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Measurement of spectral function in the decay Motivation ~ Muon Anomalous Magnetic Moment ~Event selectionmass spectrum (unfolding)Evaluation of resultYukiko Hirano(Nara Womens Uni. , High Energy Physics Lab.)For the Belle collaborationOutline
JPS 2003 in Sendai
Motivation~ Muon Anomalous Magnetic Moment ( ) ~The prediction of Standard Modellargest error fromHadron vacuum polarization
JPS 2003 in Sendai
anddecaythe contribution of hadrom Vacuum polarization obtained from Experimental Data.difficult to obtain from first principle Cross section of Hadron system Hadron systemdecay is useful to determine the term ,
JPS 2003 in Sendai
and decay Hadron Vacuum polarization term from 2 system ( )
Spectral function is measured in this experiment.K(s) is known function.
JPS 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) 2003.1difference by Hadron Vacuum Polarization. term is different between and base predictions.Cross check is important !
JPS 2003 in Sendai
event selection Number of charged tracks2 or 4All charge ( ) = 0event vertex position :
Separate the event into 2 hemisphere by the event axis.
Event axis direction :
Back Ground rejection (next slide)
Physics trigger
Event selection Data : accumulated from 2000.10 to 2000.12 at Belle.(corresponding to production.)
JPS 2003 in Sendai
event selection (Back ground rejection) Missing mass and Missing angle cut ( plot) about 1,300,000 events are remained.
Event selection
JPS 2003 in Sendai
signalrightleftSide-band region
JPS 2003 in Sendai
mass spectraumB.G. fraction
JPS 2003 in Sendai
Unfolding acceptanceMass square resolution : 0.03 GeV2 Acceptance include both the tau-pair and pipi0 selection.Acceptance and bin-by-bin migration effects are corrected via Singular-Value-Decomposition method.
JPS 2003 in Sendai
Unfolded mass spectrumRed line : Breit Wigner fitting function ( and are included. )
JPS 2003 in Sendai
Breit Wigner fitting formfree parameterGS model is known that it can fit wilder mass region that the commonly used BW.Gounaris and Sakurai (G&S) Model
JPS 2003 in Sendai
fit result and compare with previous Experiments parameters : good agreement with previous Exp. parameters : Belle results are most precise.
JPS 2003 in Sendai
Evaluation of
JPS 2003 in Sendai
Systematic error ()External systematics ~Normalization factors~Largest error from
JPS 2003 in Sendai
Systematic error ()Internal systematics
JPS 2003 in Sendai
resultResult of is preliminarycf. ALEPH
JPS 2003 in Sendai
Backup slide
JPS 2003 in Sendai
AnalysisFlow of this analysis
JPS 2003 in Sendai
2.Event selectionExp. DataData reconstructionMonte Carlo simulationSimulator of event productionDetector simulation
JPS 2003 in Sendai
event selectionThere are few charged tracks in the event.72%13%There are missing of momentum and mass because of neutrino ( ) .missing
JPS 2003 in Sendai
event selection (Back ground rejection) Missing mass and Missing angle cutThen ,we obtained about 1,300,000 event of . Low-multiplicity event :
JPS 2003 in Sendai
Missing mass VS. Missing angleDataMC(tau)MC(Bhabha)MC(2photon)
JPS 2003 in Sendai
Time dependence
JPS 2003 in Sendai
Time dependence
JPS 2003 in Sendai
Momentum of and Good agreement between Data and MC .
JPS 2003 in Sendai
Fitting result of Breit Wigner modelK&S modelG&S model
JPS 2003 in Sendai
Fitting result
K&SK&SG&SG&S
JPS 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 UnfoldingUnfolding is carried out by Singular Value Decomposition (SVD) method.
JPS 2003 in Sendai
Spectral function
JPS 2003 in Sendai
Systematic detail 1(1) BG estimation (two photon )(2) BG estimation (hadron)Two photon B.G. estimated by Data using control sample.Hadron BG contribution also estimated by Data using control sample.
JPS 2003 in Sendai
Systematic detail2(3) Energy scale(4) Gamma energy thresholdUncertainty of as gamma-threshold function.
JPS 2003 in Sendai
Hadron Vacuum polarization and DataThe term of hadron vacuum polarization
JPS 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
JPS 2003 in Sendai