Determination of |Vcb| Using Moments of Inclusive B
Decay Spectra
Alex Smith
University of Minnesota






Introduction
Hadron Mass Moments in BXcln
Lepton Energy Moments in BXcln
Photon Energy Moments in BXsg decays
Combined Fit to Determine |Vcb| and HQET parameters
Summary
BEACH04 Conference
June 28-July 3, 2004
Chicago, IL
Alex Smith – University of Minnesota
Measuring |Vcb|
• |Vcb| is a fundamental parameter of the Standard Model
• Inclusive semileptonic bc transitions provide a good
laboratory in which to measure |Vcb|
– Exclusive semileptonic modes suffer large theoretical uncertainties
– Purely hadronic final states too complicated
– Weak bcln process still obscured by strong interactions
• Strong interactions of inclusive semileptonic decays
described by
– Perturbative QCD
• Short-distance effects
– Heavy Quark Effective Theory/Operator Product Expansion
• Non-perturbative long-distance effects
Alex Smith – University of Minnesota
Heavy Quark Effective Theory
• Semileptonic rate expressed as a double expansion
in as and 1/mb
– Use “kinetic mass” formulation of Uraltsev, et al (hep-ph/0401063)
b  cn  
GF2 mb5 Vcb
192
3
2
1  Pa , ,  N m , m ,  , 
s
mb
mc
2
b
c

2
G
3
,  D3 ,  LS
: mc  c quark mass
O1 / mb  : mb  b quark mass (  )


O 1 / mb2 : 2  Fermi momentum of b quark ( 1 )


: G2  Hyperfine splitting ( 2 )
O 1 / mb3 :  D3  Darwin Term
3
:  LS
 Spin - orbit coupling
Alex Smith – University of Minnesota

Moments of Observable Spectra
• Moment of distribution defined in usual way:
eg., lepton energy moment:
d
dE

dE

E
(n)
E Ecut   cut
d
E dE dE
cut
En
• A commom set of HQET parameters appear in expressions
for
–
–
–
–
–
Lepton energy moments in BXcln
Hadronic mass-squared moments in BXcln
q2 moments in BXcln
Photon energy moments in BXsg
Semileptonic width
• Simultaneously fit these measurements to determine HQET
parameters
Alex Smith – University of Minnesota
The CLEO II Detector
• CESR symmetric e+ecollider
– Energy near U(4S)
• Most relevant features of
detector:
– Hermeticity of detector
neutrino reconstruction
– Excellent shower
resolution of CsI
calorimeter photons,
electrons
– Good charged particle
resolution and dE/dx of
drift chamber leptons
Alex Smith – University of Minnesota
Hadronic Mass and q2 Moments in BXcln
• Neutrino reconstruction
technique
l
hep-ex/0403052
El
qWl
Infer
X
hadronic
MX
mass
Identify
lepton
W
En
q
n
B
Reconstruct
neutrino
  
M  M  q  2 Ebeam E  En   2 pB p  pn cos q B n




2
X
2
B
2
Small
Alex Smith – University of Minnesota
Unknown
Hadronic Mass and q2 Moments in BXcln
• Neutrino reconstruction
technique
l
El
qWl
Infer
X
hadronic
MX
mass
Identify
lepton
W
En
q
n
B
Reconstruct
neutrino
  
