1. 23 Septemberl 2008Tau081         decay at Belle Tau08; Novosibirsk, 22-25, September, 2008 Hisaki Hayashii Nara women’s University

2. 8 April 20082 Introduction Hadronic decays of tau lepton provide clean environment for studying the dynamics of hadronic states.  s (s), a , V us, m s         has the largest Br CVC relation with e + e - →     Plays an important role for the h. v. p. term in the a=(g  -2)/2 muon anomalous magnetic moment. a  =(g  -2)/2 hadron +CVC

3. 8 April 20083 Introduction （ cont. ） Recent data indicate that there is a systematic difference between the 2  system in e + e － reaction and  -decays, even after applying known iso-spin violation correction. Main difference btw and is from 2  mode. not yet published preliminary a  (exp)-a  (th) is ICHEP-2006(M.Davier et al.): A hint to New Physics beyond the SM!

4. 8 April 20084 In this talk, We present update results from Belle experiment based on 5.6x 10 6         decays (72.2/fb). spectral function What should be measured Branching Fraction Mass Spectrum B-factory exp. : final state particles are separated well. c.f. LEP exp.

5. 8 April 20085 Analysis Procedure e + e    +   selection         selection Background subtraction Unfolding Br measurement Extract pion form factor |F  (s)| 2 Fit with Breit-Wigner Form Evaluation of a  distribution event selection unfolded distribution 72.2/fb unfolding （ correct the detector effect ） Extract pion form factor evaluation of the DATA Unfolded     distribution

6. 8 April 20086 e + e    +   Selection Event Selection Low multiplicity: Number of charged tracks ： 2 or 4, net charge=0 Rejection of Bhabha and     ;  |P|*< 9 GeV Physics background rejection: Use Missing Mass and Missing Angle information.(Bhabha,2photon) Low track and gamma multiplicity. (qq continuum)  charged track         Selection one charged track in the event hemisphere. one  0 in the event hemisphere. No additional g with Eg≥200MeV Tag-side condition: 1, 3 prong+ any  For Br measurement  1 prong + no  : For mass spectrum

7. 8 April 20087 e + e -     - Selection Particle multiplicity Bhabha m+m- Two photon

8. 8 April 20088  0 Signal Signal region right ： left ： Sideband region Sideband region is used to estimate the non-  0 background 5.6M events         Generally background free, but non- negligible BK In the low M  0 region. - Ｓｉｄｅ ｂａｎｄ ｒｅｇｉｏｎ： Ｄｏｍｉｎ ａｔｅｄ ｂｙ ｔｈｅ ｔａｉｌ from ｔｒｕ ｅ “  0 ” -Reproducing the signal shape by MC is important.

9. 8 April 20089 Background non-  B.G. feed down B.G. m 2  distribution Tau mass limit (0)(0) The signal level is different more than 4th order of magnitude between  (770) and  ’’(1700). BG is important at threshold and  ’’ region.

10. 8 April 200810 New MC set New  MC (include  ” to TAUOLA MC) More reliable estimate of continuum BG Estimate continuum using BG enriched sample. Require stronger cut for tag side 1 charged track + no  More reliable estimate of feed-down BG. some modes have small Br but dominate in the special region. i.e. threshold region        (    0  )       0 K L  etc. Systematic study  0 side band, efficiency check Some important features

11. 8 April 200811 Acceptance (including tagging eff.) Data are Unfolded with the Singular Value Decomposition (SVD) method. Acceptance

12. 8 April 200812 Results Br Mass Spectrum Pion form factor Extract resonance Parameters Comparison with previous exp. Evaluation of a  and iso-spin violation correction.

13. 8 April 200813 Result (1) Branching Fraction Normalized to the number of  -pairs Tau-pair selection  acceptance : 32.6 0.05% : 1.112 0.003 background : 7.8 0.03%  0 selection Acceptance: 41.0 0.1 % Background feed down: 7.02 0.08 % qq-conti. : 2.22 0.05 % Br 2  = (25.24 0.01 （ stat) 0.39(sys))% 25.24 0.04 0.39 Belle

14. 8 April 200814 Systematic on Br Measurement Source Tracking efficiency 0.47  0 efficiency 1.3 Background in  -pair 0.59 Feed down background 0.16 Continuum background 0.20  veto 0.20 Trigger 0.32 MC statistics 0.08 Total 1.52 Systematic is dominated by the uncertainty of the  0 efficiency and the BG in  -pair  0 Calibrated by  signals ( ). Checked by using electron tracks.

