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Elisabetta Barberio University of Melbourne
Beauty 2006: Oxford September 2006
Measurements of Vcb
and Form Factors
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September 2006 E. Barberio 2
Standard Model Consistency Tests
Vcb provide a test of CP violation in the Standard Model comparing the measurements on the () plane
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September 2006 E. Barberio 3
Semileptonic B decaysSemileptonic B decays
tree level, short distance:
decay properties depend directly on |Vcb|,mb
perturbative regime (s
n)
Vcb
u
+ long distance:
,u
But quarks are bound by softgluons: non-perturbative (QCD) long distance interactions of b quark with light quark
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September 2006 E. Barberio 4
heavy quark symmetry
heavy quark: the energy of soft gluon QCD~250 MeV << mb,c
heavy quark spin and mass (flavour) are good symmetry as mQ/QCD ∞
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
€
(Br B→D(*)lυ)+HQET
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September 2006 E. Barberio 5
Inclusive semileptonic decays
Short distance is calculable Long distance leading order and short distance contribution are cleanly separated
Operator Product Expansion predictions: integration over neutrino and lepton full phase space provides smearing over the invariant hadronic mass of the final state
Many theorists love inclusive semileptonic decays
Most accurate Vcb determination from inclusive decays: precision limited by theory error
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September 2006 E. Barberio 6
Vcb from inclusive semileptonic decays
sl described by Heavy Quark Expansion in (1/mb)n and sk
€
(B→ Xcl) =GF
2mb5
192π 3Vcb
2
1+ Aew[ ]Anonpert Apert ⎡ ⎣ ⎢
⎤ ⎦ ⎥
The expansion depend on mb definition: non-perturbative terms depend on the choice of mb definition
exp. |Vcb|<1%
€
sl(b→ cl −) =γth Vcb
2
=BR(b → cl −ν )
τb
non perturbative parameters need to be measured
Theory error is dominated by 1/mb3 terms and
above
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Parameters of HQEParameters of HQEDecay rate in are express in terms of OPE up to 1/mb
3
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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September 2006 E. Barberio 8
Difficulty to go from measured shape to true shape: e.g. QED corrections, accessible phase space, resolution, background
Inclusive SL decays
rate
shape
shape
|Vcb|
mc, G,
mb, 2
1.5
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September 2006 E. Barberio 9
non-perturbative parameters are extracted from the spectral moments
moments in semileptonic decays
Xn are evaluated either on the full lepton spectrum or part of it: p > pmin in the B rest frame
€
Xn
=X− Xo( )
n∫
dΓ
dXdX
dΓ
dXdX∫
= f 'OPE mb ,mc ,α s( )
E : lepton energy spectrum (BaBar Belle CLEO Delphi)
MX: hadronic mass spectrum (BaBar Belle CDF CLEO Delphi)
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10
Full reconstruction
flavour - charge - momentum
B+ and B0 decays studied separately
fully reconstruct the tag-side B meson by searching the decay modes e.g. B→D(*), B→ D(*)ρ, and B→D(*)a1
Bsig→Xl
K γ
γ
l-
BB0 0
Υ(4S)
Btag→DX
BXc
But low efficiency < 1%
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September 2006 E. Barberio 11
Most recent measurements from Belle
moments in BXc
Plmin = 0.4
GeV
P*l (GeV)P*
l (GeV)
from the moments of these distributions we get Vcb and HQ parameters
140 fb-1
sample
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September 2006 E. Barberio 12
Moments with threshold
Belle unfolded
spectrum:
B0 and B+ combined
(statistical errors only)
0.4 GeV electron energy threshold
Measure up to 4th moment!
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September 2006 E. Barberio 13
Electron energy moments and partial BR
Decrease of truncated
BR
Incr
ease
of th
e
mea
n
Decrease of the
width
Belle-Conf-0667Belle final results
Systematics: b->c model, background, electron detection
Br(B+)0.4GeV=(10.79±0.25±0.27)%
Br(B0)0.4GeV=(10.09±0.30±0.22)%
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September 2006 E. Barberio 14
BR(B→Xcl) ~ 10.5%
21 %
54%
~25%
Grounds states Broad states Narrow states
Hadronic Xc system
Important to understand the shape and branching fractions of each hadronic contribution: B→D**l not measured well
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Select (4S) decays with fully reconstructed hadronic B decays “Btag”
Select events with one identified lepton (electron or muon)
Constrain neutrino mass to zero:
pX = pbeam-pBtag-pl-pν
K γ
γ
l-
ν
B B00
Υ(4S)
Mx
M2miss < 3 GeV2/c4
Belle hadronic mass moment analysis
Bsig→Xlν
Btag→DX
Measure Mx mass on signal side of the event:
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September 2006 E. Barberio 16
Hadronic-Mass Spectrum
Measured Mx2
spectrum for different El
*cut
Main systematics: b→c model, background subtraction
Belle ICHEP06
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September 2006 E. Barberio 17
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
0.7 GeV
El*cut
1.5 GeVdecrease in higher mass final
states
D*
D**
D
BelleUnfolded Mx
