1. JPS 2003 in Sendai 2003.3.28 Measurement of spectral function in the decay 1. Motivation ~ Muon Anomalous Magnetic Moment ~ 2. Event selection 3. mass spectrum (unfolding) 4. Evaluation of 5. result Yukiko Hirano (Nara Women’s Uni., High Energy Physics Lab.) For the Belle collaboration Outline

2. 2003.3.28JPS 2003 in Sendai Motivation ~ Muon Anomalous Magnetic Moment ( ) ~  The prediction of Standard Model Muon Anomalous Magnetic Moment ： hadron largest error from Hadron vacuum polarization

3. 2003.3.28JPS 2003 in Sendai and decay and decay the contribution of hadrom Vacuum polarization （ ） obtained from Experimental Data. difficult to obtain from first principle ！ Cross section of Semi-Leptonic decay Hadron system decay is useful to determine the term, 73% from system

4. 2003.3.28JPS 2003 in Sendai and decay Hadron Vacuum polarization term from 2 system ( ) Spectral function is measured in this experiment. mass square spectrum K(s) is known function.

5. 2003.3.28JPS 2003 in Sendai Present status ; Muon Anomalous Magnetic Moment ( )  Exp. ・・・ measured by BNL (g-2) experiment. （ 2002.9 ）  Theoretical prediction ・・・ new data (CMD-2) and data (ALEPH) （ 2003.1 ） base difference by agree within ・ Hadron Vacuum Polarization. term is different between and base predictions. ・ Cross check is important !

6. 2003.3.28JPS 2003 in Sendai event selection Number of charged tracks ： 2 or 4 All charge ( ) = 0 event vertex position : Separate the event into 2 hemisphere by the event axis. Event axis direction : Back Ground rejection (next slide) Physics trigger event selection criteria Event selection Data : accumulated from 2000.10 to 2000.12 at Belle. (corresponding to production.)

7. event selection (Back ground rejection)  Missing mass and Missing angle cut ( plot) about 1,300,000 events are remained. Missing angle Missing Mass(MM) Bhabha, and two photon rejection Hadron( ) rejection  Reject high-multiplicity event ( ) Missing Mass (GeV) Missing Angle MC Two photon BG Bhabha BG Data Missing Mass (GeV) Missing Angle

8. 2003.3.28JPS 2003 in Sendai Event selection selection criteria ＊ We do analysis each hemispheres. one charged track in hemisphere. one in the hemisphere. gamma condition : gamma-like shower shape : veto the additional gamma (with high momentum (more than 200 MeV/c))

9. 2003.3.28JPS 2003 in Sendai signal signal Mass invariant mass distribution resolution of Signal region right ： left ： Side-band region 320,000 events. Side-band region are used for estimation of BG in signal region.

10. 2003.3.28JPS 2003 in Sendai mass spectraum B.G. fraction sourceB.G. fraction non- B.G.( ) Two photon Feed across B.G. ( ) Total Clear peak of. is dominant. peak. is also included.

11. 2003.3.28JPS 2003 in Sendai Unfolding acceptance Mass square resolution : 0.03 GeV 2 Acceptance include both the tau-pair and pipi0 selection. Acceptance and bin-by-bin migration effects are corrected via Singular-Value-Decomposition method.

12. 2003.3.28JPS 2003 in Sendai Unfolded mass spectrum Red line : Breit Wigner fitting function ( and are included. )

13. 2003.3.28JPS 2003 in Sendai Breit Wigner fitting form mass distribution Spectral function free parameter GS model is known that it can fit wilder mass region that the commonly used BW. Gounaris and Sakurai (G&S) Model

14. 2003.3.28JPS 2003 in Sendai Fit Parameter BelleCLEOALEPH parameters : good agreement with previous Exp. parameters : Belle results are most precise. fit result and compare with previous Experiments

