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”
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Precise determination with reliable errors important for:
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predicting B decay rates
 testing unitarity of the CKM matrix
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Semileptonic B decays offer best probe
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Leptonic current factors out cleanly
Tree-level rate

b
G(b  c  )  Vcb mb2 (mb  mc )3
2
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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
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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
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 Ex: 4 parameters up to O (1/ mb ) in the kinetic scheme
Strategy: Measure rate + as many moments as possible
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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
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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
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Unlike-sign events
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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
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
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
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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
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Use ~1000 hadronic decay chains
Rest of the event contains one “recoil” B
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Flavor and momentum known
Find a lepton with E > Ecut in the recoil-B
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Lepton charge consistent with the B flavor
mmiss consistent with a neutrino
All left-over particles belong to Xc
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Fully reconstructed
B  hadrons
v
lepton
Improve mX with a kinematic fit  s = 350 MeV
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Xc
4-momentum conservation; equal mB on both sides; mmiss = 0
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Hadron Mass Moments
Measured mX < true mX
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Linear relationship
 Calibrate using simulation
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BABAR
Depends (weakly) on decay
2
multiplicity and mmiss
Validate calibration procedure
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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
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Electron energy moments
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Tracking and electron ID efficiencies
 Background from secondary leptons (B  D/Ds/t  e)
 Bremsstrahlung correction
 B  Xuℓv subtraction
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Hadron mass moments
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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)
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Kinetic mass scheme to O (1/ mb3 )
Eℓ moments O (a s2 )
mX moments O (a s )
8 parameters to determine
Vcb
kinetic
chromomagnetic
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mb mc B( B  X c  ) mp2 mG2  D3  LS
8 moments available with several Ecut
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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
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Difference from fit using the full expression small
Data points (48 of them) are strongly correlated
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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
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Fully correlated for each moment at different Ecut
 Uncorrelated between different moments
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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
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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
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|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|
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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
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It also determines mb and mc precisely
mb (mb )  4.22  0.06GeV
mc (mc )  1.33  0.10GeV
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