Measurement of |V ub | using Inclusive Semileptonic B Decays at the B-Factories Wolfgang Ehrenfeld University of Hamburg/DESY, Germany • Theoretical Calculations • Experimental Methods • Latest Results • Uncertain Future
Semileptonic B Decays ν Semileptonic B decays allow measurement of |V cb | and |V ub | from tree level processes. − l W b , c u , V V Presence of a single hadronic current allows cb ub control of theoretical uncertainties. Wolfgang Ehrenfeld, Univ. of Hamburg/DESY b → clv is background to b → ulv: 2 Γ → ν ( ) 1 V l b u ≈ ≈ ub Γ → ν 2 ( ) 50 l b c V cb B → Xlv decays are E l = lepton energy E l = lepton energy described by 3 variables l ν q 2 = lepton-neutrino mass squared q 2 = lepton-neutrino mass squared B m X = hadron system mass m X = hadron system mass X u quark turns into u one or more hadrons favoured P + = E X - |p X | P + = E X - |p X | 2 by theory
B Factories PEPII: L peak ~ 1.2 34 cm -2 s -1 TOF counter L int ~ 390 fb -1 Wolfgang Ehrenfeld, Univ. of Hamburg/DESY ElectroMagnetic BaBar Detector Calorimeter 6580 CsI(Tl) crystals 1.5 T solenoid KEKB: Č erenkov Detector e + (3.1 GeV) (DIRC) L peak ~ 1.7 10 34 cm -2 s -1 144 quartz bars 11000 PMTs L int ~ 690 fb -1 e - (9 GeV) Drift CHamber 40 stereo layers Instrumented Flux Return iron/RPCs/LSTs Silicon Vertex Tracker 3 (muon/neutral hadrons) 5 layers, double sided strips
Luminosity at the B-factories BaBar: 1.2x10 -34 -> 17 fb -1 /month • Run 1-2: ~94 fb -1 • Run 3-4: ~148 fb -1 ~242 fb -1 • Run 5: Wolfgang Ehrenfeld, Univ. of Hamburg/DESY ~149 fb -1 ~391 fb -1 • Run 6/7: ~550 fb -1 ~910 fb -1 Belle: 1.7x10 -34 -> 29 fb -1 /month • Now: ~694 fb -1 • At least: ~1000 fb -1 4
Experimental Approach The standard approach is to choose a method to tag the semileptonic event and a set of kinematic variables to suppress the large b->clv background. From this a partial branching fraction is measured. Tagging: low purity, Wolfgang Ehrenfeld, Univ. of Hamburg/DESY • untagged high statistics • semileptonic tag • hadronic tag q 2 (GeV 2 ) high purity, Points are b � u ℓ ν low statistics simulation Suppress b->clv events: low • E e acceptance • E e /q 2 • m x , m x /q 2 , p + b � c allowed high acceptance E e (GeV) 5
Traditional Theoretical Calculations Take your favorite theory calculations ( ) Δ → ν l B B X and convert the partial branching fraction = u V Δ ζ ⋅ τ ub into |Vub|: B OPE gives good results for full phase space but breaks down in the so-called shape function (SF) region (low m x and low q 2 ). There are three approaches to solve this problem: Wolfgang Ehrenfeld, Univ. of Hamburg/DESY BLNP (Bosch, Lange, Neubert, Paz) PRD72:073006(2005) Handle SF region by introducing a parameterization • Shape function form is unknown -> assume form • Shape function moments are related to HQE parameters (m b , μ π 2 ) -> can be measured • Leading shape functions universal in b->clv, b->ulv, b->s γ • Subleading shape functions depend on decay BLL (Bauer, Ligeti, Luke) PRD64:113004(2001) OPE based calculation excluding the region of sizable non-perturbative effects. • Residual dependence on SF effects • Only depend on m b • Only valid in non-SF region (m x < m D and q 2 > 8) DGE/AG (Anderson, Gardi) JHEP0601:097(2006) Using Dressed Gluon Exponentiation (DGE) to convert on-shell b-quark calculations into meson decay spectra • Only depend on m b 6
Alternative Approaches The fact that the leading shape functions are universal to first order allows the direct use of information from either b->clv or b->s γ decays in the measurement of |V ub |. The spectrum of a kinematic variable in b->ulv decays is relate to the spectrum in b->clv or b->s γ decays using a weighting function. Wolfgang Ehrenfeld, Univ. of Hamburg/DESY Results! LLR (Leibovich, Low, Rothstein) PRD61:053005(2000), PLB513:83(2001) • Relates |V ub | 2 /|V tb V ts * | to m x or E l spectrum in b->ulv and E γ spectrum in b->s γ • Includes higher order corrections Neubert PLB513:88(2001) • Similar to LLR BLNP/Lange JHEP0601:104(2006) • Relates |V ub | to the measured partial BF(b->ulv) and normalised E γ spectrum in b->s γ decays BFMP (Boos, Feldmann, Mannel, Pecjak) JHEP0605:056(2006) • Relate |V ub |/|V cb | to measured spectrum in b->ulv and b->clv decays 7
