Determination of and related results from B A B AR
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Transcript of Determination of and related results from B A B AR
Determination ofand related results from BABAR
Masahiro Morii, Harvard Universityon behalf of the BABAR Collaboration
|Vcb|
MESON 2004, Krakow, June 4-8, 2004
|Vcb| from inclusive B semileptonic decays
Lepton energy moments Hadron mass moments
HQE fit
|Vcb|, mb, mc, (B Xcℓv), etc.
June 5, 2004 M. Morii, Harvard 2
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
QCD corrections relate this to the measured rates Inclusive (B Xcℓv) Exclusive (B D*ℓv), (B Dℓv), etc.
2 2 3( ) ( )cb b b cb c V m m m
b
c
cbV
June 5, 2004 M. Morii, Harvard 3
Inclusive |Vcb| Measurement
B
cX
Heavy Quark Expansion allows calculation of Inclusive rate Lepton energy (Eℓ) moments Hadron mass (mX) moments
Expansion in terms of 1/mb and s(mb) Separate short- and long-distance effects at ~ 1 GeV
Perturbative corrections calculable from mb, mc, s(mb) Non-perturbative corrections cannot be calculated
Ex: 4 parameters up to 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
3(1/ )bmO
June 5, 2004 M. Morii, Harvard 4
ObservablesDefine 8 moments from inclusive Eℓ and mX spectra
Eℓ is measured in the B rest frame Integrations are done for Eℓ > Ecut, with Ecut varied in 0.6–1.5 GeV
0B
dM
1
E dM
d
1 ( 2,3)i
i
E M dM i
d
( 1, 2,3,4)iXX
i
m dM i
d
Partial branching fraction
Lepton energymoments
Hadron massmoments
June 5, 2004 M. Morii, Harvard 5
Electron Energy MomentsBABAR data, 47.4 fb-1 on (4S) resonance + 9.1 fb-1 off-peak Select events with 2 electrons One (1.4 < p* < 2.3 GeV) to
“tag” a BB event The other (p* > 0.5 GeV) to
measure the spectrumUse charge correlation Unlike-sign events
dominated by B Xcev Like-sign events
D Xev decays, B0 mixing
hep-ex/0403030, to appear in PRD
Unlike-sign
Like-sign
BABAR
June 5, 2004 M. Morii, Harvard 6
Electron Energy MomentsTurn the like-/unlike-signspectra Eℓ spectrum 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 (4S) to B rest frame Correct for the final state radiation using PHOTOS Subtract B Xuℓv
BABAR
Into the HQE fit
June 5, 2004 M. Morii, Harvard 7
Hadron Mass MomentsBABAR data, 81 fb-1 on (4S) resonanceSelect 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
Improve mX with a kinematic fit = 350 MeV 4-momentum conservation; equal mB on both sides; mmiss = 0
hep-ex/0403031, to appear in PRD
Fully reconstructedB hadrons
lepton
v
Xc
June 5, 2004 M. Morii, Harvard 8
Hadron Mass MomentsMeasured mX < true mX
Linear relationship Calibrate using simulation Depends (weakly) on decay
multiplicity and
Validate calibration procedure Simulated events in exclusive
final states D*± D0± in real data, tagged
by the soft ±
Calculate mass moments with Ecut = 0.9 … 1.6 GeVInto the HQE fit
BABAR
2missm
June 5, 2004 M. Morii, Harvard 9
Inputs to HQE FitmX moments
Eℓ moments
BABAR
hep-ex/0404017, to appear in PRL
Error bars are stat. & syst.with comparable sizes
June 5, 2004 M. Morii, Harvard 10
Systematic ErrorsDominant experimental systematic errors Electron energy moments
Tracking and electron ID efficiencies Background from secondary leptons (B D/Ds/ e) Bremsstrahlung correction B Xuℓv subtraction
Hadron mass moments Detector efficiency and resolution Background in fully-reconstructed B Other background
Hadron mis-ID, +–, B Xuℓv, secondary leptons
June 5, 2004 M. Morii, Harvard 11
HQE ParametersCalculation by Gambino & Uraltsev (hep-ph/0401063 & 0403166) Kinetic mass scheme to Eℓ moments mX moments
8 parameters to determine
8 moments available with several Ecut
Sufficient degrees of freedom to determineall parameters without external inputs
Fit quality tells us how well HQE works
cbV bm cm 2 2
G 3D 3
LS( )cB X B
kinetic
chromomagnetic
Darwin
spin-orbit
2(1/ )bmO
3(1/ )bmO
3(1/ )bmO2( )sO
( )sO
June 5, 2004 M. Morii, Harvard 12
Fitting MethodUse 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
±20% for the terms, ±30% for the terms Fully correlated for each moment at different Ecut
Uncorrelated between different moments Fit results stable for different treatment of the theory errors
2(1/ )bmO 3(1/ )bmO
June 5, 2004 M. Morii, Harvard 13
HQE Fit ResultsmX moments
Eℓ moments
● = used, ○ = unusedin the nominal fit
Red line: HQE fitYellow band: theory errors
BABAR
2/ndf = 20/15
June 5, 2004 M. Morii, Harvard 14
HQE Fit ConsistencyHQE describes BABAR data very well 2/ndf = 20/15 Separate fit of Eℓ and mX moments agree
BABAR
June 5, 2004 M. Morii, Harvard 15
HQE Fit Results
and consistent with B-B* mass splitting and QCD sum rules
s
s
s
3exp HQE th
exp HQE
exp HQE
exp HQE
2 2exp HQE
2exp HQE
(41.4 0.4 0.4 0.6 ) 10
(10.61 0.16 0.06 )%
(4.61 0.05 0.04 0.02 )GeV
(1.18 0.07 0.06 0.02 )GeV
(0.45 0.04 0.04 0.01 )GeV
(0.27 0.06 0.03 0.0
cb
c
b
c
G
V
m
m
B
s
s
s
2
3 3exp HQE
3 3exp HQE
2 )GeV
(0.20 0.02 0.02 0.00 )GeV
( 0.09 0.04 0.07 0.01 )GeVD
LS
2 3
LS
kinetic mass scheme with = 1 GeV
Uncalculatedcorrections to
June 5, 2004 M. Morii, Harvard 16
In PerspectiveNew BABAR result compares well with previous measurements
|Vcb| is now measured to ±2%
June 5, 2004 M. Morii, Harvard 17
Heavy Quark MassesConvert mb and mc into MS scheme (N. Uraltsev)
( ) 4.22 0.06GeV( ) 1.33 0.10GeV
b b
c c
m mm m
kinexp HQE th
kinexp HQE th
(1GeV) (4.61 0.05 0.04 0.02 )GeV
(1GeV) (1.18 0.07 0.06 0.02 )GeVb
c
m
m
theorytheory
References in PDG 2002
June 5, 2004 M. Morii, Harvard 18
SummaryBABAR has made significant progress in determination of |Vcb| HQE fit of Eℓ and mX moments 2% error on |Vcb|
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
s
3exp HQE th
exp HQE
kinexp HQE
kinexp HQE
(41.4 0.4 0.4 0.6 ) 10
(10.61 0.16 0.06 )%
(1GeV) (4.61 0.05 0.04 0.02 )GeV
(1GeV) (1.18 0.07 0.06 0.02 )GeVs
cb
c
b
c
V
m
m
B
( ) 4.22 0.06GeV( ) 1.33 0.10GeV
b b
c c
m mm m