V cb : experimental and theoretical highlights Marina Artuso Syracuse University 1
The method b q W - e, µ, ν c or u q τ Ultimate goal: a precise determination of V cb The challenge: precise evaluation of the hadronic matrix element
The exclusive approach: HQET & V cb Heavy Quark Effective THEORY (HQET) (Isgur & Wise) QCD is flavor independent, so in the limit of infinitely heavy quarks q a q b occurs with unit form-factor [F(1)=1] when the quarks are moving with the same invariant 4-velocity, w=1. Example: for B D*l ν: All form-factors are related to one universal shape that can be measured Corrections to F(1) due to finite quark masses are calculable along with QCD corrections. These corrections are parameterized in a series: Σ n C n (1/m qi ) n, n=1, 3
V cb from B D*l ν HQET: dγ = K(w) F (w) V dw F( w) = F (1) g( w) D * The shape, g(w) not a clearly predictable quantity, but is constrained by theoretical bounds and measured form factors Experiments can measure dγ/dw To find V cb measure value of decay rate at w=1 F(1) V cb cb th 4
F(1) V cb using B D*l ν 0.05 F(1)V cb V cb F(ω) 0.04 0.03 Data Dispersion relation Caprini et al. 0.0 Belle ω 1 1.1 1. 1.3 1.4 1.5 Fit to function shape given by Caprini et al. Yields value of F(1) V cb & shape, parameterized by ρ. F(1) V cb = (36.7 ±0.8 ) 10-3 (HFAG) ρ =1.44 +/- 0.14 (HFAG) 5
Theoretical calculations of F(1) F(1)=η QED η QCD (1+δ 1/m + ) Lukes theorem: no δ 1/m corrections (would be in D l ν) η QED =1.007, η QCD =0.960±0.007 at two loops δ 1/m involves 1/m b, 1/m c, 1/m c m b First Lattice Gauge calculations (quenched-no light quark loops) 0.913 + + ultimate solution PDG (Artuso & Barberio) F(1)=0.91±0.05 0.04 0.017 0.017 0.030 6
V cb Exclusive Averages ALEPH 33.6.1 1.6 OPAL (partial reco) 38.4 1..4 OPAL (excl) 39.1 1.6 1.8 DELPHI (partial reco) 36.8 1.4.5 BELLE 36.7 1.9 CLEO 43.6 1.3 1.9 1.8 DELPHI (excl) 38.5 1.8.1 BABAR 34.1 0. Average 36.7 0.8 1.3 HFAG LP 003 /dof = 30.3/14 5 30 35 40 45-3 F(1) V cb [10 ] excl V cb = (40.03±0.9 exp ±1.8 th )x10-3 7
Another exclusive channel: B Dl ν Renewed interest on this channel: Lattice calculations QCD sum rules evaluation of G(1) Using G(1)=1.058 ±0.07 (Artuso-Barberio PDG00) V cb =(39.8 ±3.5 exp ±.9 th )x10-3 8
9 V cb from inclusive B X c l ν From B(B X c l ν) extract the experimental decay width: Compare with the theoretical prediction from Operator Product Expansion: + π α µ µ µ π = Γ π... (1) 0 0 3 5 3 1 1 19 z m m m m z V m G s b G b c b G cb b F c sl b c c sl l X b τ ν Γ ) B( Known phase space factors
The Heavy Quark Expansion Theoretical framework: Heavy Quark Expansion: Inclusive properties expressed as asymptotic expansion in terms of the energy release m b -m c Underlying theoretical accuracy: are all the uncertainties quantified? In particular ansatz of quark-hadron duality. Experimental determination of the Heavy quark expansion parameters, in particular: m b,m c at the relevant mass scale µ π [λ 1 ] kinetic energy of the b quark [λ ] expectation value of chromomagnetic op. µ G 10
