Measurement of the CKM Sides at the B-Factories

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

CKM Matrix and Unitarity Triangle V V ud V V cd weak and mass eigenstates of the quarks are not the same changes in base are described by unitarity transformations Cabibbo Kobayashi Maskawa (CKM) matrix η ub cb V V + V V + V V = 0 ud ub cd cb td tb γ ρ α V V td V V cd β tb cb 1 Wolfenstein parametrisation 1-λ c λ c A λ c3 (ρ-iη) -λ c 1- λ c / A λ c Aλ c3 (1- ρ-iη) -A λ c 1 CP violation + O(λ c 4 ) [ λ c = sinθ c ] angles α, β, γ 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 ) See talk by Y. Iwasaki See talk by Y. Kwon

Unitarity Triangle Fits J/ψK 0 : sinβ interference in B DK: γ 3 kaon decays: ε K b ulν: V ub b clν: V cb charmless two-body: α ρ http://ckmfitter.inp3.fr B d mixing: m d B s mixing: m s / m d Sides complementary to angles V ub / V cb complementary to sinβ

B Factories PEPII: Lpeak ~ 1034cm-s-1 TOF counter Lint ~ 330 fb-1 BaBar Detector ElectroMagnetic Calorimeter 6580 CsI(Tl) crystals 1.5 T solenoid Čerenkov Detector (DIRC) 144 quartz bars 11000 PMTs e- (9 GeV) Instrumented Flux Return iron/rpcs/lsts (muon/neutral hadrons) 4 e+ (3.1 GeV) Drift CHamber 40 stereo layers Silicon Vertex Tracker 5 layers, double sided strips KEKB: Lpeak ~ 1.6 1034cm-s-1 Lint ~ 560 fb-1

Semileptonic B Decays b V cb W, V ub ν c, u l 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. 5 B Xlv decays are described by 3 variables B c/u quark turns into one or more hadrons b clv is background to b ulv: l ν X u Γ( b ulν ) V 1 Γ ub ( b clν ) V 50 cb E l = lepton energy q = lepton-neutrino mass squared m X = hadron system mass P + = E X - p X favoured by theory

6 V cb from b clv decays

Inclusive Decays: V cb from b clv Operator Product Expansion (OPE): double expansion in α s and m b -1 5 GFmb Γclν = Vcb (1+ Αew )ΑpertΑnonpert V f (m,m,a 3 cb OPE b c 19π Fit moments of inclusive distributions lepton energy, hadron invariant mass n < X > (E Determine OPE parameters and V cb Measurements from B Factories, CDF, Delphi Recent measurements from Belle: Hadronic mass, hep-ex/0509013 140 fb -1 140 fb -1 Benson, Bigi, Mannel, Uraltsev, hep-ph/0410080 Gambino, Uraltsev, hep-ph/0401063 Benson, Bigi, Uraltsev, hep-ph/0410080 i cut ) ) = (X X dγ dx Electron energy, hep-ex/0508056 Depends on scheme, order of expansion 0 ) n dγ dx dx dx 7

Results Global fit in the kinetic scheme V cb = (41.96 exp HQE Γ SL ± 0.3 ± 0.35 ± 0.59) 10-3 8 V cb < % m b < 1% m c = 5% Buchmüller, Flächer: hep-ph/050753 Based on: Babar: PRD69, 111103 (004) PRD69, 111104 (004) PRD7, 05004 (005) hep-ex/0507001 Belle: PRL93, 061803 (004) hep-ex/0508005 CLEO: PRD70, 0300 (004) PRL87, 51807 (001) CDF: PRD71, 051103 (005) DELPHI: EPJ C45, 35 (006) b a i BR clv = m b = m c = µ π = µ G, ρ D 3,ρ LS 3 10.71 4.590 1.14 0.401 Use inputs from BaBar, Belle, CLEO, CDF & DELPHI: b->clv and b->sγ W c l v b γ ± 0.10 ± 0.05 ± 0.037 ± 0.019 s ± 0.08 ± 0.030 ± 0.045 ± 0.035 % GeV GeV GeV b sγ b clν combined

