )  10  19 (  0.04  1.6  0.17)  10  19 ( 0.1  0.2  1.07 )  10  19 11.4  10 6 e +, e  9.4  10 6 e + 975  10 6 e  CERN (1974~76) E821 (1999, 2000, Trace back detector, Fig.7)* E821 （ 2001, PSD1-5, Tbl. IV)* Predic -tion (1.4  1.5 )  10  25 Mass scale of lepton EDMs > 10 -23 Extended SM model Our goal 10  22 level 10  24 level ~10 13 @  magic =29.3 ~10 17 @  magic =29.3 ~ 3  10 14 @  =3 ~ 3  10 18 @  =3 EDM sensitivity: “Improved Limit on the Muon Electric Dipole Moment “ 2EAPS/123-QCD

19. y vs. cos  y cos  19

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