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Determination of | V cb | Using Moments of Inclusive B Decay Spectra. BEACH04 Conference June 28-July 3, 2004 Chicago, IL. Alex Smith University of Minnesota. Introduction Hadron Mass Moments in B  X c l n Lepton Energy Moments in B  X c l n Photon Energy Moments in B  X s g decays

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determination of v cb using moments of inclusive b decay spectra
Determination of |Vcb| Using Moments of Inclusive B Decay Spectra

BEACH04 Conference

June 28-July 3, 2004

Chicago, IL

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

Alex Smith – University of Minnesota

measuring v cb
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
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)

Alex Smith – University of Minnesota

moments of observable spectra
Moments of Observable Spectra
  • Moment of distribution defined in usual way:
  • 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

eg., lepton energy moment:

Alex Smith – University of Minnesota

the cleo ii detector
The CLEO II Detector
  • 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

hadronic mass and q 2 moments in b x c l n

l

El

qWl

X

W

MX

En

q

n

B

Hadronic Mass and q2 Moments in BXcln
  • Neutrino reconstruction technique

Identify

lepton

1

hep-ex/0403052

Infer

hadronic

mass

3

Reconstruct

neutrino

2

Alex Smith – University of Minnesota

hadronic mass and q 2 moments in b x c l n1

l

El

qWl

X

W

MX

En

q

n

B

Hadronic Mass and q2 Moments in BXcln
  • Neutrino reconstruction technique

Identify

lepton

1

Infer

hadronic

mass

3

Reconstruct

neutrino

2

Alex Smith – University of Minnesota

hadronic mass and q 2 moments in b x c l n2
Hadronic Mass and q2 Moments in BXcln
  • Selection criteria applied to suppress continuum and enhance neutrino reconstruction
  • Fit differential decay rate in three dimensions:
    • q2
    • MX2
    • cosqWl
  • Fit Components and models:
    • BDlnHQET+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

Fit Components

Note: histograms

normalized to same area

Alex Smith – University of Minnesota

hadronic mass and q 2 moments in b x c l n3
Hadronic Mass and q2 Moments in BXcln
  • 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

hadronic mass and q 2 moments in b x c l n4
Hadronic Mass and q2 Moments in BXcln
  • 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

lepton energy moments in b x c l n
Lepton Energy Moments in BXcln
  • Di-lepton event sample
  • Use one lepton as the “tag”:
    • pl > 1.4 GeV/c, e or m
    • ~97% of sample is primaryBXln
    • 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

lepton energy moments in b x c l n1
Lepton Energy Moments in BXcln

Unmixed B0 Mixed B0

Primary Events

Opposite B Secondaries

Same B Secondaries

Alex Smith – University of Minnesota

lepton energy moments in b x c l n2
Lepton Energy Moments in BXcln

Unmixed B0 Mixed B0

Primary Events

Opposite B Secondaries

Same B Secondaries

Easily vetoed with kinematic cut

66% efficient

X25 rejection

Alex Smith – University of Minnesota

lepton energy moments in b x c l n3
Subtract backgrounds

Correct for efficiencies

Algebraically solve for primary spectrum

Lepton Energy Moments in BXcln

Alex Smith – University of Minnesota

lepton energy moments in b x c l n4
Lepton Energy Moments in BXcln
  • 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

photon energy moments in b x s g
Photon Energy Moments in BXsg
  • 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

photon energy moments in b x s g1
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 v cb
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)

Combined Fit to Determine |Vcb|

Alex Smith – University of Minnesota

combined fit to determine v cb1
Combined Fit to Determine |Vcb|

CLEO data

(GeV2)

Preliminary

(GeV/c2)

Alex Smith – University of Minnesota

combined fit to determine v cb2
Combined Fit to Determine |Vcb|

CLEO data

(GeV2)

Preliminary

1st and 2nd Lepton

Energy Moments

(GeV/c2)

Alex Smith – University of Minnesota

combined fit to determine v cb3
Combined Fit to Determine |Vcb|

CLEO data

(GeV2)

Preliminary

1st and 2nd Photon

Energy Moments

(GeV/c2)

Alex Smith – University of Minnesota

combined fit to determine v cb4
Combined Fit to Determine |Vcb|

CLEO data

(GeV2)

Preliminary

1st and 2nd Hadronic

Mass Moments

(GeV/c2)

Alex Smith – University of Minnesota

combined fit to determine v cb5
Combined Fit to Determine |Vcb|

CLEO data

(GeV2)

Preliminary

1stq2 Moments

(GeV/c2)

Alex Smith – University of Minnesota

combined fit to determine v cb6
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 mp2

Combined Fit to Determine |Vcb|

Alex Smith – University of Minnesota

combined fit to determine v cb7
Combined Fit to Determine |Vcb|

CLEO data

(GeV/c2)

Preliminary

(GeV/c2)

Alex Smith – University of Minnesota

combined fit to determine v cb8
Combined Fit to Determine |Vcb|

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

combined fit to determine v cb9
Combined Fit to Determine |Vcb|

Preliminary

1stq2 Moment

1st Hadronic Mass

Moment

2nd Hadronic Mass

Moment

Preliminary

Preliminary

Alex Smith – University of Minnesota

combined fit to determine v cb10
Combined Fit to Determine |Vcb|

Preliminary

measurement key

Alex Smith – University of Minnesota

combined fit to determine v cb11
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

Combined Fit to Determine |Vcb|

Preliminary

Alex Smith – University of Minnesota

summary
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
    • 2ndq2 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

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