Spin precession note T-BMT equation, Spin motion study (Analytic and GEANT4) g-2 motion in unique M-field in J-PARC g-2 case, EDM motion for J-PARC g-2 case, Spin-dependent muon decay revisit Expected positron time spectra for EDM case 2010/04/14 Hiromi Iinuma 1 Spin equation (T-BMT equation + EDM) Our case: 2 Spin equation (T-BMT equation + EDM) Our case: 3 Spin motion study 4 G-2 motion in M-field (1) nsec 5 G-2 motion in M-field (2) Precession : nsec sec Sx component in the rest frame 6 S=(Sx, Sy, Sz) =(momvx, momvy, momvz) S =cos( a t) nsec sec GEANT4 check: g-2 motion 7 JPARC EDM (Analytically-approach) s x and s y components are the sum of T-BMT and EDM effects Initially s x =s y =0 later s x 0, s y 0 J-PARC Initially s z =0 later s z 0 E821 8 GEANT4 Anal. Check! 9 We confirmed s z is correct. Then I have s z / t =s z (t 1 )-s z (t 2 )/(t 1 -t 2 ) by GEANT4. Extract from GEANT4 calculation Left-hand side Right-hand side Left-hand side (1-s z 2 ) Check! Although I can not figure out sx and sy by analytically, but I check their scalar product is correct! 10 S Precession : Amplitude does not growth as a function of time. s x, s y J-PARC EDM (GEANT4) (1-Sz 2 ) Sx component in the rest frame 11 S /|s|| | S /|s|| | comparison between G-2 and EDM X= X=1 12 S /|s|| | comparison S /|s|| | comparison PSI vs. JPARC 13 Spin-dependent muon decay revisit & Expected positron time spectra for EDM case 14 ++ e + momentum spin cos S * g-2 EDM 15 Kinematic in the rest frame th = Expected time spectrum (1) 0.65 0.75 =8.5E-4 17 Expected time spectrum (2) M, + 18 Expected time spectrum (3) 0.65 /2 2 3E-6=6E-6 19 PSI EDM (try spin frozen by GEANT4) 20 Cyclotron motion Try Spin-frozen (PSI) 21 I use G4EqEMFieldWithSpin of Geant4.9.2.p02 (bug fixed) Apply B=(0, 0, Bz), Bz =1 Tesla, R=0.42 m =1.55 (125MeV/c) and radial electric field |E R |= E+6 volt/m nsec G-2 precession should be frozen! Parameters from hep-ph/ v1 Spin motion expectation: I will explain how to get spin and momentum vector information in the next page. Yes, frozen (PSI) 22 S=(Sx, Sy, Sz) p/|p|=(momvx, momvy, momvz) S =cos( a t) G-2 precession is completely canceled:Spin-Frozen!! I set initial (t=0) values: s/|s|=(0,1,0) /| |=(0,1,0) Precession : PSI EDM 23 GEANT4 check: PSI EDM S /|s|| | szsz E R is exact value. But s 0, because 0 !! Sz 0 and s 0 How to distinguish between 0 and E R error? 24 If + stays in storage ring forever? PSI-EDM 25 In case of E R =E R 0.995, =0 26 s z =0 No Frozen!! Sz=0, but s 0 S 0.5% level control Precession : Backup 27 But, I got wrong statement Sx, Sy, Sz (Sx0, Sy0, Sz0)=(0,0,1) I tried very large value to check behavior and have wrong expectation. wrong? Envelope is sin function 28