Elisabetta Barberio

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Measurements of Vcband Form Factors

• Elisabetta Barberio
• University of Melbourne
• Beauty 2006 Oxford September 2006

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Standard Model Consistency Tests
Vcb provide a test of CP violation in the
Standard Model comparing the measurements on the
(?, ?) plane
3
Semileptonic B decays
tree level, short distance
decay properties depend directly on
Vcb,mb perturbative regime (?sn)
But quarks are bound by soft gluons
non-perturbative (?QCD) long distance
interactions of b quark with light quark
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heavy quark symmetry
heavy quark the energy of soft gluon ?QCD250
MeV ltlt mb,c heavy quark spin and mass (flavour)
are good symmetry as mQ/?QCD ?8 departure from
the heavy quark symmetry can be expressed as
(?QCD/mQ)n corrections

• Two methods to extract Vcb
• Inclusive ?b Br(b ?cl?) shapes
• Exclusive

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Inclusive semileptonic decays
Many theorists love inclusive semileptonic decays
Short distance is calculable Long distance
leading order and short distance contribution
are cleanly separated
Most accurate Vcb determination from inclusive
decays precision limited by theory error
Operator Product Expansion predictions
integration over neutrino and lepton full phase
space provides smearing over the invariant
hadronic mass of the final state
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Vcb from inclusive semileptonic decays
exp. ?Vcblt1
?sl described by Heavy Quark Expansion in (1/mb)n
and ?sk
non perturbative parameters need to be measured
The expansion depend on mb definition
non-perturbative terms depend on the choice of mb
definition
Theory error is dominated by 1/mb3 terms and
above
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Parameters of HQE
Decay rate in are express in terms of OPE up to
1/mb3

• Calculations available in different
  renormalization schemes (mb definition)
• Kinetic running mass (P. Gambino, N.Uraltsev,
  Eur. Phys. J. C 34, 181 (2004))
• 1S mass (C.Bauer, Z.Ligeti, M.Luke, A.Manohar,
  M.Trott PRD 70 094017)
• Pole mass not used anymore not well behaved,
  irreducible error on mb

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Inclusive SL decays
Difficulty to go from measured shape to true
shape e.g. QED corrections, accessible phase
space, resolution, background
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moments in semileptonic decays
non-perturbative parameters are extracted from
the spectral moments
Xn are evaluated either on the full lepton
spectrum or part of it p? gt pmin in the B rest
frame
E? lepton energy spectrum (BaBar Belle CLEO
Delphi) MX hadronic mass spectrum ( BaBar Belle
CDF CLEO Delphi)
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Full reconstruction
B?Xc? ?
fully reconstruct the tag-side B meson by
searching the decay modes e.g. B?D()?, B? D()?,
and B?D()a1
flavour - charge - momentum
Bsig?Xl?
Btag?DX
B and B0 decays studied separately
B
B
0
But low efficiency lt 1
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moments in B?Xc? ?
Most recent measurements from Belle
140 fb-1 sample
Pl (GeV)
Pl (GeV)
Plmin 0.4 GeV
from the moments of these distributions we get
Vcb and HQ parameters
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Moments with threshold
(statistical errors only)
Belle unfolded spectrum B0 and B combined
0.4 GeV electron energy threshold
Measure up to 4th moment!
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Electron energy moments and partial BR
Belle final results
Belle-Conf-0667
Br(B)0.4GeV(10.790.250.27) Br(B0)0.4GeV(10.
090.300.22)
Systematics b-gtc model, background, electron
detection
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Hadronic Xc system
BR(B?Xcl?) 10.5
Grounds states
Broad states
Narrow states
Important to understand the shape and branching
fractions of each hadronic contribution B?Dl?
not measured well
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Belle hadronic mass moment analysis
Select ?(4S) decays with fully reconstructed
hadronic B decays Btag Select events with one
identified lepton (electron or muon)
Bsig?Xl?
Measure Mx mass on signal side of the event
Mx
pX pbeam-pBtag-pl-p?
Btag?DX
Constrain neutrino mass to zero
B
B
0
M2miss lt 3 GeV2/c4
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Hadronic-Mass Spectrum
Measured Mx2 spectrum for different Elcut
Belle ICHEP06
Main systematics b?c model, background
subtraction
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Results and systematic uncertainties
The moments are derived from the unfolded
spectrum down to 0.7 GeV minimum lepton energy in
the B rest frame
Mx2 (GeV2/c4)
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Vcb extraction