M  M  q  2 Ebeam E  En   2 pB p  pn cos q B n




2
X
2
B
2
Small
Alex Smith – University of Minnesota
Unknown
Hadronic Mass and q2 Moments in BXcln
Fit Components
• Selection criteria applied to
suppress continuum and enhance
neutrino reconstruction
• Fit differential decay rate in three
dimensions:
– q2
– MX2
– cosqWl
• Fit Components and models:
Note: histograms
normalized to same area
–
–
–
–
–
–
–
BDln HQET+measured FF’s
BD*ln HQET+measured FF’s
BD**ln
ISGW2
B(Xc)non-resln Goity-Roberts
BXuln
ISGW2+NR
Secondary leptons CLEO MC
Continuum and fakes
data
Alex Smith – University of Minnesota
Hadronic Mass and q2 Moments in BXcln
q2
MX2 • Fit projections
– Fit provides reasonable
description of the data
• Branching fractions of
individual modes are
|pl|
very model-dependent
• Inclusive differential
decay rate much less
model-dependent
cosqWl
En
Alex Smith – University of Minnesota
Hadronic Mass and q2 Moments in BXcln
hep-ex/0403052
• Results are consistent with previous CLEO
measurements
• Uncertainties and results comparable to BaBar
measurements
• q2 moments expected to be somewhat
complementary to MX moments
– Only measured by CLEO
Alex Smith – University of Minnesota
Lepton Energy Moments in BXcln
• Di-lepton event sample
• Use one lepton as the “tag”:
hep-ex/0403053
– pl > 1.4 GeV/c, e or 
– ~97% of sample is primary
BXln
– Lepton charge tags flavor of
parent B meson
• Look for signal electron in
“tagged” events
Monte Carlo simulation of electron
daughters from B decay
– pe > 0.6 GeV/c
– Correct for backgrounds and
efficiencies
– Use charge and kinematic
correlations to separate the
spectra from primary and
secondary leptons
• Primary leptons are the signal
Alex Smith – University of Minnesota
Lepton Energy Moments in BXcln
Unmixed B0
Mixed B0
  b b  e
  b b  e
Primary Events
Opposite B Secondaries    b b  c  e     b b  c  e 
Same B Secondaries
b  c   e
Alex Smith – University of Minnesota
Lepton Energy Moments in BXcln
Unmixed B0
Mixed B0
  b b  e
  b b  e
Primary Events
Opposite B Secondaries    b b  c  e     b b  c  e 
Same B Secondaries
b  c   e
Easily vetoed with kinematic cut
66% efficient
X25 rejection
Alex Smith – University of Minnesota
Lepton Energy Moments in BXcln
• Subtract backgrounds
• Correct for efficiencies
• Algebraically solve for
primary spectrum