Exclusive V cb and Form Factors Reconstruct B -> D* + ev as D* + D 0 π + with D 0 Kπ BABAR hep-ex/06003 G(w) known phase space factor F(w) Form Factor (FF) w = D* boost in B rest frame 9 F(1)=1 in heavy quark limit; lattice QCD says: F(1) = 0.919 +0.030 Shape of F(w) unknown Parametrized with ρ (slope at w = 1) and form factor ratios R 1, R ~ independent on w h A1 expansion a-la Caprini-Lellouch-Neubert dq * ( B Dlυ) = V f ( q, θ, θ, χ, ρ, R, R ) dγ d cosθ d cosθ dχ l -> measure form factors from multi-dimensional fit to diff rate -> measure V cb with V cb l V 1-0.035 Hashimoto et al, PRD 66 (00) 014503 l l W Nucl. Phys. B 530, 153 (1998) B s D* V D

B D*lν Form Factors and V cb stat sys theo R 1 = 1.396 ± 0.060 ± 0.035 ± 0.07 R = 0.885 ± 0.040 ± 0.0 ± 0.013 1D projections of fit result hep-ex/06003 ρ = 1.145 ± 0.059 ± 0.030 ± 0.035 10 Factor 5 improvement of FF uncertainty from previous CLEO measurement (1996). Using latest form factors with previous BaBar analysis: PRD71, 05150(005) +1.5 V cb = (37.6±0.3±1.3 ) x 10-3 -1.3 Reducing FF error:.8% -> 0.5% Total sys error: 4.5% -> 3.5% 80 fb -1 80 fb -1

Summary of V cb Results The new BaBar form factors are not included. Work is going on. 11 V cb [x10-3 ] from B->D*lv: +1.1-1.3 40.9±1.0 exp F(1) V cb [x10-3 ] from b->clv: 4.0±0. exp ±0.4 HQE ±0.6 Γ good agreement! New BaBar result B->D*lv

1 V ub from b ulv decays

Inclusive b ulν : Strategies Use kinematic cuts to separate b ulv from b clv decays: Experimental resolution not included! b b c u E l b smaller acceptance -> theory error increase OPE breaks down shape function to resum non-pert. corrections measure partial branching fraction B get predicted partial rate ζ from theory b c u q b V u ub b = c B Not to scale! m X ( B X lν ) ζ τ B u 13

14 Lepton Endpoint Select electrons with.0(1.9) < E l <.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 >.8 GeV fit b->clv composition in bkg subtraction Measure the partial BF V ub [10-3 ]: BaBar: L = 80 fb -1, E l =.0-.6 GeV +0.4 4.44 ± 0.5 exp SF ± 0. theo -0.38 Belle: L = 7 fb -1, E l = 1.9-.6 GeV +0.6 5.08 ± 0.47 stat ± 0.4 SF -0.3theo BABAR PRD73, 01006 (006) MC bkgd. b clv BABAR Data Data bkgd. MC signal b ulv

Hadronic B Tag fully reconstruct one B in hadronic decay mode study the recoiling B -> known momentum and flavour access to all kinematic variables (m x, q, P + ) v lepton X hep-ex/0505088 m X <1.7GeV, q >8GeV 53M B 53M B m X <1.7GeV P + =E X - p X <0.66 +0.3-0.4 V ub = (4.70 ± 0.4 stat ± 0.8 syst ± 0.0 SF theo ) 10-3 +0.14-0.16 V ub = (4.09 ± 0.19 stat ± 0.0 syst ± 0.18 SF theo ) 10-3 +0.14-0.15 error[%] V ub = (4.19 ± 0.0 stat ± 0.30 syst ± 0.4 SF theo ) 10-3 10% 9% 11% 15 10M B hep-ex/0507017 m X <1.7GeV, q >8GeV V ub =

