1. Updated sensitivity estimate Suguru Shimizu Osaka University Sep. 1, 2007 JPARC TREK Collaboration meeting at Saskatchewan (1)Statistical error (2)Systematic error

2. FOM ∝ A T √ N was calculated by this formula (see FIFC and PAC reports). Analyzing power is α=0.38 (at FOM max.) e + energy measurement is not so important. Just accept high energy e + component. Best e + angle threshold is about 0.4 Analyzing power and FOM 0.92 0.96 e+e+ θ y cosθ beam e + energy (MeV) cosθ e + energy (MeV) cosθ e + energy (MeV) e + angle cut is effective to improve FOM, while e + energy measurement is less important.

3. FOM for  0 angle threshold for the  0 fwd/bwd analysis FOM was determined as a function of cos θ π (see FIFC and PAC reports). =0.68 (at FOM max.) π0π0 θ Beam axis cosθπ Summary of FOM study parameters: e + energy, e + angle,  0 angle A T α  =0.38 =0.68 ΔP T =1.2x10 -4 is obtained with 2.4G K  3 events under the best FOM condition (only pi0 fwd/bwd analysis). PT＝PT＝

4. Systematic error from B field rotation 1mrad. uncertainty of B field  P T = 10 -3   fwd   bwd  P N fwd P N bwd spectrometer Side ViewEnd View P N fwd P N bwd LeftRight LeftRight B π 0 fwd 1+  P N bwd 1   P N fwd/bwd = 1+2  P N ≠1 systematic error Calibration of the polarimeter misalignment using experimental data is very important. B P T fwd P T bwd π 0 fwd 1+  P T bwd 1   P T fwd/bwd = 1+2  P T

5. R comp. Z comp. Asymmetry Rot(  z) misalignment Rot(  r) misalignment Asymmetry Offset is generated from R component of muon spin Systematic error due to misalignments offset Offset is generated from Z component of muon spin R comp. Z comp. beam ideal B

6. R comp. Z comp. Asymmetry Rot(  z) misalignment Rot(  r) misalignment Introduction of  0 (See E06 technical note No.2) T ime integrated e + left/right asymmetry  z sin  0 +  r cos  0 Asymmetry Offset is generated from R component of muon spin Systematic error due to misalignments offset Offset is generated from Z component of muon spin R comp. Z comp. beam ideal B

7. Time integrated asymmetry  0 : the muon spin phase at t=0 In general, e + left/right asymmetry can be described by oscillating terms and constant terms (see E06 technote No.2) K  Black: π 0 fwd Red : π 0 bwd  0 (deg) Oscillation terms can be canceled out by the time integration.  0 is determined event by event.

8. Cancellation mechanism for misalignments Characteristic θ 0 dependence of P T and . K  3 MC, Non-zero P T π 0 fwd π 0 bwd K  3 MC, P T =0, δz=5 deg π 0 fwd π 0 bwd A(  0 )fwd= A(  0 )bwd =  r cos  0  z sin  0 A(  0 )fwd≠ A(  0 )bwd

9. Cancellation mechanism for misalignments Characteristic θ 0 dependence of P T and . K  3 MC, Non-zero P T K  3 MC, P T =0, δz=5 deg A sub A sum A sub A sum =(A fwd +A bwd )/2. = 0 A sub =(A fwd −A bwd )/2. ≠ 0  effect is drastically reduced by A sub. Effect of misalignments are cancelled out by the θ 0 analysis. A sum ≠ 0 A sub = 0

10. Separation of P T and misalignments effect Misalignments are now harmless! A sum =(A fwd +A bwd )/2. A sub =(A fwd −A bwd )/2. Black: no misalignment, non-zero P T Blue: δz=5deg, non-zero P T i/o : No misalignment δ ： δz=δr= 5 deg. A sum A sub i/o δ δ  P T (stat)= 1.3 x 10 -4  P T (syst)< 10 -4 with 2.4G K  3 events

11. Estimation of systematic error due to misalignments Misalignments: Assumption in MC is 5 degree Misalignments: Real case is ~mrad. In case of 5 degree,  P T sys = 10 -4 x 5deg. /mrad ~ 10 -2  P T sys = (2±7)x10  4 was obtained in MC The systematic error is expected to be much smaller than 10 -4. If  P T sys ~10  4 in real case, should be compare

12. Summary of  0 fwd/bwd analysis Sensitivity of  0 fwd/bwd analysis: statistical error 1.2x10 -4 systematic error <1.0x10 -4 in total 1.2x10 -4 To improve the sensitivity (1)  0 left/right analysis (2) Can we use high energy 1  detection with veto counter hit events?

13. P T determination for  0 left/right events  0 left/right analysis P L component are also rotated, together with P T. P L component can be removed by comparing  0 left and right events. Beat pattern due to the finite P T can be observed.

14.  0 left/right analysis A sub =(A left -A right )/2 is calculated before time integration of  decay time. Large P L component can be removed by this subtraction. Black:  0 left Red:  0 right e + asymmetry Large P L component is seen. A sub =(A left -A right )/2 P T component can be extracted. K  3 MC, Non-zero P T

15.  0 left/right analysis A sub =(A left −A right )/2 is fitted with,  cos(  t+  +  )  : fitting parameter  for e + fwd/bwd analysis  /2for e + in/out analysis bwd-fwd bwd+fwd e + asymmetry in  out in+out A sub =(A left −A right )/2. fwd bwd in out Z R e + detection e+e+   black: e + fwd/bwd red:e + in/out dP T = 1.7 x 10 -4 for 2.4G K  3 events