Wolfgang Menges, Queen Mary Measurement of the CKM Sides at the B-Factories Wolfgang Menges On behalf of the BaBar and Belle Collaborations Queen Mary, University of London, UK CKM matrix and Unitarity Triangle Semileptonic B decays (|V ub |, |V cb |) Summary

Wolfgang Menges, Queen Mary 2 weak and mass eigenstates of the quarks are not the same changes in base are described by unitarity transformations Cabibbo Kobayashi Maskawa (CKM) matrix 1 - c 2 c A c 3 (  - i  ) - c 1 - c 2 /2 A c 2 A c 3 ( 1 -  - i  ) - A c O( c 4 ) [ c = sin  c ] CP violation CKM Matrix and Unitarity Triangle angles  can be measured with CPV of B decays sides from: - semileptonic B decays (|V cb | and |V ub |) - rare B decays (|V ts |, |V td | and |V ub |) Wolfenstein parametrisation See talk by Y. Kwon See talk by Y. Iwasaki

Wolfgang Menges, Queen Mary 3 Unitarity Triangle Fits B d mixing:  m d B s mixing:  m s /  m d J/  K 0 : sin2  b  ul : |V ub | b  cl : |V cb | kaon decays: ε K charmless two-body:  interference in B  DK:  Sides complementary to angles |V ub |/|V cb | complementary to sin2 

Wolfgang Menges, Queen Mary 4 B Factories Čerenkov Detector (DIRC) 144 quartz bars PMTs 1.5 T solenoid ElectroMagnetic Calorimeter 6580 CsI(Tl) crystals Drift CHamber 40 stereo layers Instrumented Flux Return iron/RPCs/LSTs (muon/neutral hadrons) Silicon Vertex Tracker 5 layers, double sided strips e + (3.1 GeV) e - (9 GeV) BaBar Detector PEPII: L peak ~ cm -2 s -1 L int ~ 330 fb -1 KEKB: L peak ~ cm -2 s -1 L int ~ 560 fb -1 TOF counter

Wolfgang Menges, Queen Mary 5 Semileptonic B Decays u quark turns into one or more hadrons B → Xlv decays are described by 3 variables q 2 = lepton-neutrino mass squared m X = hadron system mass E l = lepton energy P + = E X - |p X | Semileptonic B decays allow measurement of |V cb | and |V ub | from tree level processes. Presence of a single hadronic current allows control of theoretical uncertainties. b  clv is background to b  ulv: favoured by theory

Wolfgang Menges, Queen Mary 6 |V cb | from b  clv decays

Wolfgang Menges, Queen Mary 7 Operator Product Expansion (OPE): double expansion in  s and m b -1 Fit moments of inclusive distributions –lepton energy, hadron invariant mass –Determine OPE parameters and |V cb | Measurements from B Factories, CDF, Delphi Recent measurements from Belle: Depends on scheme, order of expansion Benson, Bigi, Mannel, Uraltsev, hep-ph/ Gambino, Uraltsev, hep-ph/ Benson, Bigi, Uraltsev, hep-ph/ Electron energy, hep-ex/ Hadronic mass, hep-ex/ fb -1 Inclusive Decays: |V cb | from b  clv

Wolfgang Menges, Queen Mary 8 Results Global fit in the kinetic scheme |V cb | < 2% m b < 1% m c = 5% Buchmüller, Flächer: hep-ph/ |V cb | =(41.96± 0.23± 0.35± 0.59) BR clv = 10.71± 0.10± 0.08% m b = 4.590± 0.025± 0.030GeV m c = 1.142± 0.037± 0.045GeV μ π 2 = 0.401± 0.019± 0.035GeV 2 μ G 2, ρ D 3,ρ LS 3 exp HQE  SL b → s  b → clν combined Based on: Babar: PRD69, (2004) PRD69, (2004) PRD72, (2005) hep-ex/ Belle: PRL93, (2004) hep-ex/ CLEO: PRD70, (2004) PRL87, (2001) CDF: PRD71, (2005) DELPHI: EPJ C45, 35 (2006) Use inputs from BaBar, Belle, CLEO, CDF & DELPHI: b->clv and b->s  aiai b s  b c W l v

Wolfgang Menges, Queen Mary 9 Shape of F(w) unknown Parametrized with  2 (slope at w = 1) and form factor ratios R 1, R 2 ~ independent on w h A1 expansion a-la Caprini-Lellouch-Neubert Exclusive |V cb | and Form Factors Reconstruct B -> D* + ev as D* +  D 0  + with D 0  K  G(w) known phase space factor F(w) Form Factor (FF) w = D* boost in B rest frame BABAR hep-ex/ F(1)=1 in heavy quark limit; lattice QCD says: F(1) = Hashimoto et al, PRD 66 (2002) > measure form factors from multi-dimensional fit to diff rate -> measure |V cb | with Nucl. Phys. B 530, 153 (1998)

Wolfgang Menges, Queen Mary 10 B  D*l Form Factors and |V cb | hep-ex/ Using latest form factors with previous BaBar analysis: PRD71, (2005) |V cb | = (37.6±0.3±1.3 ) x Reducing FF error: 2.8% -> 0.5% Total sys error: 4.5% -> 3.5% 80 fb -1 Factor 5 improvement of FF uncertainty from previous CLEO measurement (1996). 1D projections of fit result R 1 = ± ± ± R 2 = ± ± ±  2 = ± ± ± stat sys theo

Wolfgang Menges, Queen Mary 11 Summary of |V cb | Results |V cb |[x10 -3 ] from B->D*lv: 40.9±1.0 exp F(1) |V cb |[x10 -3 ] from b->clv: 42.0±0.2 exp ±0.4 HQE ±0.6  The new BaBar form factors are not included. Work is going on B->D*lv  good agreement! New BaBar result

Wolfgang Menges, Queen Mary 12 |V ub | from b  ulv decays

Wolfgang Menges, Queen Mary 13 Inclusive b → ul Strategies Use kinematic cuts to separate b  ulv from b  clv decays: Not to scale! smaller acceptance -> theory error increase OPE breaks down shape function to resum non-pert. corrections measure partial branching fraction  B get predicted partial rate  from theory Experimental resolution not included!

