Determination of |Vcb|
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Transcript Determination of |Vcb|
Determination of |V
and related results from BABAR
|
cb
Masahiro Morii, Harvard University
on behalf of the BABAR Collaboration
|Vcb| from inclusive B semileptonic decays
Lepton energy moments
Hadron mass moments
HQE fit
|Vcb|, mb, mc, B(B Xcℓv), etc.
MESON 2004, Krakow, June 4-8, 2004
Why |Vcb| — and How
Vcb is the “mother of (almost) all B decays”
Precise determination with reliable errors important for:
predicting B decay rates
testing unitarity of the CKM matrix
Semileptonic B decays offer best probe
Leptonic current factors out cleanly
Tree-level rate
b
G(b c ) Vcb mb2 (mb mc )3
2
QCD corrections relate this to the measured rates
Vcb
c
Inclusive G(B Xcℓv)
Exclusive G(B D*ℓv), G(B Dℓv), etc.
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Inclusive |Vcb| Measurement
Heavy Quark Expansion allows calculation of
Inclusive rate
Lepton energy (Eℓ) moments
Hadron mass (mX) moments
B
Expansion in terms of 1/mb and as(mb)
Separate short- and long-distance effects at m ~ 1 GeV
Perturbative corrections calculable from mb, mc, as(mb)
Xc
Non-perturbative corrections cannot be calculated
3
Ex: 4 parameters up to O (1/ mb ) in the kinetic scheme
Strategy: Measure rate + as many moments as possible
Determine all parameters by a global fit
Over-constrain to validate the method
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Observables
Define 8 moments from inclusive Eℓ and mX spectra
M0
M1
M iX
dG
Partial branching fraction
GB
E dG
dG
m dG
dG
i
X
Mi
E
M1 d G
i
dG
(i 1, 2,3, 4)
(i 2,3)
Lepton energy
moments
Hadron mass
moments
Eℓ is measured in the B rest frame
Integrations are done for Eℓ > Ecut, with Ecut varied in 0.6–1.5 GeV
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hep-ex/0403030, to appear in PRD
Electron Energy Moments
BABAR data, 47.4 fb-1 on U(4S) resonance + 9.1 fb-1 off-peak
Select events with 2 electrons
Unlike-sign
BABAR
One (1.4 < p* < 2.3 GeV) to
“tag” a BB event
The other (p* > 0.5 GeV) to
measure the spectrum
Use charge correlation
Unlike-sign events
Like-sign
dominated by B Xcev
Like-sign events
D Xev decays, B0 mixing
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Electron Energy Moments
Turn the like-/unlike-sign
spectra Eℓ spectrum
BABAR
Divide by the efficiency
Account for B0 mixing
Correct for the detector
material (Bremsstrahlung)
Calculate the moments for Ecut = 0.6 … 1.5 GeV
Move from U(4S) to B rest frame
Correct for the final state radiation using PHOTOS
Subtract B Xuℓv
Into the HQE fit
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hep-ex/0403031, to appear in PRD
Hadron Mass Moments
BABAR data, 81 fb-1 on U(4S) resonance
Select events with a fully-reconstructed B meson
Use ~1000 hadronic decay chains
Rest of the event contains one “recoil” B
Flavor and momentum known
Find a lepton with E > Ecut in the recoil-B
Lepton charge consistent with the B flavor
mmiss consistent with a neutrino
All left-over particles belong to Xc
Fully reconstructed
B hadrons
v
lepton
Improve mX with a kinematic fit s = 350 MeV
Xc
4-momentum conservation; equal mB on both sides; mmiss = 0
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Hadron Mass Moments
Measured mX < true mX
Linear relationship
Calibrate using simulation
BABAR
Depends (weakly) on decay
2
multiplicity and mmiss
Validate calibration procedure
Simulated events in exclusive
final states
D*± D0p ± in real data, tagged
by the soft p ±
Calculate mass moments with Ecut = 0.9 … 1.6 GeV
Into the HQE fit
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hep-ex/0404017, to appear in PRL
Inputs to HQE Fit
Error bars are stat. & syst.