2 spectrum
Mx2 (GeV2/c4)
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Vcb extraction
mkinb ,mkin
c (m1Sb) - mass of b and c
quarks
ΛQCD2/mb
2μ
2(λ1) - kinetic energy of b quark,
μG2
(λ 2) - chromomagnetic coupling
ΛQCD3/mb
3 ρD, ρLS (ρ1,τ1-3)
well behaving renormalization schemes are used:• Kinetic running mass• 1S mass
both schemes have 7 free parameters:
higher moments are sensitive to 1/mb3 terms
reduce theory error on Vcb and Heavy Quark parameters
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Kinetic SchemeBelle
/dof =17.8/24
mb = 4.564 ± 0.076 GeV, mc = 1.105 ± 0.116 GeV
Contours =1
|Vcb| = (41.93 ± 0.65fit ± 0.48αs ± 0.63th )×10-3
BRBR EEe,1e,1
EEe,2e,2
EEe,3e,3
MMxx22
EEγγ,1,1
MMxx44
EEγγ,2,2
Yellow band: theory errorYellow band: theory errorFilled circles: used in Filled circles: used in fitfit
Preliminar
Preliminaryy
Belle ICHEP06
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September 2006 E. Barberio 20
|Vcb| = (41.5 ± 0.5fit ± 0.2 )×10-3
1S Scheme
mb1s= 4.73 ± 0.05 GeV
1 = -0.30 ± 0.04 GeV
Belle ICHEP06
EEe,3e,3
MMxx22
EEγγ,1,1
MMxx44
EEγγ,2,2
2020
Yellow band: fit errorYellow band: fit errorRed band: Theory + FitRed band: Theory + Fit
BRBREEe,1e,1
EEe,2e,2
Filled circles: used Filled circles: used in fitin fit
/dof = 6/17
Contours =1
Preliminar
Preliminaryy
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September 2006 E. Barberio 21
Vcb and HQ parameters
Exp HQ sl
Global fit Kinetic scheme expansion - all experiments (Buchmuller, Flasher PRD73:073008 (2006))
Belle new measurements missing
Vcb @ 2%
mb < 1% crucial for
Vub
mc @ 5%
|Vcb|
=(41.96±0.23exp±0.35HQE±0.59SL)10-3
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September 2006 E. Barberio 22
c
q
-
w=1
HQET and B D*l
w=1 D* produced at rest in B rest frame
€
w=mB2+m
D*2 −q2
2mBmD*
l
Vcb
b c
q2q2 4-momentum transfer
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
c
q
-
w>1
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September 2006 E. Barberio 23
Vcb from B D*l
d(B→D*l)
dw=K(w)F (w)V
cb
measure d/dw and extrapolate at w=1 the slope is important
fit for both intercept F(1)|Vcb| and slope 2
when mQ∞ (1)=1 Vcb extraction
F(1
)Vcb
w
F(1)~(1)~ 1K(1) =0
DelphiK(w): phase space (known function)F(w): unknown form factor F(1)•g(w)
in the heavy quark limit
F(1)=(1)=1
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September 2006 E. Barberio 24
signal and w reconstruction
B D*lD* +
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 BD**l, D** resonant and non resonant
CLEO
Signal region
cos(θB−D* l
) =E
BE
D* l−m
B
−mD* l
pBp
D* l
cos(θ
B−D* l)
cos(θ
B−D* l)
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September 2006 E. Barberio 25
€
F (w)=hA1(w) f1 (r, w) 1 +R1 (w)
w−1
w +1
⎛
⎝⎜⎜
⎞
⎠⎟⎟+ f (r, w) 1 + 1−R (w)
w−1
r−1
⎛
⎝⎜⎜
⎞
⎠⎟⎟
⎛
⎝
⎜⎜⎜
⎞
⎠
⎟⎟⎟
⎧
⎨⎪
⎩⎪
⎫
⎬⎪
⎭⎪
extrapolation: form factor shape expansion around w=1 up to second order:
Caprini,Lellouch,Neubert NP B530(98)153 and Boyd,Grinstein,Lebed PRD56(97)6895
use dispersive relations to constraint the shape
R1,R2 calculated using QCD sum rules
R1(w)1.27-0.12(w-1)+0.05(w-1)2 R2(w) 0.80+0.11(w-1)-0.06(w-1)2
measured by CLEO:
R1(1)=1.18±0.30±0.12 R2(1)=0.71±0.22±0.07
For long time R1,R2 uncertainty was the major source of systematic on A
2
used in the oldworld average
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September 2006 E. Barberio 26
form factor shape
one-dimension projection
of fitted distributions:
Fit w and 3 angles
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September 2006 E. Barberio 27
form factor and Vcb
Simultaneous fit of the Form factors and Vcb
F (1)|Vcb|=(34.680.321.15)10-3
Br(B0 D*+l)=(4.840.39)%
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September 2006 E. Barberio 28
F (1)|Vcb|
2/dof = 38.7/14
2=1CL=37%
New HFAG average uses R1, R2
from Babar: this decrease F (1)|Vcb|
F (1)|Vcb|=(36.20.8)10-3 A2
=1.190.06
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September 2006 E. Barberio 29
non-perturbative QCD calculations
F(1) =0.9070.0070.0250.017
F(1) =0.9000.0150.0250.025
F(1) =0.919
-0.035
+0.030
|Vcb|excl=(39.40.9exp1.5theo)10-3
F(1) and Vcb
from lattice and sum rule
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September 2006 E. Barberio 30
Vcb from Bd0D+ decays
BELLE
G(1)|Vcb|=(42.64.5) x 10-3
G2 =1.17 0.18
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
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September 2006 E. Barberio 31
(BD*,**)/(BDX) Measurement
There is disagreement between inclusive and exclusive b cl branching fractions
(BD*,**)/(BDX) 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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September 2006 E. Barberio 32
(BD*,**)/(BDX) Measurement
This measurement is not solving the puzzle …
RD*
=Br (B
−
→ D*0
l)
Br (B0
→ D* −
l)=1.3 ±0.07
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September 2006 E. Barberio 33
Conclusions
|Vcb|
inc=(41.96±0.23exp±0.35HQE±0.59SL)10-3
|Vcb|excl=(39.40.9exp1.5theo)10-3
Vcb is now a precision measurement:
The measurement of mb from the inclusive spectrum arecrucial for the precise extraction of Vub
BD** are still a puzzle and a concern….
Inclusive and exclusive analyses give consistent results