Status of Inclusive V ub V ub world average winter 006 V ub determined to ±7.4% 16 Numbers rescaled by HFAG. SF parameters from hep-ex/050743, predicted partial rates from BLNP Experimental Error SF parameters (m b,µ π ) Theory Error V ub [x10-3 ]: ±4.5% ±4.1% ±4.% BLNP: Shape Function PRD7:073006(005) 4.45 ± 0.0 exp ± 0.18 SF ± 0.19 theo NEW! Andersen-Gardi: DGE JHEP0601:097(006) 4.41 ± 0.0 exp ± 0.0 theo

Reducing Model Dependence relate charmless SL rate to b sγ spectrum reduced dependence from shape function ( ) ( ) V ub s u W ( E ) d Γ B B X X γ Γ lν = de γ V de ts γ γ Weight function 17 L = 80 fb -1 m X cut theory uncertainties hep-ex/0601046 following Leibovich, Low, Rothstein hep-ph/000514,0105066 LLR : M X < 1.67 GeV: V ub = (4.43 ± 0.38 stat ± 0.5 syst ± 0.9 theo ) 10-3 OPE: M X <.50 GeV: V ub = (3.84 ± 0.70 stat ± 0.30 syst ± 0.10 theo ) 10-3 Acceptance: 7% 98%

Exclusive b ulν measure specific final states, e.g., B πlv can achieve good signal-to-background ratio branching fractions are O(10-4 ) statistics limited 18 need form factors to extract V ub dγ( B πlν ) dq G 4π F = 3 V ub 3 p π f+ ( q ) One FF for B πlv (massless lepton) Need to measure q theo. uncertainties complementary to inclusive approach! f + (q ) calculations exist based on: Lattice QCD (q > 15 GeV ) 11% uncertainty hep-lat/0409116, PRD73, 07450(006) Light Cone Sum Rules (q < 14 GeV ) 10% uncertainty PRD71, 014015(005), PRD71, 01409(005) Quark models (ISGW) and other approaches PRD5, 783(1995)

q Distributions and FF Calculations select B -> πlv and ρlv without reconstructing other B well-identified high energetic lepton, π ±, π 0 (γγ), ρ 0 (π + π ), ρ ± (π ± π 0 ) missing momentum and energy in event reconstruct neutrino 19 PRD 7:05110 πlν dγ/dq /Γ tot x 10 4 1 0.8 0.6 0.4 0. 0 53 fb -1 π lν Ball 01 ISGW UKQCD hep-ex/0508018 0 5 10 15 0 D*lv tag q 76 fb -1 recent LQCD and LCSR calculations agree well with data ISGW II shows marginal agreement ρlν also measured, exp. error still large

Status of Exclusive V ub Use BF and FF predictions to calculate V ub. tagged LCSR 0 Good agreement! SL tag untagged Incl V ub (BLNP) FF calculations dominate error on V ub! LQCD LQCD quenched LQCD

1 Summary

The Unitarity Triangle V cb determined with high precision (%) Now V ub is important! Precise determination of V ub complements sinβ 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 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 V cb determined with high precision (%) Now V ub is important! Precise determination of V ub complements sinβ 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 years Exclusive V ub : - Significant exp. progress in the last year - FF calculations need to improve Important to cross-check inclusive vs. exclusive results 3

The Unitarity Triangle V cb determined with high precision (%) Now V ub is important! Precise determination of V ub complements sinβ 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 years Exclusive V ub : - Significant exp. progress in the last year - FF calculations need to improve Important to cross-check inclusive vs. exclusive results 4

5 Backup

b sγ helps too PRL87:51807(001) PRL93:061803(004) hep-ex/0507001 Photon Spectrum Photon Moments 1 th moment CLEO Buchmüller, Flächer hep-ph/050753 nd moment PRD7:05004(005) Sum of exclusive final states 6