15. 8 April 200815 Result (2): Mass spectrum Mass spectra  ＝  Phase space  Form Factor  umber of entries /0.05 (GeV/c 2 ) 2 Unfolded Results

16. 8 April 200816 Result (3) Pion Form Factor |F π | 2 From 64M      pairs, Belle selects 5.5M        events! Error bars include both statistical and systematic Interference between  ’ and  ” Fit with BW |Fπ|2|Fπ|2 2  F

17. 8 April 200817 Systematic on the mass distribution (1) Unfolding procedure Reproducibility of the signal. （ UNF ①） Unfolding condition : value±5 （ UNF ②） Acceptance (Accept.)  0 efficiency uncertainty Effect of  -track isolation Change a cut on the cluster-track distance （ default and tighter one(30cm ） ) Momentum or energy scale (ENS) Change E  by it’s uncertainty estimated from the   mass peak position.  ±0.2 ％ )

18. 8 April 200818 Systematic on the mass distribution (2) Background Continuum BG (BKG ① ) estimate at the mass region higher than m  uncertainty is estimated to be 10% Feed down BG (BKG ② ) dominated by         systematic is estimated by changing the Br in PDG by 1  non-  0 BG (BKG ③ ) dominated in the low (M  0 ) 2 region. In this region, the size of the non-  0 background in the lower M  side is different between data and MC. This differences is corrected and the difference is included as a systematic.

19. 8 April 200819 Non-  0 background( details). 0.10<(M  0 ) 2 <0.15 F=1.375 F=1 0.55<(M  0 ) 2 <0.60 M   00

20. 8 April 200820 Systematic on the Mass Spectrum/Form Factor M 2  threshold  region  ’ region  ” region Unfolding (MC) 0.79 0.31 1.5 1.50 Unfolding (cond) 0.53 0.09 0.58 9.19 BKG (continuum) 0.09 0.01 0.52 5.76 BKG (feed-down ) 0.65 0.10 --- 0.50 BKG(non-  0 ) 4.80 --- Acceptance 1.44 0.03 0.15 0.40 Energy scale 1.08 0.59 0.05 0.50 Total 5.30.71.811.4 ( %) Systematic Region Dominant Factor 0.7-1.8%   ’ Energy scale/Unfolding 5% threshold Background (  0, feed down) 10%  ’’ Continuum BG by Toy MC

21. 8 April 200821 10 fit parameters Gounaris-Sakurai (GS) parameterization  (770),  ’(1400),  ’’(1700) Result(4) Resonance parameters The normalization of the GS form is given by Fit with BW form

22. 8 April 200822 Fit Results Fit parameter Norm fixed Norm [1.0 ] 774.6±0.2±0.5 148.1±0.4±1.7 1446±7±28 434±16±60 1728±17±89 80/52 All  ’  ’’ resonance parameters are determined at the same time! PDG2006 , e + e - Hadron reaction ± ±775.4 0.4766.5 1.1 146.4 1.1 150.2 2.4 ± ± fit with  ’’ x 2 /ndf=80/(90-10) fit w/o  ’’ x 2 /ndf=135/(90-6) Significance of  ’’ : 6.5  Most precise

23. 8 April 200823 Comparison with previous exp. BELLE & ALEPHBELLE & CLEO Ref: Phys. Rep.421 (2005) 191 Ref: Phys. Rev. D61, 112002(2000) 1 Agree with previous exp. of data. Our result is more precise especially in high mass region. 2  F 2  F

24. 8 April 200824 Effect on a   ? i Detailed Comparison:  ’ region Fit: Fit to Belle Data Belle-CLEO consistent, ALEPH is higher at (M   2 > 0.8 GeV 2 ;

25. 8 April 200825 Evaluation of a   2  ItemValue 1.0235±0.0006 ±0.20 0.9734±0.0008 ±0.42 (17.84±0.06)% ±1.82 (25.42±0.11)% ±2.30 Total ± ３．０ World average is calculated combining our new result

