Determination of and related results from B A B AR

1. Determination ofand related results from BABAR |Vcb| Masahiro Morii, Harvard University on behalf ofthe BABAR Collaboration |Vcb| from inclusive B semileptonic decays Lepton energy moments Hadron mass moments HQE fit |Vcb|, mb, mc, B(B Xcℓv), etc. MESON 2004, Krakow, June 4-8, 2004

2. Why |Vcb| — and How • Vcb is the “mother of (almost) all B decays” • Precise determination with reliable errors important for: • predicting B decay rates • testing unitarity of the CKM matrix • Semileptonic B decays offer best probe • Leptonic current factors out cleanly • Tree-level rate • QCD corrections relate this to the measured rates • Inclusive G(B Xcℓv) • Exclusive G(B D*ℓv), G(B Dℓv), etc. M. Morii, Harvard

3. Inclusive |Vcb| Measurement • Heavy Quark Expansion allows calculation of • Inclusive rate • Lepton energy (Eℓ) moments • Hadron mass (mX) moments • Expansion in terms of 1/mb and as(mb) • Separate short- and long-distance effects at m ~ 1 GeV • Perturbative corrections calculable from mb, mc, as(mb) • Non-perturbative corrections cannot be calculated • Ex: 4 parameters up to in the kinetic scheme • Strategy: Measure rate + as many moments as possible • Determine all parameters by a global fit • Over-constrain to validate the method M. Morii, Harvard

4. Observables • Define 8 moments from inclusive Eℓ and mX spectra • Eℓ is measured in the B rest frame • Integrations are done for Eℓ > Ecut, with Ecut varied in 0.6–1.5 GeV Partial branching fraction Lepton energymoments Hadron massmoments M. Morii, Harvard

5. Unlike-sign BABAR Like-sign hep-ex/0403030, to appear in PRD Electron Energy Moments • BABARdata, 47.4 fb-1 on U(4S) resonance + 9.1 fb-1 off-peak Select events with 2 electrons • One (1.4 < p* < 2.3 GeV) to“tag” a BB event • The other (p* > 0.5 GeV) tomeasure the spectrum • Use charge correlation • Unlike-sign events • dominated by B Xcev • Like-sign events • D Xev decays, B0 mixing M. Morii, Harvard

6. Electron Energy Moments • Turn the like-/unlike-signspectra Eℓ spectrum • Divide by the efficiency • Account for B0 mixing • Correct for the detectormaterial (Bremsstrahlung) • Calculate the moments for Ecut = 0.6 … 1.5 GeV • Move from U(4S) to B rest frame • Correct for the final state radiation using PHOTOS • Subtract B Xuℓv BABAR Into the HQE fit M. Morii, Harvard

7. hep-ex/0403031, to appear in PRD Hadron Mass Moments • BABARdata, 81 fb-1 on U(4S) resonance • Select events with a fully-reconstructed B meson • Use ~1000 hadronic decay chains • Rest of the event contains one “recoil” B • Flavor and momentum known • Find a lepton with E > Ecut in the recoil-B • Lepton charge consistent with the B flavor • mmiss consistent with a neutrino • All left-over particles belong to Xc • Improve mX with a kinematic fit  s = 350 MeV • 4-momentum conservation; equal mB on both sides; mmiss = 0 Fully reconstructedB hadrons v lepton Xc M. Morii, Harvard

8. Hadron Mass Moments • Measured mX < true mX • Linear relationship Calibrate using simulation • Depends (weakly) on decaymultiplicity and • Validate calibration procedure • Simulated events in exclusivefinal states • D*±  D0p± in real data, taggedby the soft p± • Calculate mass moments with Ecut = 0.9 … 1.6 GeV BABAR Into the HQE fit M. Morii, Harvard

9. hep-ex/0404017, to appear in PRL Inputs to HQE Fit Error bars are stat. & syst.with comparable sizes mX moments BABAR Eℓmoments M. Morii, Harvard

10. Systematic Errors • Dominant experimental systematic errors • Electron energy moments • Tracking and electron ID efficiencies • Background from secondary leptons (B D/Ds/t  e) • Bremsstrahlung correction • B Xuℓv subtraction • Hadron mass moments • Detector efficiency and resolution • Background in fully-reconstructed B • Other background • Hadron mis-ID, t+t–, B Xuℓv, secondary leptons M. Morii, Harvard

11. HQE Parameters • Calculation by Gambino & Uraltsev (hep-ph/0401063 & 0403166) • Kinetic mass scheme to • Eℓ moments • mX moments • 8 parameters to determine • 8 moments available with several Ecut • Sufficient degrees of freedom to determineall parameters without external inputs • Fit quality tells us how well HQE works kinetic chromomagnetic spin-orbit Darwin M. Morii, Harvard

12. Fitting Method • Use linearized expression for the HQE predictions • Difference from fit using the full expression small • Data points (48 of them) are strongly correlated • Each fit uses a subset in which all correlation coefficients are <95% • Full error matrix for experimental errors (stat. and syst.) • Theory errors: vary slopes of the linearized expressions • ±20% for the terms, ±30% for the terms • Fully correlated for each moment at different Ecut • Uncorrelated between different moments • Fit results stable for different treatment of the theory errors M. Morii, Harvard

13. HQE Fit Results ● = used, ○ = unusedin the nominal fit mX moments BABAR c2/ndf = 20/15 Eℓmoments Red line: HQE fitYellow band: theory errors M. Morii, Harvard

14. HQE Fit Consistency • HQE describes BABAR data very well • c2/ndf = 20/15 • Separate fit of Eℓ and mX moments agree BABAR M. Morii, Harvard

15. HQE Fit Results • and consistent with B-B* mass splitting and QCD sum rules Uncalculatedcorrections to G kinetic mass scheme with m = 1 GeV M. Morii, Harvard

16. In Perspective • New BABAR result compares well with previous measurements • |Vcb| is now measured to ±2% M. Morii, Harvard

17. Heavy Quark Masses • Convert mb and mc into MS scheme (N. Uraltsev) theory theory References in PDG 2002 M. Morii, Harvard

18. Summary • BABAR has made significant progress in determination of |Vcb| • HQE fit of Eℓ and mX moments  2% error on |Vcb| • No external constraints on the non-perturbative parameters • Fit quality and consistency support validity of the HQE application • It also determines mb and mc precisely M. Morii, Harvard