1. MEG 実験におけるミュー粒子放射崩壊の 測定と利用 日本物理学会第６７回年次大会 24/Mar./2012 @関西学院大学 ICEPP, the University of Tokyo 内山 雄祐

2. 2 JPS 67 th Annual, 24/Mar/2012 Introduction Yusuke UCHIYAMA, the University of Tokyo μ e μ e ＋

3. 3 JPS 67 th Annual, 24/Mar/2012 Yusuke UCHIYAMA, the University of Tokyo x z y x θ φ 2009 2009+2010 2008 MEG limit MEG sensitivity(expected) B < 2.4×10 -12 at rest MEG experiment (PRL 107,171801(2011)) RMD 3×10 7  + /s giving stringent constraint on new physics EeEe EE tete cos  e 

4. 4 JPS 67 th Annual, 24/Mar/2012 SM process RMD is explicitly & accurately calculated in electroweak theory. Differential BR of RMD in V-A structure can be written Polarization of decaying muon in MEG target is preserved  Measured 0.89±0.04 with Michel spectrum. Theory Yusuke UCHIYAMA, the University of Tokyo Polarization of muon Y.Kuno and Y.Okada, Rev. Mod. Phys. 73, 151 (2001) P=0.9 e+e+  ee ee x=2E e /M  y=2E  /M  d=1-  cos  e  E e >45 MeV E  >40 MeV

5. 5 JPS 67 th Annual, 24/Mar/2012 MEG setup limits the phase space able to be measured. MEG acceptance & efficiency Yusuke UCHIYAMA, the University of Tokyo MC (smeared) ○ Lower-thre trigger ● Normal-thre trigger Michel(theo)⊗response Response ●Data Best-fit

6. 6 JPS 67 th Annual, 24/Mar/2012 Direction-match in trigger also deforms RMD spectrum  Angle efficiency depends on E e  Calculate efficiency table based on MC, and check with measured distribution of accidental background. Yusuke UCHIYAMA, the University of Tokyo

7. 7 JPS 67 th Annual, 24/Mar/2012 Counting RMD events Yusuke UCHIYAMA, the University of Tokyo Accidental BG RMD peak

8. 8 JPS 67 th Annual, 24/Mar/2012 2009+2010 BG are subtracted Projected Distributions Yusuke UCHIYAMA, the University of Tokyo P=0.89 P=0 Normalized to Michel positrons Gray bands show systematic (diagonal elements)

9. 9 JPS 67 th Annual, 24/Mar/2012 measure BR of RMD for possible largest window: E e >45, E  >40 MeV Fit to time distribution 45 < E e < 53 MeV 40 < E  < 53 MeV |  e  | < 0.3 rad |  e  | < 0.3 rad  N obs = 12920±299 event Normalization to Michel  in pre-scaled unbiased trigger BR measurement Yusuke UCHIYAMA, the University of Tokyo uncertainties

10. 10 JPS 67 th Annual, 24/Mar/2012 Ratio to theory (SM) Comparisons Yusuke UCHIYAMA, the University of Tokyo PDG Preliminary PDG BR exp /BR theo = 0.98 ± 0.09 likelihood fit in  →e  search (spectrum assumed) No definition of ‘total’ BR (infrared divergent) BR in limited phase space

11. 11 JPS 67 th Annual, 24/Mar/2012 Compare spectrum shape with theory Extract {polarization, normalization} from RMD Fit distribution in multi dimensions  binned fit  (E e, E ,  e  ) = 2x2x6, total 24 bins bins in  e  for polarization measurement To incorporate correlations of systematic uncertainties among bins, covariance (error) matrix should be used Chi-square definition Spectrum analysis Yusuke UCHIYAMA, the University of Tokyo 45 4853 40 45 53 EE EeEe (  : normalization scale parameter)

12. 12 JPS 67 th Annual, 24/Mar/2012 no constraint on pol nor norm Fit result Yusuke UCHIYAMA, the University of Tokyo 45 48 53 40 45 53 EE EeEe Chi2 / NDF = 11.9 / 22 = 0.541 Pol 0.70 ± 0.16 Norm 0.95 ± 0.044 (a) (b) (c) (d) □predicted □best fit measured value with Michel Pol 0.89 ± 0.04 Norm 1 ± 0.04 1,1.64,2 