26. 8 April 200826 a  （２  ）  contribution from each mass range range (GeV 2 ) BelleALEPH 0.08-0.20 39.55 38.20 0.20-0.35 70.62 66.84 0.35-0.50123.25119.10 0.50-0.65196.78194.00 0.65-0.80 62.35 0.80-0.95 15.64 16.40 0.95-1.10 5.74 6.50 1.10-1.25 2.86 3.27 1.25-1.40 1.65 1.89 1.40-3.20 2.43 2.77 0.08-3.20522.0511.1 Belle> ALEPH Belle<ALEPH No iso-spin violation correction is applied X 10 -10 Total

27. 8 April 200827 Iso-spin Violation Correction Ref. V. Cirgliano et al., J. High Energy Phys. 08, 002(2002) A.Flores-Tlalpa et al., Phys. Rev. D 74, 071301 (2006) Source Correction Uncertainty Short distance rad. Cor (S EW ) - 12.0 ± 0.2 Long distance rad. Cor.(G EM ) - 1.0 m  - = m  0 (in phase space) - 7.0  -  interference + 3.5 ± 0.6 m  - = m  0 (in decay width) +4.2 Electromagnetic decays -1.4 ± 1.4 m  0 = m  – - ± 2.0 Total -13.7 ± 2.5 X10 -10 FSR correction in e + e -  V  ->      : +4.2  Total+FSR = -9.5 2.5 ±

28. 8 April 200828 Results (5) a  （２  ） Belle(  ) ALEPH, CLEO, OPAL (  ) CMD2,SND (e + e  ) After applying the known iso-spin violation correction. Integrated region:  results are higher than those from e + e -. Ref. Eur. Phys. J. C27, 497 (2003) Ref. Nucl. Phys. Proc. Suppl. 169, 288 (2007)

29. 8 April 200829 Summary We have studied          using high statistics Belle data Br measurement: (1.6% accuracy) Precise 2  mass spectrum and the pion form factor are determined. We can provide them by a table. In addition to  (700),  ’(1400),  the production of  ’’(1700) is unambiguously identified and its parameters are determined. Our results for agree with the previous  based results but are higher than those from e + e -. The results are accepted by PRD, will appear in Oct. issue. The paper is accepted by PRD and will appear in Oct. issue.

30. 8 April 200830 Backup Slide

31. 8 April 200831 Comparison :   - >  -  0  and e + e - - >     by F. Jegerlehner (private commun.)

32. 8 April 200832 Internal Systematic Error source Background estimation ・ non-  （ ee->hadron ） ・ feed-down h≥2  0 ・ feed-down K －  0 ±0.11 ±0.09 ±0.15  0 /  selection efficiency/shape cuts ±0.35 Energy scale ±0.10 Gamma veto ±0.93  /track overlap 0.24 Tagging Dependence <0.1 Smearing/Migration effect Total ±1.04

33. 8 April 200833  interference  -  interference effects are estimated using following form for the amplitude.

34. 8 April 200834 Pion Form Factor |F π | 2 Low mass region  mass region (linear scale) Error bars include both statistical and systematic

35. 8 April 200835 Systematic of resonance parameters Source of systematics  ’  ’   ’’  ’’  Fit bias 0.31.625490.028475100.03813 Unfold 0.3 4240.001411140.00212 B.G. 0.3--1125+0.14 -0.03 +41 - 5 13+86 -10 +0.053 -0.020 +117 - 22 Acceptance --0.114---0.60.17---1 Momentum scale 0.30.621---24515---1 total 0.51.72860+ 0.15 -0.04 + 41 -8 89+89 -26 +0.065 -0.009 +118 - 28 (MeV) (MeV) (MeV)(MeV) (deg.) (MeV) (MeV) (deg.)

36. 8 April 200836 e + source Ares RF cavity Belle detector World record: L = 1.7118 x 10 34 /cm 2 /sec SCC RF(HER) ARES(LER) 8 x 3.5 GeV 22 mrad crossing ~ 1 km in diameter Mt. Tsukuba KEKB Belle since 1999 First successful op. of Crab cavities The KEKB Collider

37. 8 April 200837  / K L detection 14/15lyr. RPC+Fe Central Drift Chamber Tracking +dE/dx Small cell +He/C 2 H ６ CsI(Tl) 16X 0 Si vtx. det. 3 lyr. DSSD TOF counter SC solenoid 1.5T 8 GeV e  3.5 GeV e  Good tracking and particle identification Belle detector  0 mass resolution ;   ~ 5 -8MeV Aerogel Cherenkov cnt. n=1.015~1.030