15. 2003.3.28JPS 2003 in Sendai Evaluation of Evaluation of

16. 2003.3.28JPS 2003 in Sendai Systematic error ( Ⅰ ) sourcevalue total External systematics ~Normalization factors~ Largest error from

17. 2003.3.28JPS 2003 in Sendai Systematic error ( Ⅱ ) source comment B.G. estimationB.G. fraction non- BG hadron 2 photon Feed across BG Energy scale efficiency Minimum energy 80MeV – 200MeV non- BG Use side-band total Internal systematics 1.Non- BG. ・ estimated by B.G. MC. ・ control data sample are used for the calibration. 2. Feed-across ・ of measured Br. 3. Energy scale ・ uncertainty estimated from mass peak. 4. Selection ・ estimated from the uncertainty of side-band. 5. minimum energy

18. 2003.3.28JPS 2003 in Sendai result Result of is … preliminary cf. ALEPH ( base) excluding common error Consistent within error

19. 2003.3.28JPS 2003 in Sendai Backup slide

20. 2003.3.28JPS 2003 in Sendai Analysis Data from Belle Unfolding (reject detector contribution) Spectral function measurement Calculation of the term hadron vacuum polarization event selection mass spectrum of Data decide mass spectrum Flow of this analysis

21. 2003.3.28JPS 2003 in Sendai 2.Event selection Exp. Data Data reconstruction Monte Carlo simulation event selection event Belle detector Data taking system Raw Data Simulator of event production Detector simulation Used Data data accumulated from 2000.10 to 2000.12 at Belle data :

22. 2003.3.28JPS 2003 in Sendai event selection There are few charged tracks in the event. decay to 1 charged track ： about 85% decay to 3 charged tracks ： about 15% decay 72%13% There are missing of momentum and mass because of neutrino ( ). missing

23. 2003.3.28JPS 2003 in Sendai event selection (Back ground rejection)  Missing mass and Missing angle cut Then,we obtained about 1,300,000 event of. Missing angle Missing Mass(MM) Bhabha, and two photon rejection  clean Bhabha and mumu event rejection :  Low-multiplicity event : Hadron( ) rejection

24. 2003.3.28JPS 2003 in Sendai Missing mass VS. Missing angle Data MC(tau) MC(Bhabha) MC(2photon)

25. 2003.3.28JPS 2003 in Sendai Time dependence data at Belle detector Time dependence of event is stable within 0.5%.

26. 2003.3.28JPS 2003 in Sendai Time dependence Time dependence of event is stable within 0.5%.

27. 2003.3.28JPS 2003 in Sendai Momentum of and Good agreement between Data and MC.

28. 2003.3.28JPS 2003 in Sendai Fitting result of Breit Wigner model K&S modelG&S model

29. 2003.3.28JPS 2003 in Sendai Fitting result K&S G&S

30. 2003.3.28JPS 2003 in Sendai Unfolding of invariant mass The observed distribution includes contribution of detector acceptance,and smeared. We can obtain true distribution by using Unfolding. About Unfolding Unfolding is carried out by Singular Value Decomposition (SVD) method.

31. 2003.3.28JPS 2003 in Sendai Spectral function

32. 2003.3.28JPS 2003 in Sendai Systematic detail 1 (1) BG estimation (two photon ) (2) BG estimation (hadron) Data MC (two photon) Two photon B.G. estimated by Data using control sample. Hadron BG contribution also estimated by Data using control sample.

33. 2003.3.28JPS 2003 in Sendai Systematic detail2 (3) Energy scale (4) Gamma energy threshold (5) side-band subtraction 2% uncertainty of mass spectrum is assumed. Uncertainty of as gamma-threshold function. Use control sample of side-band.

34. 2003.3.28JPS 2003 in Sendai Hadron Vacuum polarization and Data The term of hadron vacuum polarization

35. 2003.3.28JPS 2003 in Sendai Data and Data Iso-spin 、 Cnserve of Vectro Current We can treat data as same condition as data. semi-Leptonic dacayc decay