V cb. Determination of. and related results from BABAR. Masahiro Morii, Harvard University on behalf of the BABAR Collaboration

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

2 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 b cb b b c Γ( b c ν ) V m ( m m ) QCD corrections relate this to the measured rates Inclusive Γ(B X c lv) Exclusive Γ(B D * lv), Γ(B Dlv), etc. V cb c ν June 5, 2004 M. Morii, Harvard 2

3 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 α s (m b ) Separate short- and long-distance effects at µ ~ 1 GeV Perturbative corrections calculable from m b, m c, α s (m b ) Non-perturbative corrections cannot be calculated 3 Ex: 4 parameters up to O(1/ ) in the kinetic scheme Strategy: Measure rate + as many moments as possible m b Determine all parameters by a global fit Over-constrain to validate the method B X c ν June 5, 2004 M. Morii, Harvard 3

4 Observables Define 8 moments from inclusive E l and m X spectra M 0 dγ = Γ B i E dγ ( E M1 ) dγ M1 = Mi = ( i = 2,3) dγ dγ M X i i mx dγ = ( i= 1,2,3,4) dγ Partial branching fraction E l is measured in the B rest frame Hadron mass moments Lepton energy moments Integrations are done for E l > E cut, with E cut varied in GeV June 5, 2004 M. Morii, Harvard 4

5 hep-ex/ , to appear in PRD Electron Energy Moments BABAR data, 47.4 fb -1 on Υ(4S) resonance fb -1 off-peak Select events with 2 electrons Unlike-sign 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 Like-sign BABAR June 5, 2004 M. Morii, Harvard 5

6 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 = GeV Move from Υ(4S) to B rest frame Correct for the final state radiation using PHOTOS Subtract B X u lv Electrons / 50 MeV/c Into the HQE fit BABAR * p [GeV/c] June 5, 2004 M. Morii, Harvard 6

7 Hadron Mass Moments hep-ex/ , to appear in PRD BABAR data, 81 fb -1 on Υ(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 v lepton Fully reconstructed B hadrons All left-over particles belong to X c Improve m X with a kinematic fit σ = 350 MeV 4-momentum conservation; equal m B on both sides; m miss = 0 X c June 5, 2004 M. Morii, Harvard 7

8 Hadron Mass Moments Measured m X < true m X Linear relationship Calibrate using simulation Depends (weakly) on decay 2 multiplicity and m miss Validate calibration procedure Simulated events in exclusive final states D *± D 0 π ± in real data, tagged by the soft π ± Calculate mass moments with E cut = GeV BABAR Into the HQE fit June 5, 2004 M. Morii, Harvard 8

9 hep-ex/ , to appear in PRL Inputs to HQE Fit m X moments Error bars are stat. & syst. with comparable sizes M 1 X (GeV) M 2 X (GeV 2 ) M 3 X (GeV 3 ) M 4 X (GeV 4 ) M M 1 (GeV) M 2 (GeV2 ) M 3 (GeV3 ) BABAR E l moments E cut (GeV) June 5, 2004 M. Morii, Harvard 9

10 Systematic Errors Dominant experimental systematic errors Electron energy moments Tracking and electron ID efficiencies Background from secondary leptons (B D/D s /τ 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, τ + τ, B X u lv, secondary leptons June 5, 2004 M. Morii, Harvard 10

11 HQE Parameters Calculation by Gambino & Uraltsev (hep-ph/ & ) Kinetic mass scheme to 2 E l moments O( α s ) m X moments O( α s ) 8 parameters to determine Vcb mb mc B( B X ν ) 2 µ π 2 µ G 3 ρ D 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 O c 3 (1/ m b ) kinetic chromomagnetic 3 ρ LS spin-orbit Darwin O O 2 (1/ m b ) 3 (1/ m b ) June 5, 2004 M. Morii, Harvard 11

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 2 3 O(1/ ) O(1/ ) m b ±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 m b June 5, 2004 M. Morii, Harvard 12

13 HQE Fit Results m X moments = used, = unused in the nominal fit M 1 X (GeV) (a) M 2 X (GeV 2 ) M 3 X (GeV 3 ) M 4 X (GeV 4 ) 18 (b) 8.4 (c) (d) 20 M M 1 (GeV) M 2 (GeV2 ) M 3 (GeV3 ) BABAR 0.04 (e) 1.4 (f) (g) (h) χ 2 /ndf = 20/15 E l moments E cut (GeV) Red line: HQE fit Yellow band: theory errors June 5, 2004 M. Morii, Harvard 13

14 HQE Fit Consistency HQE describes BABAR data very well χ 2 /ndf = 20/15 Separate fit of E l and m X moments agree V cb (10-3 ) Lepton Moments Hadron Moments BABAR Lepton Moments All Moments (a) Hadron Moments m b (GeV) (b) All Moments June 5, 2004 M. Morii, Harvard 14

15 HQE Fit Results V cb Bc ν m m b c exp HQE th exp exp exp HQE HQE HQE 2 2 µ π exp HQE α µ ρ ρ 2 G = (41.4 ± 0.4 ± 0.4 ± 0.6 ) 10 = (10.61± 0.16 ± 0.06 )% = (4.61± 0.05 ± 0.04 ± 0.02 ) GeV = (1.18 ± 0.07 ± 0.06 ± 0.02 ) GeV = (0.45 ± 0.04 ± 0.04 ± 0.01 ) GeV = (0.27 ± 0.06 ± 0.03 ± 0.02 )GeV exp HQE 3 3 D exp HQE α 3 3 LS exp HQE α µ π = (0.20 ± 0.02 ± 0.02 ± 0.00 ) GeV = ( 0.09 ± 0.04 ± 0.07 ± 0.01 ) GeV ρ LS 2 3 and consistent with B-B* mass splitting and QCD sum rules α α s s s α s s s 3 2 Uncalculated corrections to Γ kinetic mass scheme with µ = 1 GeV June 5, 2004 M. Morii, Harvard 15

16 In Perspective New BABAR result compares well with previous measurements V cb is now measured to ±2% June 5, 2004 M. Morii, Harvard 16

17 Heavy Quark Masses m m Convert m b and m c into MS scheme (N. Uraltsev) kin b kin c (1GeV) = (4.61± 0.05 ± 0.04 ± 0.02 )GeV exp HQE th (1GeV) = (1.18 ± 0.07 ± 0.06 ± 0.02 )GeV exp HQE th m ( m ) = 4.22 ± 0.06 GeV b b m ( m ) = 1.33± 0.10 GeV c c theory theory References in PDG 2002 June 5, 2004 M. Morii, Harvard 17

18 Summary BABAR has made significant progress in determination of V cb HQE fit of E l and m X moments 2% error on V cb m m kin b kin c V cb Bc ν = (41.4 ± 0.4 ± 0.4 ± 0.6 ) 10 exp HQE th = (10.61± 0.16 ± 0.06 )% 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 exp exp exp HQE (1GeV) = (4.61± 0.05 ± 0.04 ± 0.02 )GeV HQE (1GeV) = (1.18 ± 0.07 ± 0.06 ± 0.02 )GeV HQE m ( m ) = 4.22 ± 0.06 GeV b m ( m ) = 1.33 ± 0.10 GeV c b c α α s s 3 June 5, 2004 M. Morii, Harvard 18