Wolfgang Menges, Queen Mary Semileptonic B Decays at BaBar Wolfgang Menges Queen Mary, University of London, UK Teilchenphysik Seminar, Bonn, 4 th May 06

Wolfgang Menges, Queen Mary Outline Introduction & motivation –CKM Matrix & Unitarity Triangle –PEP-II and BABAR –Why semileptonic decays? Measurements –Inclusive b  cl –Exlusive B  D*l –Inclusive b  ul –Exclusive B   l How  it all fits  together Outlook / Conclusions |V cb | |V ub |

Wolfgang Menges, Queen Mary B Decays – a Window on the Quark Sector The weak and mass eigenstates of the quarks are not the same The changes in base are described by unitarity transformations  Cabibbo Kobayashi Maskawa (CKM) matrix  The only 3rd generation quark we can study in detail V ud V us V ub V cd V cs V cb V td V ts V tb 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 | V ub | e -i  | V td | e -i  |V ub |

Wolfgang Menges, Queen Mary Unitarity Triangle Unitarity of V CKM –this is neatly represented by the familiar Unitarity Triangle –angles  can be measured with CPV of B decays –side from semileptonic B decays (|V cb | and |V ub |)

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

Wolfgang Menges, Queen Mary Consistency tests Compare measurements in the (  )-plane –If the SM is the whole story, they must all overlap The tells us that this is true (status winter 2005) –But still large enough for New Physics to hide Precision of sin2  from B factories dominates determination of  –Must improve the others to get more stringent tests Left side of the UT is –Uncertainty dominated by ca.  7% error on |V ub | Measurement of |V ub | is complementary to sin2 

Wolfgang Menges, Queen Mary Experiments

Wolfgang Menges, Queen Mary Collides 9 GeV e − against 3.1 GeV e + –E CM = GeV = mass of  (4S) –Boost  = 0.56 allows measurement of B decay times PEPII Asymmetric B Factory

Wolfgang Menges, Queen Mary The BaBar Detector 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)

Wolfgang Menges, Queen Mary Datasets: Run 1/2: ~80 fb -1 Run 3/4:~140 fb -1 Run 1-4:~220 fb -1 Data Taking Run 5 Run 4 Run 3 Run 2 Run 1 Run 5: collected: ~100 fb -1 expected: ~230 fb -1 Peak luminosity 1×10 34 /cm2/s  B B production ~10 Hz Belle: collected: ~560 fb -1 1 fb -1 -> 1.1 x 10 6 B B

Wolfgang Menges, Queen Mary KEKB and Belle Detector

Wolfgang Menges, Queen Mary Physics

Wolfgang Menges, Queen Mary Semileptonic B Decays c/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 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:

Wolfgang Menges, Queen Mary |V cb |

Wolfgang Menges, Queen Mary free-quark rate |V cb | & the „Atomic Physics“ of B Decays Contains b- and c-quark masses, m b and m c   2 related to kinetic energy of b-quark  G 2 related to chromomagnetic operator (B/B* mass splitting) Darwin term (ρ D 3 ) and spin-orbit interaction (ρ LS 3 ) enter at 1/m b 3  = scale which separates effects from long- and short-distance dynamics r = m c /m b ; z 0 (r), d(r): phase space factors; A EW = EW corrections; A pert = pert. corrections (  s j,  s k  0 )  Strategy: Global fit of all parameters  measure rate, moments (NB: Several HQE schemes exist; operators and coeff’s are scheme dependent) Inclusive rate described by Heavy Quark Expansion (HQE) in terms of a s (m b ) and 1/m b

Wolfgang Menges, Queen Mary Inclusive Decays: |V cb | from b  clv Fit moments of inclusive distributions: lepton energy hadronic mass –Determine OPE parameters and |V cb | Measurements from B Factories, CDF, Delphi We’ll look at an example: Hadronic Mass Moments

