measurements of Vcb

1
measurements of Vcb

• E.Barberio
• University of Melbourne
• Daphne04 Frascati 7-11 June 2004

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precision electroweak tests

• e.w. process at tree level are computed from 3
  parameters ?, GF , mZ
• and the CKM matrix elements Vij.

Vij are less well known (if at all) extraction
limited by theory error CP Violation
3
physics motivation
Vcb governs b?c transition

• ultimate goal precise determination of Vcb !
• quarks are inside hadrons bound by soft gluons ?
  both
• perturbative (mb) and non-perturbative (LQCD) QCD
  effects
• Tools
• Heavy quark symmetry and lattice QCD

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heavy quark symmetry
asymptotic freedom

• when the energy of soft gluon LQCD250 MeV ltlt
  mb,c? heavy quark
• heavy quark is invisible to gluon probes with
  de Broglie wavelegnth lggtgt1/mc,b
• heavy quark spin and mass (flavour) are good
  symmetry as
• (mQ/LQCD) ?8
• - departure from the heavy quark symmetry can be
  expressed as (LQCD/mQ)n corrections

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Heavy Quark Effective Theory
Heavy Quark Effective Theory (HQET) simplified
description of processes involving heavy ? heavy
quark transitions non-perturbative effects
described by form factors
all B ?D()ln transitions are described by one
form factor ? (Isgur-Wise function) as a function
of w the D boost in B rest frame
q2 ? 4-momentum transfer
w1? D produced at rest in B rest frame

• in mQ?8 ?(1)1? Vcb extraction with little model
  dependence
• bonus B?D()ln largest branching fraction of B
  decay modes

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Vcb from B ?Dln
in HQET

• K(w) is the phase space (known function)
• F(w) unknown form factor F(1)g(w)
• in the heavy quark limit mQ?8 F(1) ?(1)1

measure dG/dw(w) and extrapolate at w1 ? g(w)
slope important fit for both intercept F(1)Vcb
and slope (r2) Caprini, Lellouch, Neubert,
Nucl.Phys.B530(98)
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signal and w reconstruction
B ? Dln
D ? pslowD0 m(D)-m(D0)m(p) the p is
almost at rest close to K(w1) in the B rest
frame p difficult or impossible to
reconstruct if the B is produced at rest or has
little boost
w ? pn and En? need good resolution for Enpn
easy if the B is produced at rest of with little
boost
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B ?D()ln
U(4S) ? B0 at rest or almost large data sample,
good w resolution, low D background

• LEP Z? bb B0 large variable
• momentum 30 GeV
• good efficiency at w1 less
• extrapolation uncertainty at w1

poor efficiency at w1
poorer w resolution large background from higher
D
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background from B?Dln
B?Dln with D? pD/pD0 resonant (narrow and
wide) and non resonant
LEP resonant Ddifferent form factors
depending on assumption on quark decay dynamics
Leibovich,Ligeti,Stewart,Wise D shape from
constraints on D rates Br(B?D2ln )/
Br(B?D1ln) lt0.4
U(4S)

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F(1)Vcb
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F (1)Vcb
F (1)Vcb(36.5?0.3tat?0.8syst)x10-3 rA2
1.47?0.02stat?0.13syst
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F(1) and Vcb
non-perturbative QCD calculations
F(1) 0.907?0.007?0.025?0.017
F(1) 0.900?0.015?0.025?0.025
future error reduction from unquenched
calculations
from lattice and sum rule
F(1)0.91 ? 0.04
Vcbexcl(40.1?0.9exp?1.8theo) 10-3
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Vcb from Bd0?D?-? decays
large combinatorial background non-zero 1/mQ
corrections to G(1)
consistency check and test of the theory from
Belle D and D results r2D-r2D-0.23?0.29
?0.20 G(1)/F(1)1.16?0.14 ?0.12 compatible with
expectations
G(1)Vcb(41.8?3.7) x 10-3 rG2 1.15 ? 0.16
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Vcb from inclusive semileptonic decays
exp. DVcb1
Gsl described by Heavy Quark Expansion in (1/mb)n
and ask
non perturbative parameters to be measured and
arise at each order
expansions depend on mb definition different
expation different non-perturbative terms, but
they related
pole mass
low scale running quark masses
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inclusive Vcb
rate
W
shape
c
shape
from the shape get non-perturbative parameters
though the moments
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moments of kinematic variables
how much is there? (area)
where is it? (mean)
how wide is it? (width)
skewness
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moments in semileptonic decays
E? lepton energy spectrum in B?Xc? n (CLEO,
DELPHI) MX 2 hadronic mass spectrum in B?Xc? n
(CLEO, BaBar, DELPHI) Eg photon energy
spectrum in B? Xsg (CLEO,Belle)
On1,2,.. different sensitivities to
non-perturbative parameters evaluated on the full
spectrum or part of it (p? gt pmin) OPE
predictions can be compared with experiments
after smearing ? integration over neutrino and
lepton phase space provides smearing over
the invariant hadronic mass of the final
state test of OPE predictions, quark-hadron
duality
higher moments used to get sensitivity to 1/mb3
parameters reduced uncertainty on Vcb from
inclusive semileptonic decay
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photon energy spectrum
photon energy spectrum in B? Xsg is not sensitive
to new physics and give information on B structure
without Belle
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hadronic moments
hadronic mass spectra Mx
Mx from ln MX2 mB2m?n2-2EBE?n fit relative
contributions of D,D,D
CLEO 3.2 fb-1
B-meson fully reconstructed
BABAR 51 fb-1
B?X?n
Pmin 1.5 GeV
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lepton energy spectrum
spectra background subtracted
ratios of truncated lepton spectra
e m
Cleo
Babar, lower momentum cut in the B rest
frame small B boost and larger statistics
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moments at LEP
large momentum of b-hadron 30 GeV full lepton
energy spectrum in B rest frame ? non-truncated
spectra
lepton spectrum
?MM(D()?)-M(D()) fits with resonant and non
resonant states
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parameters extraction
CLEO photon spectrum and hadronic mass spectrum
evaluated at 1/mB3 and as2 bo Ligeti,Luke,Manohar
,Wise Falk,Luke,Savage
L 0.35?0.07 ? 0.1 GeV l1-0.238? 0.071?0.078
GeV2
photon, hadronic mass and lepton energy spectrum
evaluated at 1/mB3and as2 bo