13. 13 JPS 67 th Annual, 24/Mar/2012 Discussions Yusuke UCHIYAMA, the University of Tokyo

14. 14 JPS 67 th Annual, 24/Mar/2012 In general, RMD rate can be written as ( Fronsdal&Ueberall, Phys.Rev.113-2(1959)654), RMD rate and parameters Yusuke UCHIYAMA, the University of Tokyo V-A ¾ ¾ 1 1 0 0

15. 15 JPS 67 th Annual, 24/Mar/2012 Current status Yusuke UCHIYAMA, the University of Tokyo previous μ→eγ experiment @ SIN (PSI) No measurement of  parameter

16. 16 JPS 67 th Annual, 24/Mar/2012 Analyzed RMD from polarized muon decay in MEG data Measure BR for MEG acceptance range  BR (Ee>45,E  >40MeV) = (6.03±0.14±0.53)×10 -8  BR exp /BR theo = 0.98 ± 0.09  Good agreement with SM Spectrum analysis (fit)  Good agreement with SM (  2/NDF = 11.9/22)  Extract polarization and normalization RMD only : Polarization : 0.70 ± 0.16 Normalziation factor: 0.95 ± 0.043 (relative to one from Michel) Consistent result with prediction  less powerfull for polarization measurement  Normalization uncertainty goes down to 4% Possibility of measuring Michel parameters. Next step. Conclusion Yusuke UCHIYAMA, the University of Tokyo

17. 17 JPS 67 th Annual, 24/Mar/2012 surface muons are fully polarized depolarization effects  beam angular acceptance : 2.5%  multiple scattering in production target : <0.5%  contribution from ‘cloud muon’: 4.5%  E-field in beamline (separator): 0.7%  In plastic target (moderation, muonium formation): 3% Polarization Yusuke UCHIYAMA, the University of Tokyo MEG magnet center 1.3 T Polyethtlene A.Buhler et al. Nouvo Cimento 39, 824 (1965) A.Buhler et al. Nouvo Cimento 39, 812 (1965)

18. 18 JPS 67 th Annual, 24/Mar/2012 Polarization measurement Yusuke UCHIYAMA, the University of Tokyo ● Data ● MC P = 0 P = 1 Measure polarization from angular distribution of Michel positrons Two-dimensional fit to E e vs  e distribution gives P = 0.90±0.04

19. 19 JPS 67 th Annual, 24/Mar/2012 papers  “Radiative corrections to background of m→eg decay”, A.B.Arbuzov et al., Phys. Lett. B 432, 421-426 (1998)  “One-loop corrections to radiative muon decay”, A.B.Arbuzov et al., Phys. Lett. B 597, 285-290 (2004) Now under evaluation for MEG case Radiative correction to RMD Yusuke UCHIYAMA, the University of Tokyo real (soft or hard) photon emission +

20. 20 JPS 67 th Annual, 24/Mar/2012 Define chisquare Chisquare Yusuke UCHIYAMA, the University of Tokyo (  : normalization scale parameter)

21. 21 JPS 67 th Annual, 24/Mar/2012 correlation matrix Error matrix Yusuke UCHIYAMA, the University of Tokyo

22. 22 JPS 67 th Annual, 24/Mar/2012 For the energy range,  e  < 0.048 rad is allowed. Yusuke UCHIYAMA, the University of Tokyo Not allowed by momentum conservation 83%

23. 23 JPS 67 th Annual, 24/Mar/2012 Constrain pol & norm Fit result 2 Yusuke UCHIYAMA, the University of Tokyo Pol -0.88+- 0.04 Norm 0.96 +- 0.038 Chi2 / NDF = 13.6 / 22 = 0.617 □predicted □best fit

24. 24 JPS 67 th Annual, 24/Mar/2012 From previous studies Yusuke UCHIYAMA, the University of Tokyo W.Eichenberger et al. Nucl. Phys A412 (1984) 523

25. 25 JPS 67 th Annual, 24/Mar/2012 Michel parameters in PDG Yusuke UCHIYAMA, the University of Tokyo Normal Michel parameters are measured very precisely by dedicated experiments. No chance to improve with MEG data