m b : a multifaceted fundamental parameter Important for V c(u)b m kin (GeV) m b (m b ) method (GeV) Beneke,Signer, - 4.6±0.1 Sum rules Smirnov Melnikov 4.56±0.06 4.0±0.1 Sum rules Hoang 4.57±0.06 4.5±0.09 Sum rules Jamin,Pich - 4.19±0.06 Sum rules, no resummation Pineda,Yndurain - -0.04 4.44 +0.03 (1S) mass NRQCD - 4.8±0.03±0.03±0.10 Lattice HQET (n f =) Υ expansion Jet observables sensitive to b mass(lep) + pole mass m b pole m kin +0.55 GeV Bigi-Mannel hep/ph/0101 11
Problems with HQE Terms in 1/m b3 are multiplied by unknown functions; hard to evaluate error due to these higher order terms Duality is assumed: integrated over enough phase space the exclusive charm bound states & the inclusive hadronic result will match at quark-level. But no way to evaluate the error Appears to miss Λ b lifetime by 10±5% & b-baryon by 18 ±3%; however semileptonic decay may be easier Need experimental tests to evaluate errors Sharpen our knowledge of B meson semileptonic decays with high M x hadronic states Perhaps use V cb as a test? 1
How to Measure λ 1 & Λ Can determine λ 1 and Λ, and thus V cb by measuring moments in semileptonic decays Hadronic mass moments (ex: M X -M D, M D is spin-averaged D, D * mass) where B Xl ν Semileptonic moments Can also use b sγ decays, here we use the 1 st moment of the photon energy W - b t,c,u s,d γ 13
Hadronic Mass & Lepton Energy moments found in semileptonic decays detecting the neutrino using missing energy b sγ moment determination shown later Fitting this & other data Bauer, Ligeti, Luke Manohar find V cb =(40.8±0.9)x10-3 & m b =4.74±0.10 GeV (hep-ph/01007) Moments (CLEO) I I I I I I I I I I 1 (GeV ) 0 0.05 0.10 0.15 0.0 0.5 0.30 0.35 0.40 0.45 1 st Moment of Lepton Energy 1 Total Experimental Ellipse Λ=0.35 ±0.07 GeV λ 1 = -0.4±0.07 GeV exp errors only 0 th Moment of Lepton Energy 1 st Hadronic Mass Moment 0.50 0 0.1 0. 0.3 0.4 0.5 0.6 0.7 0.8 (GeV) I 163080-010 1 st Moment of Photon Energy (b s ) 14
BaBar Moments Result Using only BaBar hadronic moments & B sl : V cb =(4.1±1.0±0.7)x10-3 again within ±7% of D*l ν m 1S b =4.64±0.09±0.09 GeV (M x as function of lepton momentum, is now consistent with theory) 1σ contours M x moments 00 Doesn t include 1/m 15 b3 errors
Comparison of Hadron & Lepton Moments (BaBar) Lepton & Hadron moments differ somewhat. Does this indicate a Duality violation? Difference of 0. GeV in m b leads to 0% difference in V ub ] -3 V cb [10 44 43 4 41 40 39 9% Hadron moments BABAR CLEO DELPHI 00 38 4.4 4.6 4.8 [GeV] 16 5 1S m b χ =1 contours 3.5% difference Lepton moments CLEO DELPHI 00
New versus old CLEO & BaBar Moments Refined experimental results agree with theory. Can we draw any definitive conclusion? DELPHI NO E lep cut M x = 0.534 ±0.041 ± 0.074 M X Moment (GeV ) 0.9 0.8 0.7 0.6 0.5 0.4 0.3 New CLEO Previous CLEO 0. New BaBar Previous BaBar 0.1 HQET fixed by 1.5 GeV CLEO moment and B X s γ 1st photon energy moment 0 0. 0.4 0.6 0.8 1 1. 1.4 1.6 E lepton cut (GeV) 17
Summary of experimental results excl V cb =(40.03±0.9 exp ±1.8 th )x10-3 incl V cb =(41.5 ± 0.4 Γ ±0.4 λ1λ meas ±0.9 th )x10-3 Future prospects: Precise form factor calculations from lattice gauge calculation sl More extensive exploration of inclusive semileptonic decay observables: in particular high M x component More detailed evaluation & validation of theoretical errors A measure of the consistency between theoretical approaches 18