V cb : experimental and theoretical highlights. Marina Artuso Syracuse University

Transcription

1 V cb : experimental and theoretical highlights Marina Artuso Syracuse University 1

2 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

3 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

4 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

5 F(1) V cb using B D*l ν 0.05 F(1)V cb V cb F(ω) Data Dispersion relation Caprini et al. 0.0 Belle ω 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 +/ (HFAG) 5

6 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) ultimate solution PDG (Artuso & Barberio) F(1)=0.91±

7 V cb Exclusive Averages ALEPH OPAL (partial reco) OPAL (excl) DELPHI (partial reco) BELLE CLEO DELPHI (excl) BABAR Average HFAG LP 003 /dof = 30.3/ F(1) V cb [10 ] excl V cb = (40.03±0.9 exp ±1.8 th )x10-3 7

8 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 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) 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

10 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

11 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± ±0.1 Sum rules Hoang 4.57± ±0.09 Sum rules Jamin,Pich ±0.06 Sum rules, no resummation Pineda,Yndurain (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 GeV Bigi-Mannel hep/ph/

12 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

13 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

14 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 ) 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 (GeV) I st Moment of Photon Energy (b s ) 14

15 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

16 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 [ % Hadron moments BABAR CLEO DELPHI [GeV] S m b χ =1 contours 3.5% difference Lepton moments CLEO DELPHI 00

17 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 = ±0.041 ± M X Moment (GeV ) 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 E lepton cut (GeV) 17

18 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