Belle General meeting Measurement of spectral function in the decay 1. Motivation 2. Event selection 3. mass spectrum (unfolding) 4. Evaluation of vacuum polarization contribution of Muon Anomalous Magnetic Moment ( ) 5. Summary H. Hayashii (Nara Women’s Uni.) BGM Outline See Belle note 622 and 623 for details

Belle General meeting Motivation decay and the anomalous magnetic moment of the muon decay is important to evaluate term Error of is dominated by the h.v.p. term dominated in low mass region +CVC Hadron

Belle General meeting Present status  Experiment ・・・ BNL2002  Theory ・・・ Davier et al. Hagiwara et al., data based new CMDII ee data data based (ALEPH) difference Need a cross check with new data difference from h.v.p. term ７０％ of h.v.p. term from channel. hep-ph/ hep-ph/

Belle General meeting and and 2pi h.v.p. term （ ） Spectral function is measured in this experiment. mass square spectrum

Belle General meeting event selection Number of charged tracks ： 2 or 4 All charge ( ) = 0 event vertex position : < 2.5 cm, < 0.5 cm 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 to at Belle. ( statistically large enough ） )

Belle General meeting 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

Belle General meeting selection selection criteria one charged track in hemisphere. one in the hemisphere. gamma condition : gamma-like shower shape : veto the additional gamma

Belle General meeting signal signal Mass invariant mass distribution resolution of Signal region right ： left ： Side-band region 3,200,000 decays Side-band region are used for estimation of BG in signal region.

Belle General meeting Time dependence of yield is stable within Stability of the event ratio

Belle General meeting While the variation of is about at maximum

Belle General meeting mass spectraum B.G. fraction sourceB.G. fraction non- B.G.( ) Two photon Feed across B.G. ( ) Total qq, two-photon back. has been calibrated by using control sample

Belle General meeting 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.

Belle General meeting Unfolded mass spectrum Red line : fit with Breit Wigner including and

Belle General meeting Breit Wigner fitting form mass distribution Spectral function free parameter Gounaris and Sakurai (G&S) Model GS form is known that it can fit wider mass regions than the commonly used BW form.

Belle General meeting Fit Parameter BelleCLEOALEPH : good agreement with previous Exp. : Belle results are most precise. Fit result and comparison with previous results Mev deg.

Belle General meeting Evaluation of Evaluation of external parameters Integration is carried out bin-by-bin bases. Error matrix （ ） is taken into account in the evaluation of the stat. error.

Belle General meeting Systematic error(I) sourcevalue total External systematics ~Normalization factors~ Largest error from PDG2002 Tau02:hep-ex/ M.Davier et al.,hep- ph/

Belle General meeting Systematic error(II) source comment B.G. estimationB.G. fraction non- BG hadron 2 photon Feed down BG Energy scale efficiency non- BG /selection Estimate from Side-band minimum energy 80MeV-200MeV total Internal systematics 1. Non-tau BG. estimated by bkgd. MC control data sample are used for the caliblation. 2. Feed-down of measured Br 3. Energy scale uncertainty estimated from mass peak. 4. Selection estimated from the uncer. of side-band 5. minimum energy

Belle General meeting Control sample of background estimation (1) non-tau BG estimation (two photon ) (2) BG Data High-multicity sample. Two-photon Bhabha Other cuts: Use the same selection scriteria as the one of Tau-pair selection Tau-pairs

Belle General meeting Dependence of the gamma minimum energy It is found that the pi0 efficiency has systematics for the variation of the gamma minimum energy. gamma minimum energy  Acceptance itself chages by a factor of 3 for the change of  Systematics on is estimated by changing Largest source

Belle General meeting Other cross check 1.SVD unfolding program and its error matrix.--- check by toy-MC using known distribution. 2. : checked. But the uncertainty ( 3-4%) is large compared to the current level of the precision Dependence on the gamma minimum energy is largest source for the measurement of Br, also. See Belle note 622

Belle General meeting Results cf. ALEPH ( base) excluding common error Consistent within error Belle note 622/623 Updated soon

Belle General meeting Spectrum function Belle vs CLEO

Belle General meeting Backup slide

Belle General meeting Missing mass VS. Missing angle Data MC(tau) MC(Bhabha) MC(2photon)

Belle General meeting Momentum of and Good agreement between Data and MC.

Belle General meeting Fitting result of Breit Wigner model K&S modelG&S model

Belle General meeting Fitting result K&S G&S

Belle General meeting Motivation ~ Muon Anomalous Magnetic Moment ( ) ~ Magnetic moment ： …. for Dirac particle (spin )  Exp. ・・・ measured by BNL (g-2) exp.  The prediction from Standard Model In Muon, there are small discrepancy Muon Anomalous Magnetic Moment ： The largest error in ・・・ Hadron vacuum polarization hadron

Belle General meeting 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

Belle General meeting Present status ; Muon Anomalous Magnetic Moment ( )  Exp. ・・・ measured by BNL (g-2) experiment. （ ）  Theoretical prediction ・・・ new data (CMD-2) and data (ALEPH) （ ） base difference by agree within ・ h.v.p. term is different for and base predictions. ・ Cross check on the experimental data is important.

Belle General meeting Hadron Vacuum polarization and Data The term of hadron vacuum polarization

Belle General meeting Data and Data Iso-spin 、 Cnserve of Vectro Current We can treat data as same condition as data. semi-Leptonic dacayc decay

Belle General meeting 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.