• well behaving renormalization schemes are used
• Kinetic running mass
• 1S mass

both schemes have 7 free parameters
mkinb ,mkinc (m1Sb) - mass of b and c quarks
?QCD2/mb2 µ?2(?1) - kinetic energy of b quark,µG2(? 2) - chromomagnetic coupling
?QCD3/mb3 ?D, ?LS (?1,t1-3)
higher moments are sensitive to 1/mb3 terms ?
reduce theory error on Vcb and Heavy Quark
parameters
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Kinetic Scheme
Preliminary
Belle
Belle ICHEP06
Vcb (41.93 0.65fit 0.48as 0.63th )10-3
mb 4.564 0.076 GeV, mc 1.105 0.116 GeV
Contours ????1
???/dof 17.8/24
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1S Scheme
Preliminary
Belle ICHEP06
Vcb (41.5 0.5fit 0.2t )10-3
mb1s 4.73 0.05 GeV ?1 -0.30 0.04 GeV
Contours ????1
??/dof 6/17
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Vcb and HQ parameters
Global fit Kinetic scheme expansion - all
experiments (Buchmuller, Flasher PRD73073008
(2006)) Belle new measurements missing
Vcb(41.960.23exp0.35HQE0.59?SL)10-3
?Vcb _at_ 2 mb lt 1 ? crucial for Vub mc _at_ 5
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HQET and B ?Dl?
Heavy Quark Effective Theory (HQET) simplified
description of processes involving heavy ? heavy
quark transitions
B ?D()l? transitions non-perturbative effects
are described by one form factor ?, Isgur-Wise
function, as a function of w
q2 ? 4-momentum transfer
w1 ? D produced at rest in B rest frame
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Vcb from B ?Dl?

• when mQ?8 ?(1)1? Vcb extraction

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

measure d?/dw and extrapolate at w1 ? the slope
is important fit for both intercept F(1)Vcb
and slope ?2
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signal and w reconstruction
B ? Dl?????????????????D ? ?slowD0
m(D)-m(D0)m(?) ? is almost at rest in the
B rest frame ? difficult to reconstruct when the
B is almost at rest
Main physics background B?Dl?, D resonant and
non resonant
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extrapolation form factor shape
expansion around w1 up to second order
use dispersive relations to constraint the shape
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 measured by CLEO
R1(1)1.180.300.12 R2(1)0.710.220.07
used in the old world average
For long time R1,R2 uncertainty was the major
source of systematic on ?A2
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form factor shape
one-dimension projection of fitted distributions
Fit w and 3 angles
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form factor and Vcb
Simultaneous fit of the Form factors and Vcb
F (1)Vcb(34.68?0.32?1.15)10-3 Br(B0 ?
Dl?)(4.84?0.39)
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F (1)Vcb
New HFAG average uses R1, R2 from Babar this
decrease F (1)Vcb
?2/dof 38.7/14
F (1)Vcb(36.2?0.8)10-3 ?A2 1.19?0.06
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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
from lattice and sum rule
Vcbexcl(39.4?0.9exp?1.5theo)10-3
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Vcb from Bd0?D?-? decays
large combinatorial background but very good
prospective on the theory side for G(1)
Worth to measure as it will may cross-check Vcb
excluisve
G(1)Vcb(42.6?4.5) x 10-3 ?G2 1.17 ? 0.18
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?(B?D,?-?)/?(B?DX?-?) Measurement
There is disagreement between inclusive and
exclusive b ?cl? branching fractions ?(B?D,?-?)
/?(B?DX?-?) is sensitive to non resonant states
Measure simultaneously D, D and D components
using the fully reconstructed events
211 fb-1
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?(B?D,?-?)/?(B?DX?-?) Measurement
This measurement is not solving the puzzle
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Conclusions
Vcb is now a precision measurement
Vcbinc(41.960.23exp0.35HQE0.59?SL)10-3
Inclusive and exclusive analyses give consistent
results
Vcbexcl(39.4?0.9exp?1.5theo)10-3
The measurement of mb from the inclusive
spectrum are crucial for the precise extraction
of Vub
B?D?-? are still a puzzle and a concern.