Untagged Lepton Endpoint Select electrons with E low < E l < 2.6 GeV – Push below the charm threshold � Larger signal acceptance B A B AR � Smaller theoretical error – Accurate subtraction of b->clv background is crucial • off-resonance data Data • events with p e > 2.8 GeV • fit b->clv composition in bkg subtraction Wolfgang Ehrenfeld, Univ. of Hamburg/DESY MC bkgd. – Measure partial BF b → c l v |V ub | [10 -3 ]: BLNP BaBar: E l = 2.0-2.6 GeV PRD73:012006(2006) Data – bkgd. 11% 88M B B 4.39 ±0.16 stat ±0.19 exp ±0.32 SF ±0.24 theo HFAG MC signal Belle: E l = 1.9-2.6 GeV PLB621:28(2005) b → u l v 12% +0.17 29M B B 4.82 ±0.11 stat ±0.44 exp SF ±0.23 theo -0.23 HFAG CLEO: E l = 2.1-2.6 GeV PRL88:231803(2002) 15% 9.7M B B +0.20 4.09 ±0.14 stat ±0.46 exp SF ±0.26 theo 8 -0.27 HFAG
Untagged 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 q 2 (GeV 2 ) max < m D 2 removes 2 5 • Cutting at s h Wolfgang Ehrenfeld, Univ. of Hamburg/DESY b → clv while keeping most of the signal 2 0 – S/B = 1/2 achieved for E l > 2.0 GeV and b → u l v 1 5 max < 3.5 GeV 2 s h 1 0 – Measured partial BF 5 b → c l v 0 . 5 1 1 . 5 2 2 . 5 E l (GeV) |V ub | [10 -3 ]: BLNP B A B AR BaBar: 88M B B PRL95:111801(2005), PRL97:019903(2006) +0.23 12% 4.57 ± 0.22 stat ± 0.22 exp SF ± 0.30 theo -0.31 HFAG 9 Extract signal normalize bkg Extract signal normalize bkg
Hadronic B Tag • fully reconstruct one B in hadronic decay mode v • study the recoiling B -> known momentum and flavour • access to all kinematic variables (m x , q 2 , P + ) lepton X Wolfgang Ehrenfeld, Univ. of Hamburg/DESY 253M B B error[%] +0.23 10% |V ub | = (4.70 ± 0.24 stat ± 0.28 syst ± 0.20 SF theo ) × 10 -3 m X <1.7GeV, q 2 >8GeV -0.24 253M B B +0.14 9% |V ub | = (4.09 ± 0.19 stat ± 0.20 syst ± 0.18 SF theo ) × 10 -3 m X <1.7GeV -0.16 PRL95:241801(2005) +0.14 11% |V ub | = (4.19 ± 0.20 stat ± 0.30 syst ± 0.24 SF theo ) × 10 -3 P + =E X -|p X | <0.66 -0.15 +0.23 210M B B m X <1.7GeV, 11% |V ub |= (4.75 ±0.25 stat ±0.25 sys SF ±0.25 theo ) x 10 -3 10 -0.31 q 2 >8GeV hep-ex/0507017 HFAG
Reducing Model Dependence NEW! • relate charmless SL rate to b → s γ spectrum 2 Γ → γ Following LLR ( ) V d B X ∫ Γ → ν = ( ) ub ( ) l s B X W E dE γ γ u 2 dE V PRD61:053005(2000) γ ts PLB513:83(2001) Weight function • reduced dependence from shape function Wolfgang Ehrenfeld, Univ. of Hamburg/DESY theory uncertainties L = 80 fb -1 m X cut Acceptance: 88M B B PRL96:221801(2006) 12% 72% LLR : M X < 1.67 GeV: |V ub | = (4.43 ± 0.38 stat ± 0.25 syst ± 0.29 theo ) 10 -3 98% 20% OPE: M X < 2.50 GeV: |V ub | = (3.84 ± 0.70 stat ± 0.30 syst ± 0.10 theo ) 10 -3 11
Reinterpretation of Lepton Endpoint Take the partial branching fraction from the BaBar lepton endpoint measurement and use the BaBar semi-inclusive photon spectrum from b->s γ and calculate |V ub |: • Try different methods (LLR, Neubert, BLNP/Lange) • Try different cuts Wolfgang Ehrenfeld, Univ. of Hamburg/DESY Do we see the effect of SSF here? 12
Status of Inclusive | V ub | | V ub | world average summer 2006 |V ub | determined to ± 7.3% Wolfgang Ehrenfeld, Univ. of Hamburg/DESY Statistical Error ± 2.2% Experimental Error ± 3.7% SF parameters (m b , μ π 2 ) ± 4.1% ± 4.2% Theory Error |V ub | [x10 -3 ]: BLNP 4.45 ± 0.20 exp ± 0.18 SF ± 0.19 theo Numbers rescaled by HFAG. SF parameters from hep-ex/0507243, 13 predicted partial rates from BLNP
Comparision of Theory m x -q 2 Measurements All Measurements 6% theory error Wolfgang Ehrenfeld, Univ. of Hamburg/DESY 6.7% theory error 4.5% theory error 4.7% theory error 6.5% theory error 7.4% theory error Perfect agreement! Good agreement! Can BLL improve? Why is DGE so good? 14
Theoretical Uncertainties Breakdown BLNP: What can we • Shape Function 4.2% -> 2.1 % improve in the • Subleading shape function 3.8% -> ? % future? • Weak Annihilation 1.9% -> ? % total: 6.0% -> Can we half the DGE: errors on Wolfgang Ehrenfeld, Univ. of Hamburg/DESY Δ m b and Δμ π 2 ? • m b 1.2% -> 0.6% • α s 1.0% • Total semileptonic B width 3.0% -> ? % What to do with • Method/scale of matching theory the SFF? 2.9% -> ? % total: 4.5% -> BLL: Measurement of / • Residual shape function effects 3.0% -> ? % limit on WA • Higher order terms in α s expansion 3.0% -> ? % • m b 4.5% -> 2.2% BLL: Improve • 3 rd order terms in OPE expansion 4.0% -> 2.0% calculations? total: 7.4% -> 15
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