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Determination of | V cb | Using Moments of Inclusive B Decay Spectra

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BEACH04 Conference

June 28-July 3, 2004

Chicago, IL

Alex Smith

University of Minnesota

- Introduction
- Hadron Mass Moments in BXcln
- Lepton Energy Moments in BXcln
- Photon Energy Moments in BXsg decays
- Combined Fit to Determine |Vcb| and HQET parameters
- Summary

Alex Smith – University of Minnesota

- |Vcb| is a fundamental parameter of the Standard Model
- Inclusive semileptonic bc transitions provide a good laboratory in which to measure |Vcb|
- Exclusive semileptonic modes suffer large theoretical uncertainties
- Purely hadronic final states too complicated
- Weak bcln 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

- Perturbative QCD

Alex Smith – University of Minnesota

- Semileptonic rate expressed as a double expansion in as and 1/mb
- Use “kinetic mass” formulation of Uraltsev, et al(hep-ph/0401063)

Alex Smith – University of Minnesota

- Moment of distribution defined in usual way:
- A commom set of HQET parameters appear in expressions for
- Lepton energy moments in BXcln
- Hadronic mass-squared moments in BXcln
- q2 moments in BXcln
- Photon energy moments in BXsg
- Semileptonic width

- Simultaneously fit these measurements to determine HQET parameters

eg., lepton energy moment:

Alex Smith – University of Minnesota

- CESR symmetric e+e- collider
- 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

l

El

qWl

X

W

MX

En

q

n

B

- Neutrino reconstruction technique

Identify

lepton

1

hep-ex/0403052

Infer

hadronic

mass

3

Reconstruct

neutrino

2

Alex Smith – University of Minnesota

l

El

qWl

X

W

MX

En

q

n

B

- Neutrino reconstruction technique

Identify

lepton

1

Infer

hadronic

mass

3

Reconstruct

neutrino

2

Alex Smith – University of Minnesota

- Selection criteria applied to suppress continuum and enhance neutrino reconstruction
- Fit differential decay rate in three dimensions:
- q2
- MX2
- cosqWl

- Fit Components and models:
- BDlnHQET+measured FF’s
- BD*ln HQET+measured FF’s
- BD**ln ISGW2
- B(Xc)non-resln Goity-Roberts
- BXuln ISGW2+NR
- Secondary leptons CLEO MC
- Continuum and fakes data

Fit Components

Note: histograms

normalized to same area

Alex Smith – University of Minnesota

- Fit projections
- Fit provides reasonable description of the data

- Branching fractions of individual modes are very model-dependent
- Inclusive differential decay rate much less model-dependent

q2

MX2

cosqWl

|pl|

En

Alex Smith – University of Minnesota

- 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

hep-ex/0403052

Alex Smith – University of Minnesota

- Di-lepton event sample
- Use one lepton as the “tag”:
- pl > 1.4 GeV/c, e or m
- ~97% of sample is primaryBXln
- Lepton charge tags flavor of parent B meson

- Look for signal electron in “tagged” events
- 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

hep-ex/0403053

Monte Carlo simulation of electron daughters from B decay

Alex Smith – University of Minnesota

Unmixed B0Mixed B0

Primary Events

Opposite B Secondaries

Same B Secondaries

Alex Smith – University of Minnesota

Unmixed B0Mixed B0

Primary Events

Opposite B Secondaries

Same B Secondaries

Easily vetoed with kinematic cut

66% efficient

X25 rejection

Alex Smith – University of Minnesota

Subtract backgrounds

Correct for efficiencies

Algebraically solve for primary spectrum

Alex Smith – University of Minnesota

- Correct for
- EW radiation
- B boost

- Results consistent with previous CLEO measurements
- Systematics-limited--- Uncertainty on moments comparable to BaBar
- Integrate measured spectrum

hep-ex/0403053

Alex Smith – University of Minnesota

- Large photon background from continuum processes
- p0 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 p0

- Large subtraction necessary

hep-ex/0108032

Alex Smith – University of Minnesota

- bsg measurement is key to extracting HQET parameters
- Sensitive to mb
- Mean energy (1st moment) roughly equal to mb/2

- Independent of mc

- Sensitive to mb
- 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

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

1stq2 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

CLEO data

(GeV2)

Preliminary

(GeV/c2)

Alex Smith – University of Minnesota

CLEO data

(GeV2)

Preliminary

1st and 2nd Lepton

Energy Moments

(GeV/c2)

Alex Smith – University of Minnesota

CLEO data

(GeV2)

Preliminary

1st and 2nd Photon

Energy Moments

(GeV/c2)

Alex Smith – University of Minnesota

CLEO data

(GeV2)

Preliminary

1st and 2nd Hadronic

Mass Moments

(GeV/c2)

Alex Smith – University of Minnesota

CLEO data

(GeV2)

Preliminary

1stq2 Moments

(GeV/c2)

Alex Smith – University of Minnesota

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 BXsg,mb and mc almost completely correlated in fit

Most of the sensitivity to mb comes from BXsg 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 mp2

Alex Smith – University of Minnesota

CLEO data

(GeV/c2)

Preliminary

(GeV/c2)

Alex Smith – University of Minnesota

1st Lepton Energy

Moment

Preliminary

2nd Lepton Energy

Moment

Preliminary

1st Photon Energy

Moment

2nd Photon Energy

Moment

Preliminary

Preliminary

Alex Smith – University of Minnesota

Preliminary

1stq2 Moment

1st Hadronic Mass

Moment

2nd Hadronic Mass

Moment

Preliminary

Preliminary

Alex Smith – University of Minnesota

Preliminary

measurement key

Alex Smith – University of Minnesota

Measurement of |Vcb| and HQET parameters, including mb(m), mc(m), mp2(m) at m=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

Preliminary

Alex Smith – University of Minnesota

- 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
- 2ndq2 moments – should have corrections soon
- Complementary sensitivity to parameters

- Improved BXsg 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