Wolfgang Menges, Queen Mary 14 BaBar: L = 80 fb -1, E l = GeV 4.44 ± 0.25 exp SF ± 0.22 theo Belle: L = 27 fb -1, E l = GeV 5.08 ± 0.47 stat ± 0.42 SF theo Select electrons with 2.0(1.9) < E l < 2.6 GeV –Push below the charm threshold  Larger signal acceptance  Smaller theoretical error –Accurate subtraction of background is crucial! off-resonance data events with p e > 2.8 GeV fit b->clv composition in bkg subtraction –Measure the partial BF Lepton Endpoint B A B AR B A B AR PRD73, (2006) MC signal b  ulv Data – bkgd. Data MC bkgd. b  clv |V ub | [10 -3 ]:

Wolfgang Menges, Queen Mary 15 fully reconstruct one B in hadronic decay mode study the recoiling B -> known momentum and flavour access to all kinematic variables (m x, q 2, P + ) m X <1.7GeV, q 2 >8GeV |V ub |= hep-ex/ M BB P + =E X -|p X | <0.66 m X 8GeV m X <1.7GeV hep-ex/ M BB |V ub | = (4.70 ± 0.24 stat ± 0.28 syst ± 0.20 SF theo ) × |V ub | = (4.09 ± 0.19 stat ± 0.20 syst ± 0.18 SF theo ) × |V ub | = (4.19 ± 0.20 stat ± 0.30 syst ± 0.24 SF theo ) × lepton v X Hadronic B Tag 253M BB % 9% 11% error[%]

Wolfgang Menges, Queen Mary 16 Status of Inclusive |V ub | |V ub | world average winter 2006 Experimental Error  4.5% SF parameters (m b,   2 )  4.1% Theory Error  4.2% |V ub | determined to  7.4% BLNP: Shape Function PRD72:073006(2005) 4.45  0.20 exp  0.18 SF  0.19 theo Andersen-Gardi: DGE JHEP0601:097(2006) 4.41  0.20 exp  0.20 theo |V ub | [x10 -3 ]: NEW! Numbers rescaled by HFAG. SF parameters from hep-ex/ , predicted partial rates from BLNP

Wolfgang Menges, Queen Mary 17 theory uncertainties relate charmless SL rate to b → s  spectrum reduced dependence from shape function Weight function Leibovich, Low, Rothstein hep-ph/ , m X cut LLR : M X < 1.67 GeV: |V ub | = (4.43 ± 0.38 stat ± 0.25 syst ± 0.29 theo ) OPE: M X < 2.50 GeV: |V ub | = (3.84 ± 0.70 stat ± 0.30 syst ± 0.10 theo ) hep-ex/ L = 80 fb -1 Reducing Model Dependence following Acceptance: 72% 98%

Wolfgang Menges, Queen Mary 18 Exclusive b  ul measure specific final states, e.g., B →  lv –can achieve good signal-to-background ratio –branching fractions are O(10 -4 )  statistics limited need form factors to extract |V ub | –theo. uncertainties complementary to inclusive approach! f + (q 2 ) calculations exist based on: –Lattice QCD (q 2 > 15 GeV 2 )  11% uncertainty hep-lat/ , PRD73, (2006) –Light Cone Sum Rules (q 2 < 14 GeV 2 )  10% uncertainty PRD71, (2005), PRD71, (2005) –Quark models (ISGW2) … and other approaches PRD52, 2783(1995) One FF for B →  lv (massless lepton) Need to measure q 2

Wolfgang Menges, Queen Mary fb -1   l d  /dq 2 /  tot x 10 4 q2q2 recent LQCD and LCSR calculations agree well with data ISGW II shows marginal agreement  l also measured, exp. error still large PRD 72: q 2 Distributions and FF Calculations  l  — Ball’01  — ISGW2  — UKQCD hep-ex/ D*lv tag select B ->  lv and  lv without reconstructing other B –well-identified high energetic lepton,                  –missing momentum and energy in event  reconstruct neutrino 76 fb -1

Wolfgang Menges, Queen Mary 20 Status of Exclusive |V ub | Use BF and FF predictions to calculate |V ub |. Incl |V ub | (BLNP) LQCD LCSR LQCD quenched LQCD Good agreement! untagged SL tag tagged FF calculations dominate error on |V ub |!

Wolfgang Menges, Queen Mary 21 Summary

Wolfgang Menges, Queen Mary 22 |V cb | determined with high precision (2%)  Now |V ub | is important! Precise determination of |V ub | complements sin2  to test the validity of the Standard Model Close collaboration between theory and experiment is important Inclusive |V ub | : - 7.4% accuracy achieved so far  5% possible? –much experimental and theoretical progress in the last 2 years Exclusive |V ub | : - Significant exp. progress in the last year - FF calculations need to improve Important to cross-check inclusive vs. exclusive results The Unitarity Triangle

Wolfgang Menges, Queen Mary 23 Backup

Wolfgang Menges, Queen Mary 24 CLEO Photon Moments Buchmüller, Flächer hep-ph/ th moment 2 nd moment Photon Spectrum b→s  helps too… Sum of exclusive final states PRL87:251807(2001)PRL93:061803(2004)hep-ex/ PRD72:052004(2005)