Wolfgang Menges, Queen Mary m ES [GeV/c 2 ] Events / 1.8 MeV/c 2 BABARBABAR L = 81 fb -1 Select events with a fully-reconstructed B –Use ca decay chains B  D(*) + (n  ) + (mK) –Flavor and momentum of “recoil” B are 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 remaining particles belong to X c –Improve m X with a kinematic fit (require m B2 =m B1 and m miss =0) –Yields resolution  (m X ) = 350 MeV Hadronic Mass Moments Fully reconstructed B  hadrons lepton v X B A B AR PR D69:111103

Wolfgang Menges, Queen Mary Hadronic Mass Moments Unmeasured particles  measured m X < true m X –Calibrate using simulation –Depends (weakly) on decay multiplicity and m miss –Validate in MC after applying correction –Validate on data using partially reconstructed D * ±  D 0  ±, tagged by the soft  ± and lepton Calculate 1 st -4 th mass moments with E cut = 0.9 … 1.6 GeV  input to HQE fit B A B AR Validation: high mass charm states M x 2 [GeV 2 /c 4 ] D,D* B A B AR PRL 93:011803

Wolfgang Menges, Queen Mary Calculation by Gambino & Uraltsev –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 Fit Parameters kinetic chromomagnetic Darwin spin-orbit Benson, Bigi, Mannel, Uraltsev, hep-ph/ Gambino, Uraltsev, hep-ph/ Benson, Bigi, Uraltsev, hep-ph/

Wolfgang Menges, Queen Mary 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  b s  b c W l v

Wolfgang Menges, Queen Mary 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 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 MC sys

Wolfgang Menges, Queen Mary Summary of |V cb | Results Excl: |V cb | = (40.9±1.0 exp F(1) ) x (D*lv) Incl: |V cb | = (42.0±0.2 exp ±0.4 HQE ±0.6  ) x The new BaBar form factors and |V cb | result are not included. Work is going on. B->D*lvB->Dlv

Wolfgang Menges, Queen Mary |V ub |

Wolfgang Menges, Queen Mary How to Measure b → ul Need to suppress the large b → c l  background (×50) Inclusive: –m u << m c  differences in kinematics –Maximum lepton energy 2.64 vs GeV –< 10 % of signal accessible How accurately do we know this fraction? Exclusive: –Explicit reconstruction of final-state hadrons –B   lv, B   lv, B   lv, B   lv, … –Need form factors (FF) to describe hadronization effects –Example: the rate for B   lv is How accurately do we know the FF ? (for vector mesons 3 FFs) Form Factor

Wolfgang Menges, Queen Mary 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 Lepton Endpoint Select electrons with 2.0 < E l < 2.6 GeV –Push below the charm threshold  Larger signal acceptance  Smaller theoretical error –Accurate subtraction of background is crucial! –S/B =1/15 for the endpoint E l > 2.0 GeV –Measure the partial BF L(fb -1) E (GeV)  B (10 -4 ) BABAR: – ± 0.41 stat ± 0.65 sys Belle: – ± 0.37 stat ± 1.53 sys CLEO: 92.2 – ± 0.15 stat ± 0.35 sys B A B AR total BF is ~2  10  3 B A B AR hep-ex/ MC signal b  ulv Data – bkgd. Data MC bkgd. b  clv

Wolfgang Menges, Queen Mary E l and q 2 Try to improve signal-to-background Use p v = p miss in addition to p e  calculate q 2 –Define s h max (E l, q 2 ) = the maximum m X squared Cutting at s h max < m D 2 removes b  clv while keeping most of the signal –S/B = 1/2 achieved for E l > 2.0 GeV and s h max < 3.5 GeV 2  B (10 -4 ) BABAR 80fb ± 0.33 stat ± 0.34 sys b  clvb  clv E l (GeV) q 2 (GeV 2 ) b  ulvb  ulv Smaller systematic errors B A B AR Extract signal normalize bkg Measured partial BF B A B AR PRL 95:111801

Wolfgang Menges, Queen Mary m X and q 2 Must reconstruct all decay products to measure m X or q 2 –Use (fully-reconstructed) hadronic B tag Suppress b → c l v by vetoing against D ( * ) decays –Reject events with K –Reject events with B 0 → D * + ( → D 0  + ) l − v Measure the partial BF in regions of (m X, q 2 ) – m X 8 GeV 2 :  B (10 -4 ) = 8.7 ± 0.9 stat ± 0.9 sys (211fb -1 ) B A B AR hep-ex/

