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

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

2 The method 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  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:  n C n (1/m qi ) n, n=1, 2…

4 V cb from B  D* l HQET: The shape, not a clearly predictable quantity, but is constrained by theoretical bounds and measured form factors Experiments can measure d  /dw To find V cb measure value of decay rate at w=1  F(1)|V cb | th

5 F(1)|V cb | using B  D* l Fit to function shape given by Caprini et al. Yields value of F(1)|V cb | & shape, parameterized by  2. F(1)|V cb |= (36.7  0.8 )  10 -3 (HFAG)  2 =1.44 +/- 0.14 (HFAG) F(1)V cb Belle

6 Theoretical calculations of F(1) F(1)=  QED  QCD (1+  1/m 2 +…) –Lukes theorem: no  1/m corrections (would be in D l ) –  QED =1.007,  QCD =0.960±0.007 at two loops –  1/m 2 involves 1/m b 2, 1/m c 2, 1/m c m b First Lattice Gauge calculations (quenched-no light quark loops) ultimate solution PDG (Artuso & Barberio) F(1)=0.91±0.05

7 V cb Exclusive Averages V cb = (40.03  0.9 exp  1.8 th )x10 -3 excl

8 Another exclusive channel: B  D l Renewed interest on this channel: –Lattice calculations –QCD sum rules evaluation of G(1) Using G(1)=1.058  0.07 (Artuso-Barberio PDG2002) V cb =(39.8  3.5 exp  2.9 th )x10 -3

9 |V cb | from inclusive B  X c l From B (B  X c l ) extract the experimental decay width: Compare with the theoretical prediction from Operator Product Expansion: 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 [ 1 ] kinetic energy of the b quark [ 2 ] expectation value of chromomagnetic op.

11 m b : a multifaceted fundamental parameter Important for V c(u)b  expansion Jet observables sensitive to b mass(LEP) + pole mass m b pole  m kin +0.255 GeV Bigi-Mannel hep/ph/0212021

12 Problems with HQE Terms in 1/m b 3 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  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? –…

13 How to Measure 1 &  Can determine 1 and  and thus V cb by measuring “moments” in semileptonic decays –Hadronic mass moments (ex:  M X 2 - M D 2 , M D is spin-averaged D, D * mass) where B  X l –Semileptonic moments Can also use b  s  decays, here we use the 1 st moment of the photon energy

14 Moments (CLEO) Hadronic Mass & Lepton Energy moments found in semileptonic decays “detecting the neutrino” using missing energy b  s  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/0210027)  =0.35 ±0.07 GeV 1 = -0.24±0.07 GeV 2 exp errors only

15 BaBar Moments Result Using only BaBar hadronic moments & B sl : V cb =(42.1±1.0±0.7)x10 -3 again within ±7% of D* l m b 1S =4.64±0.09±0.09 GeV (M x 2 as function of lepton momentum, is now consistent with theory) M x 2 moments Doesn’t include 1/m b 3 errors 1  contours 2002

16 Comparison of Hadron & Lepton Moments (BaBar) Lepton & Hadron moments differ somewhat. Does this indicate a Duality violation? Difference of 0.2 GeV in m b leads to 20% difference in V ub 3.5% difference 9%

17 New versus old CLEO & BaBar Moments Refined experimental results agree with theory. Can we draw any definitive conclusion? M x = 0.534  0.041  0.074 2 DELPHI NO E lep cut

18 Summary of experimental results V cb = (40.03  0.9 exp  1.8 th )x10 -3 V cb =(41.5  0.4   0.4 1  meas  0.9 th )x10 -3 excl incl A measure of the consistency between theoretical approaches Future prospects: Precise form factor calculations from lattice gauge calculation More extensive exploration of inclusive semileptonic decay observables: in particular high M x component More detailed evaluation & validation of theoretical errors sl

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