opp b
same b
 dB b 

dN   e 
dB c 
dB c 
1    



dp
dp
dp
dp


opp b

dN   e   dB b 
dB c 
1   


dp
dp
 dp

Alex Smith – University of Minnesota
Lepton Energy Moments in BXcln
• Correct for
hep-ex/0403053
– EW radiation
– B boost
• Results consistent with previous CLEO measurements
• Systematics-limited--- Uncertainty on moments comparable to BaBar
• Integrate measured spectrum
BRB  Xen   10.91  0.09  0.24%
Alex Smith – University of Minnesota
Photon Energy Moments in BXsg
• Large photon background
from continuum processes
– 0 and h veto
– Suppress using neural
network
• Several different inputs related to
event shape
– Pseudo-reconstruction
• Ks0 or K+/• 1-4 pions, at most one 0
– Large subtraction necessary
Eg  2.346  0.032  0.011 GeV
hep-ex/0108032
Eg2  Eg
2
 0.0226  0.0066  0.0020 GeV 2
Alex Smith – University of Minnesota
Photon Energy Moments in BXsg
• bsg measurement is key to extracting HQET
parameters
– Sensitive to mb
• Mean energy (1st moment) roughly equal to mb/2
– Independent of mc
• New analysis in progress
– Previous analysis optimized for branching fraction
measurement
– New analysis of old data optimized for extraction of
spectrum
– New results soon
Alex Smith – University of Minnesota
Combined Fit to Determine |Vcb|
• Measurements included in fit:
–
–
–
–
1st and 2nd photon energy moments : Eg > 2.0 GeV
1st and 2nd lepton energy moments : Ee > 0.7, 1.2, 1.5 GeV
1st and 2nd hadronic mass moments : Ee > 1.0, 1.5 GeV
1st q2 moment : Ee > 1.0, 1.5 GeV
• Chi-squared fit including full correlation matrix of
measurements
• Uses O(1/m3) formulation and code from Uraltsev and
Gambino (hep-ph/0401063)
– Includes perturbative corrections to account for lepton/photon
energy cuts
• Will also use approach of Bauer, Ligeti, et al before
finalizing results (hep-ph/0210027)
Alex Smith – University of Minnesota
(GeV2)
Combined Fit to Determine |Vcb|
CLEO data
(GeV/c2)
Alex Smith – University of Minnesota
(GeV2)
Combined Fit to Determine |Vcb|
CLEO data
1st and 2nd Lepton
Energy Moments
(GeV/c2)
Alex Smith – University of Minnesota
(GeV2)
Combined Fit to Determine |Vcb|
CLEO data
1st and 2nd Photon
Energy Moments
(GeV/c2)
Alex Smith – University of Minnesota
(GeV2)
Combined Fit to Determine |Vcb|
CLEO data
1st and 2nd Hadronic
Mass Moments
(GeV/c2)
Alex Smith – University of Minnesota
(GeV2)
Combined Fit to Determine |Vcb|
CLEO data
1st q2 Moments
(GeV/c2)
Alex Smith – University of Minnesota
Combined Fit to Determine |Vcb|
• Only CLEO has measured photon energy, q2, hadronic
mass, and lepton energy in a single experiment
– A solution consistent with all measurements is found
– Without BXsg, mb and mc almost completely correlated in fit
– Most of the sensitivity to mb comes from BXsg measurement
• First moment  mean photon energy  mb/2 (approx.)
• Other measurements primarily constrain mb-Cmc, C~0.6
– q2 moment gives some complementary information
• Nearly independent of 2
Alex Smith – University of Minnesota
(GeV/c2)
Combined Fit to Determine |Vcb|
CLEO data
(GeV/c2)
Alex Smith – University of Minnesota
Combined Fit to Determine |Vcb|
1st Lepton Energy
Moment
2nd Lepton Energy
Moment
1st Photon Energy
Moment
2nd Photon Energy
Moment
Alex Smith – University of Minnesota
Combined Fit to Determine |Vcb|
1st q2 Moment
1st Hadronic Mass
Moment
Alex Smith – University of Minnesota
2nd Hadronic Mass
Moment
Combined Fit to Determine |Vcb|
measurement key
Alex Smith – University of Minnesota
Combined Fit to Determine |Vcb|
Vcb
mb  4.564
mc  1.16
 0.10
 0.11
  0.483
2
0.073
 0.074
3


 42.4  0.8 10
GeV/ c
GeV/ c
 0.050
 0.054
2
2
GeV
2
083
G2  0.10 00..081
GeV 2
026
~D3  0.09100..029
GeV 3
3
 LS
 0.05  0.17 GeV 3
• Measurement of |Vcb| and
HQET parameters, including
mb(), mc(), 2() at =1 GeV
• Expect to reduce experimental
errors significantly with
additional measurements
• Theory errors under study and
not shown or included in fit
– Expected to be >= experimental
errors
Alex Smith – University of Minnesota
Summary
• Potential to significantly improve measurement of |Vcb|
– Experimental errors expected to be less than 2%
– Theoretical errors expected to be comparable to experimental errors
– Theoretical models will benefit from experimental constraints on
higher order parameters
• Many improvements to analysis in progress:
– 3rd lepton energy moments– work in progress
– Include more 1st and 2nd lepton energy moment measurements in fit
– 2nd q2 moments – should have corrections soon
• Complementary sensitivity to parameters
– Improved BXsg moments – soon
• Critical constraint on mb
– Include theoretical uncertainties in fit– almost ready
• CLEO has measured several different moments in a single
experiment
– Complementary to and of comparable precision to public BaBar
measurements
Alex Smith – University of Minnesota