Wolfgang Menges, Queen Mary Theory for b → ul Tree level rate must be corrected for QCD Just like b → cl …, and with similar accuracy … until limited experimental acceptance is considered Poor convergence of HQE in region where b → cl decays are kinematically forbidden Non-perturbative Shape Function (SF) must be used to calculate partial rates  = scale which separates effects from long- and short-distance dynamics A EW = EW corrections; A pert = pert. corrections (  s j,  s k  0 )

Wolfgang Menges, Queen Mary Light-cone momentum distribution of b quark: f(k + ) –Fermi motion of b quark inside B meson –Universal property of the B meson (to leading order); subleading SFs arise at each order in 1/m b Consequences: changes effective m b  smears kinematic spectra SF cannot be calculated  must be measured Rough features (mean, r.m.s.) are known Details, especially the tail, are unknown Shape Function – What is it ?

Wolfgang Menges, Queen Mary Extracting the Shape Function We can fit inclusive distributions from b → s  or b → clv decays with theory prediction –Must assume a functional form of f (k + ) Example: New calculation connects SF moments with b-quark mass m b and kinetic energy   2 (Neubert, PLB 612:13) –Determined precisely from b → s  and b  clv decays from b → s , and from b  c lv –Fit data from BABAR, Belle, CLEO, DELPHI, CDF: Use SF together with calculation of triple-diff. decay rate Bosch, Lange, Neubert, Paz (BLNP) to get |V ub | Buchmüller & Flächer hep-ph/

Wolfgang Menges, Queen Mary |V ub | from Branching Fraction Results of different calculations/ HQE parameters using the same partial branching fraction: For converting a branching fraction into |V ub |the phase space acceptance is needed: 3) |V ub |=(4.82±0.36 exp ±0.46 SF+theo )  ) |V ub |=(4.65±0.34 exp ±0.23 theo )  –0.38 SF 1) |V ub |=(5.00±0.37 exp ±0.46 SF ±0.28 theo )  ) |V ub |=(4.86±0.36 exp ±0.22 theo )  Example for m x /q 2 1) BLNP:BaBar B  X c l moments m b (SF) = 4.61 ± 0.08 GeV  π 2 (SF) = 0.15 ± 0.07 GeV 2 3) BLL: BaBar B  X c l moments m b (1S) = 4.74 ± 0.06 GeV 2) BLNP:Belle B  X s  spectrum m b (SF) = 4.52 ± 0.07 GeV  π 2 (SF) = 0.27 ± 0.23 GeV 2 4) DGE: HFAG average m b (MS) = 4.20 ± 0.04 GeV BLL – Bauer, Ligeti, Luke DGE – Anderson, Gardi

Wolfgang Menges, Queen Mary 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  7.6% Numbers rescaled by HFAG. SF parameters from hep-ex/ , predicted partial rates from BLNP 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 NEW! |V ub | [x10 -3 ]:

Wolfgang Menges, Queen Mary Summary

Wolfgang Menges, Queen Mary Exclusive b → u l v B → lvB → lv Inclusive b → ulv q2q2  l v,  l v ? b → s  Shape Function EE mbmb Inclusive b → clv mXmX ElEl HQE Fit mXmX ElEl WA duality |V ub | SSFs FF LCSRLQCD unquenching How it all fits together Exclusive b → c l v |V cb | B → DlvB → Dlv

Wolfgang Menges, Queen Mary Conclusions |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 – 7.6% accuracy achieved so far  5% possible? Close collaboration between theory and experiment is important Inclusive |V ub | : – Much exp. and theo. progress in the last 2 years Exclusive |V ub | : – Significant exp. progress in the last year, but further improvement in B →  FF calculations needed (also new calculations for B →  l  B →  l  B →  l – Accuracy of  for exclusive |V ub | in the next few years (?) Important to cross-check inclusive vs. exclusive results

Wolfgang Menges, Queen Mary The Unitarity Triangle: 2004  2005 Dramatic improvement in |V ub | sin2  went down slightly  Overlap with |V ub /V cb | smaller