with comparable sizes
mX moments
BABAR
Eℓ moments
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Systematic Errors
Dominant experimental systematic errors
Electron energy moments
Tracking and electron ID efficiencies
Background from secondary leptons (B D/Ds/t e)
Bremsstrahlung correction
B Xuℓv subtraction
Hadron mass moments
Detector efficiency and resolution
Background in fully-reconstructed B
Other background
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Hadron mis-ID, t +t –, B Xuℓv, secondary leptons
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HQE Parameters
Calculation by Gambino & Uraltsev (hep-ph/0401063 & 0403166)
Kinetic mass scheme to O (1/ mb3 )
Eℓ moments O (a s2 )
mX moments O (a s )
8 parameters to determine
Vcb
kinetic
chromomagnetic
3
mb mc B( B X c ) mp2 mG2 D3 LS
8 moments available with several Ecut
Sufficient degrees of freedom to determine
all parameters without external inputs
Fit quality tells us how well HQE works
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O (1/ mb2 )
M. Morii, Harvard
spin-orbit
Darwin
O (1/ mb3 )
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Fitting Method
Use linearized expression for the HQE predictions
Difference from fit using the full expression small
Data points (48 of them) are strongly correlated
Each fit uses a subset in which all correlation coefficients are <95%
Full error matrix for experimental errors (stat. and syst.)
Theory errors: vary slopes of the linearized expressions
2
3
±20% for the O (1/ mb ) terms, ±30% for the O (1/ mb ) terms
Fully correlated for each moment at different Ecut
Uncorrelated between different moments
Fit results stable for different treatment of the theory errors
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HQE Fit Results
● = used, ○ = unused
in the nominal fit
mX moments
BABAR
c 2/ndf = 20/15
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Red line: HQE fit
Yellow band: theory errors
Eℓ moments
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HQE Fit Consistency
HQE describes BABAR data very well
c 2/ndf = 20/15
Separate fit of Eℓ and mX moments agree
BABAR
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HQE Fit Results
Vcb (41.4 0.4exp 0.4 HQE 0.6 th ) 10 3
Bc (10.61 0.16exp 0.06 HQE )%
mb (4.61 0.05exp 0.04 HQE 0.02as ) GeV
Uncalculated
corrections to G
mc (1.18 0.07 exp 0.06 HQE 0.02as ) GeV
mp2 (0.45 0.04exp 0.04 HQE 0.01a ) GeV 2
s
mG2 (0.27 0.06exp 0.03HQE 0.02a ) GeV 2
kinetic mass scheme
with m = 1 GeV
s
D3 (0.20 0.02exp 0.02 HQE 0.00a ) GeV 3
s
3
LS
(0.09 0.04exp 0.07 HQE 0.01a ) GeV 3
s
3
consistent with B-B* mass splitting and QCD sum rules
mp2 and LS
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In Perspective
New BABAR result compares well with previous measurements
|Vcb| is now measured to ±2%
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Heavy Quark Masses
Convert mb and mc into MS scheme (N. Uraltsev)
mbkin (1GeV) (4.61 0.05exp 0.04HQE 0.02th )GeV
mb (mb ) 4.22 0.06GeV
mckin (1GeV) (1.18 0.07exp 0.06HQE 0.02th )GeV
mc (mc ) 1.33 0.10GeV
theory
theory
References in PDG 2002
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Summary
BABAR has made significant progress in determination of |Vcb|
HQE fit of Eℓ and mX moments 2% error on |Vcb|
Vcb (41.4 0.4exp 0.4HQE 0.6 th ) 10 3
Bc (10.61 0.16exp 0.06 HQE )%
mbkin (1GeV) (4.61 0.05exp 0.04 HQE 0.02a s )GeV
mckin (1GeV) (1.18 0.07 exp 0.06 HQE 0.02as )GeV
No external constraints on the non-perturbative parameters
Fit quality and consistency support validity of the HQE application
It also determines mb and mc precisely
mb (mb ) 4.22 0.06GeV
mc (mc ) 1.33 0.10GeV
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