1 Inclusive B → X c l Decays Moments of hadronic mass and lepton energy PR D69,111103, PR D69, Fits to energy dependence of moments based on HQE PRL 93, Exclusive B → D *+ l Decays Form Factors BABAR CONF-04/031 Extraction of |V cb | in the context of HQET submitted to PRD, hep-ex/ Vera Lüth, SLAC The Determination of |V cb | from Semileptonic Decays V cb

Vera Lüth - BABARICHEP04 - Beijing2 Semileptonic B Decay – Why are they Interesting Semileptonic decays relatively simple theoretically at the parton level rate depends on CKM elements |V cb | and the quark masses m b and m c the leptonic current factors out cleanly, thus one can probe strong interactions in B mesons sensitive to QCD corrections, OPE accessible experimentally, the B  D* l has the largest single decay rate. A precise determination of |Vcb| with reliable errors important for understanding B decay rates testing of the unitarity of the CKM matrix and predictions of CP violation in B mesons + V cb

Vera Lüth - BABARICHEP04 - Beijing3 HQE Expansions Heavy Quark Expansions, tool to correct for QCD effects 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 parameters cannot be calculated We choose calculation by Gambino & Uraltsev hep-ph/ & Kinetic mass scheme to E ℓ moments m X moments 8 parameters to be fitted Measure 8 moments, each as a function of minimum lepton energy E l kinetic chromomagnetic Darwin spin-orbit

Vera Lüth - BABARICHEP04 - Beijing4 Measurement of Electron Energy Moments Inclusive e ± spectrum in 3x10 6 electron- tagged BB events Corrected for detector effects Corrected for non-prompt electrons – lepton charge correlation and MC Corrected for B 0 – B 0 mixing Moments for E cut = 0.6 … 1.5 GeV Corrected for the final state radiation Translated to B rest frame Subtracted B  X u ℓ  decays B A B AR Partial BF Lepton Energy Moments /fb 156,000 e ±

Vera Lüth - BABARICHEP04 - Beijing5 high mass charm states M x 2 [GeV 2 /c 4 ] Measurement of Hadron Mass Moments BB events tagged by a fully reconstructed hadronic B decays e ± or  ± with E l > E cut Lepton charge – B flavor correlation Improve m x measurement by kinematic fit to whole event, resolution ~350 MeV To eliminate dependence of moments on uncertain BF and unknown masses of high mass charm mesons we calibrate m x measurement Calibrate m x based on MC simulation Linear relation between m x meas and m X true Validate calibration with excl. B  D (*) l Moments corrected for detector effects and bkg B A B AR Hadron mass moments 7114 Events D, D* m x meas (Gev) m X true (GeV) Events/0.5 GeV 2 m X 2 (GeV 2 )

Vera Lüth - BABARICHEP04 - Beijing6 HQE Fits to Hadron Mass and Lepton Energy Moments 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 M1xM1x M2xM2x M3xM3x M4xM4x M0lM0l M1lM1l M2lM2l M3lM3l

Vera Lüth - BABARICHEP04 - Beijing7 HQE Fit Results (kinetic mass scheme, scale  =1)  Separate fits to hadron and lepton moments give consistent results   G 2 and  LS 3 are consistent with B-B* mass splitting and HQ sum rules  Considerable improvement in precision for |V cb | (±2%) and B c l   1.6%) and quark masses (factor of 6), as well as HQE parameters Uncalculated corrections to  B A B AR

Vera Lüth - BABARICHEP04 - Beijing8 Decay Distributions for B 0  D *- l +  Differential decay rate depends on 3 helicity amplitudes  Amplitudes H i are expressed in terms of 3 form factors  Perfect HQ symmetry implies R 1 (w)=R 2 (w), i.e. all FF are identical  A 1 (w) can be related to the Isgur-Wise  Goal is to determine R 1 (w), R 2 (w),  2, c: limited data: R 1 (w)= R 1 (w=1), R 2 (w)= R 2 (w=1), c=0

Vera Lüth - BABARICHEP04 - Beijing9 B 0  D *- l +  Background Subtraction  Select: D *- l + : e ±,  ± p* l > 1.2 GeV/c D *- → D 0  S -, D 0 → K +  -, K +  -  0, K +  -  -  +  estimate bkg separately in 10 bins of w   Control data samples:  M= M(D 0  S ) – M D  Signal in |  M MeV| < 2.5 MeV  Background contributes both to peak and sidebands  MC simulated signal and bkg: cos  BY  assume missing particle in the decay is a neutrino. signal confined to |cos  BY | < 1.0,  71k events, purity 76% B Y=D* l

Vera Lüth - BABARICHEP04 - Beijing10 B  D* l : Fit to Differential 4-dim. Cross Section  Perform max. likelihood fit to 4-dim. cross sections  Projections of fitted distributions Data restricted to: e ±, D 0 →K -  +  Preliminary Results R 1 = ± stat ± syst R 2 = ± stat ± syst  2 = ±0.043 stat ± syst  stat. errors dominate (data &MC) – though improved by factor of 4 - 5! B A B AR Preliminary Dominant syst. uncertainties: Background subtraction We assume: c=0.0 Results also consistent with R 1 (w) and R 2 (w) parameterization by Caprini et al.

