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Determination of and related results from B A B AR Masahiro Morii, Harvard University on behalf of the B A B AR Collaboration |V cb | MESON 2004, Krakow, June 4-8, 2004 |V cb | from inclusive B semileptonic decays Lepton energy momentsHadron mass moments HQE fit |V cb |, m b, m c, (B X c ℓv), etc.

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June 5, 2004M. Morii, Harvard2 Why |V cb | — and How V cb 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 (B X c ℓv) Exclusive (B D * ℓv), (B Dℓv), etc.

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June 5, 2004M. Morii, Harvard3 Inclusive |V cb | Measurement Heavy Quark Expansion allows calculation of Inclusive rate Lepton energy (E ℓ ) moments Hadron mass (m X ) moments Expansion in terms of 1/m b and s (m b ) Separate short- and long-distance effects at ~ 1 GeV Perturbative corrections calculable from m b, m c, s (m b ) 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

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June 5, 2004M. Morii, Harvard4 Observables Define 8 moments from inclusive E ℓ and m X spectra E ℓ is measured in the B rest frame Integrations are done for E ℓ > E cut, with E cut varied in 0.6–1.5 GeV Partial branching fraction Lepton energy moments Hadron mass moments

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June 5, 2004M. Morii, Harvard5 Electron Energy Moments B A B AR data, 47.4 fb -1 on (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) to measure the spectrum Use charge correlation Unlike-sign events dominated by B X c ev Like-sign events D Xev decays, B 0 mixing hep-ex/0403030, to appear in PRD Unlike-sign Like-sign B A B AR

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June 5, 2004M. Morii, Harvard6 Electron Energy Moments Turn the like-/unlike-sign spectra E ℓ spectrum Divide by the efficiency Account for B 0 mixing Correct for the detector material (Bremsstrahlung) Calculate the moments for E cut = 0.6 … 1.5 GeV Move from (4S) to B rest frame Correct for the final state radiation using PHOTOS Subtract B X u ℓv B A B AR Into the HQE fit

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June 5, 2004M. Morii, Harvard7 Hadron Mass Moments B A B AR data, 81 fb -1 on (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 > E cut in the recoil-B Lepton charge consistent with the B flavor m miss consistent with a neutrino All left-over particles belong to X c Improve m X with a kinematic fit = 350 MeV 4-momentum conservation; equal m B on both sides; m miss = 0 hep-ex/0403031, to appear in PRD Fully reconstructed B hadrons lepton v XcXc

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June 5, 2004M. Morii, Harvard8 Hadron Mass Moments Measured m X < true m X Linear relationship Calibrate using simulation Depends (weakly) on decay multiplicity and Validate calibration procedure Simulated events in exclusive final states D *± D 0 ± in real data, tagged by the soft ± Calculate mass moments with E cut = 0.9 … 1.6 GeV Into the HQE fit B A B AR

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June 5, 2004M. Morii, Harvard9 Inputs to HQE Fit m X moments E ℓ moments B A B AR hep-ex/0404017, to appear in PRL Error bars are stat. & syst. with comparable sizes

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June 5, 2004M. Morii, Harvard10 Systematic Errors Dominant experimental systematic errors Electron energy moments Tracking and electron ID efficiencies Background from secondary leptons (B D/D s / e) Bremsstrahlung correction B X u ℓv subtraction Hadron mass moments Detector efficiency and resolution Background in fully-reconstructed B Other background Hadron mis-ID, + –, B X u ℓv, secondary leptons

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June 5, 2004M. Morii, Harvard11 HQE Parameters Calculation by Gambino & Uraltsev (hep-ph/0401063 & 0403166) Kinetic mass scheme to E ℓ moments m X moments 8 parameters to determine 8 moments available with several E cut Sufficient degrees of freedom to determine all parameters without external inputs Fit quality tells us how well HQE works kinetic chromomagnetic Darwin spin-orbit

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June 5, 2004M. Morii, Harvard12 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 E cut Uncorrelated between different moments Fit results stable for different treatment of the theory errors

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June 5, 2004M. Morii, Harvard13 HQE Fit Results m X moments E ℓ moments ● = used, ○ = unused in the nominal fit Red line: HQE fit Yellow band: theory errors B A B AR 2 /ndf = 20/15

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June 5, 2004M. Morii, Harvard14 HQE Fit Consistency HQE describes B A B AR data very well 2 /ndf = 20/15 Separate fit of E ℓ and m X moments agree B A B AR

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June 5, 2004M. Morii, Harvard15 HQE Fit Results and consistent with B-B* mass splitting and QCD sum rules kinetic mass scheme with = 1 GeV Uncalculated corrections to

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June 5, 2004M. Morii, Harvard16 In Perspective New B A B AR result compares well with previous measurements |V cb | is now measured to ±2%

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June 5, 2004M. Morii, Harvard17 Heavy Quark Masses Convert m b and m c into MS scheme (N. Uraltsev) theory References in PDG 2002

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June 5, 2004M. Morii, Harvard18 Summary B A B AR has made significant progress in determination of |V cb | HQE fit of E ℓ and m X moments 2% error on |V cb | No external constraints on the non-perturbative parameters Fit quality and consistency support validity of the HQE application It also determines m b and m c precisely

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