• L0.390.03stat0.06sys0.12th GeV
• l1-0.250.02stat0.05sys0.14th GeV2

from 1/mB3 as
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moments at LEP
multi-parameter c2 fit to determine relevant
1/mb3 parameters
c2/d.o.f.0.96
input mG2 0.35 0.05 GeV2 rLS3 -0.15
0.15 GeV3 mc 1.05 ? 0.30 GeV mb 4.57 ? 0.10 GeV
equivalent to B? Xsg
mb,kin (1GeV) 4.59 0.08fit0.01sys GeV mc,kin
(1GeV) 1.13 0.13fit0.03sys GeV mp2 (1GeV)
0.31 0.07fit0.02sys GeV2 rD3 (1GeV)
0.05 0.04fit0.01sys GeV3
mb(mb) 4.233 GeV mc(mc) 1.245 GeV
present accuracy no need of higher order terms

• L 0.40 0.10fit 0.02sys GeV l1-0.15
  0.07fit 0.03sys GeV2
• r1-0.01 0.03fit 0.03sys GeV3
• r2 0.03 0.03fit 0.01sys GeV3

• pole mass expantion
• (compatible with CLEO)

similar results with mb1S-l1 formalism Bauer,
Ligeti, Luke, Manohar
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parameters extraction
BABAR up to 1/mb3 fit all parameter and Vcb as
function of pcut
mb,kin (1GeV) 4.61 0.05exp0.05HQE 0.02as
GeV mc,kin (1GeV) 1.18 0.07exp 0.06HQE
0.02as GeV mp2 (1GeV) 0. 45 0.04exp
0.04HQE 0.01as GeV2 mG2 (1GeV) 0.27 0.06exp
0.03HQE 0.02as GeV2 rD3 (1GeV) 0.2
.04exp 0.02HQE GeV3 rSL3 (1GeV) -0.09
.04exp 0.07HQE 0.01as GeV3
pmin1.5GeV ? from CLEO b?sg
l1-0.170.060.07 GeV2 in agreement with CLEO
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derivation of inclusive Vcb
tB
LEP BR(B?Xc ?-?) (10.42?0.26) 10-2
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derivation of inclusive Vcb
Vcb dependence on non-perturbative parameters in
running quark mass scheme
N.Uraltsev hep-ph/0302262
Vcb Vcb0 1 -0.65 mb(1)-4.6 GeV 0.4
mc(1)-1.15 GeV 0.01 mp2 - 0.4 GeV2
0.10 rD3 -0.12 GeV3 0.05 mG2-
0.35GeV2 - 0.01 rLS3 0.15 GeV3
using ?sl(world) and Babar
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conclusion

• Vcb from exclusive B decays
• Bd0?D()?-? more statistics available and new
  measurements coming
• present precision (5) systematics limited slow
  p, Ds BR, D?
• need to understand the exeprimental spread of
  F(1)Vcb
• error on F(1)1 can be reduced in the future by
  lattice calculations

Vcbexcl(40.1 ?0.9exp ?1.8theo) ?10-3

• Vcb from inclusive B decays
• small error on BR(B?Xc?-?) and tB
• quark-hadron duality violation? no evidence of
  any effects with the present sensitivity
  constraints on non-perturbative parameters reduce
  the uncertainty on Vcb to 2.
• more measurements will consolidate the picture

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CKM mixing matrix
unitarity (AA 1)
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G(b?Xcln)
U(4S) BR(B?Xc ?-?) (10.83?0.25)
10-2 tB (1.598?0.01)
ps GB?Xc ?-? (0.446?0.010?0.003)10-10 MeV
LEP BR(B?Xc ?-?) (10.42?0.26) 10-2
tb (1.573 ? 0.01) ps GB?Xc
?-? (0.436?0.010 ?0.006)10-10 MeV
Word average
GB?Xc?-? (0.441 ?0.008) 10-10 MeV
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Systematics
BELLE
CLEO
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extrapolation form factor shape
expansion around w1 up to second order
use dispersive relations to constraint the shape
Relate F (w) to the ratios of HQET form factors
R1(w), R2(w)
Caprini,Lellouch,Neubert NP B530(98)153 and
Boyd,Grinstein,Lebed PRD56(97)6895
R1,R2 calculated using QCD sum rules

R1(w)?1.27-0.12(w-1)0.05(w-1)2 R2(w)?
0.800.11(w-1)-0.06(w-1)2 or measured by CLEO
R1(1)1.180.300.12 R2(1)0.710.220.07
R1,R2 uncertainty is the major source of
systematics on rA2, which should improve with
future new measurements
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Systematics
LEP