Vera Lüth - BABARICHEP04 - Beijing11 Extraction of |V cb | from B 0  D *- l + Decays  The decay rate integrated over angles is  extrapolate rate to w=1 and compare with HQET predictions.  With the FF definition of Caprini, Lellouch, and Neubert Nucl. Phys. B530, 217  and  with w dependence of the FF as function of single slope parameter  A1 2 We use measurements by CLEO: R 1 (1) = 1.18 ± 0.32 R 2 (1)= 0.71 ± 0.21 G ( w ) phase space factor F ( w ) Form Factor, predicted at w=1 or q 2 max

Vera Lüth - BABARICHEP04 - Beijing12  h A1 (1)|V cb |=(35.5 ±0.3 stat ±1.6 syst ) x10 -3  A1 2 = 1.29 ±0.03 stat ±0.27 syst Extraction of |V cb | from w Distribution  Perform  2 fit to w distribution, with background estimated from  M and cos  BY distributions  Fit separately e ± and  ±, and adjust efficiencies for data/MC variations  Results of the fit:  With  Branching fraction B (B 0 → D *- l + )=4.90 ± 0.07 stat ± 0.36 syst )%  Syst. errors dominated by error on R 1, R 2 w h A1 (w) |V cb | x Events [10 3 /0.05]  Decays B A B AR linear? quadratic? Hashimoto et al. PRD 66,

Vera Lüth - BABARICHEP04 - Beijing13 Conclusions  Based on 80/fb, ~30% of the current BABAR data, we have made significant advances in the analysis of semileptonic B decays.  Fits to moments result based on HQE result in B (B  X c l )= (10.61 ±0.16 exp ±0.06 HQE )% Also high precision measurement of m b and m c, and exp. determination of HQE parameters.  Analysis of B  D *- l + result in (still based on CLEO FF) B (B 0 → D *- l + ) = (4.90±0.07 stat ± 0.36 syst ) % The dominant errors remain the large uncertainties in R1 and R2. Substituting the FF with the preliminary BABAR measurement we obtain The shift is due to change in acceptance (lepton spectrum) and w dependence, including some subtle differences in the definitions of the FF  There is still need for more detailed analyses, and improvements of theoretical input!

Vera Lüth - BABARICHEP04 - Beijing14 Summary of BABAR Results on |V cb | B A B AR Conversion to MS scheme (N. Uraltsev) Exp. Determination of Quark Masses BABAR (D* l ) Recent Measurements of |V cb | inclusive exclusive

Vera Lüth - BABARICHEP04 - Beijing15 Back-up Slides

Vera Lüth - BABARICHEP04 - Beijing16 Scale Dependence of HQE in the Kinetic Scheme  Variation of the scale dependent HQE parameters simultaneously in the range  =[ ] GeV. (except c-quark mass  =[ ] GeV). *) Theoretical uncertainty from fitted HQE parameters  10% variation of O(1/m b 2 ) and O(1/m b 3 ) terms Corresponds to 0.1x10 -3 uncertainty in |V cb | *) Private communication: O. Buchmüller, P. Gambino, N. Uraltsev

Vera Lüth - BABARICHEP04 - Beijing17 Scale Dependence of HQE in the Kinetic Scheme *  The observed scale dependence of the predicted moments in the kinetic scheme is very small and even for scale variations in the range  =[ ] GeV (the default is  =1GeV),  the observed moment shifts are covered by an uncertainty of the O(1/m b 2 ) and O(1/m b 3 ) contributions of  10%.  Such an uncertainty translates to an error on |V cb | of 0.1x10 -3, compared to the assigned theoretical error of  |V cb | (theo-BABAR) =0.7x *) private communication: O. Buchmüller, P. Gambino, N. Uraltsev

Vera Lüth - BABARICHEP04 - Beijing18 |V cb | Measurements based on B  D* l Decays B A B AR

Vera Lüth - BABARICHEP04 - Beijing19 Back-up Slides