Inclusive B Decays - Spectra, Moments and CKM Matrix Elements Presented by Daniel Cronin-Hennessy (CLEO Collaboration) Feb 24, 2004

Inclusive B Decays - Spectra, Moments and

CKM Matrix Elements

Presented by Daniel Cronin-Hennessy

(CLEO Collaboration)

Feb 24, 2004

Outline

Motivation and discussion of moments Overview of CESR/CLEO

Moments Measurements and |Vcb| E spectrum in inclusive decays B Xs

MX2 spectrum in inclusive decays B Xc l

El spectrum in inclusive decays B Xc l

Extraction of |Vub| More from E spectrum and lepton energy endpoint (|Vub|)

Summary

Motivation

Motivation

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Fundamental Standard Model parameters. Must be measured.

Describes math of CP Violation.

May not describe observed matter- antimatter asymmetry.

OverviewCKM matrix relates quark mass eigenstates to weak eigenstates

Fundamental Standard Model parameters. Must be measured.

Describes math of CP Violation.

May not describe observed matter- antimatter asymmetry.

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Motivation

B Meson Decay &

The Heavy Quark Expansion

c

u

d

b c d u

b

W

b c Decay

• Still need QCD corrections• Perturbative

Hard gluon (Short distance)

s

• Non-Perturbative Soft gluon (Long distance) , 1 & 2

B D e

W

e

]D

c

B[b

Just right?

W

b c

u

d]

]DB[

B D

Very difficult

Not always 3-body

Gluons in final state.

Quark Motion

Rate of decay modifiedby motion of quark in B meson. b quark lives longer. ~p2/E2 ~ (.5/5)2

Challenges:

Quark Hidden

We know MB well. mb not so well.

Semileptonic Rate

3

522

192

||)()(

bqbF

bs

mVGqlbBRqlb

GoalRate of semileptonic decay of beauty quark CKM element(s)

HQET+OPE allows any inclusive observable to be written as a double expansion in powers of s and 1/MB:

HQET

O(1/M) energy of light degrees of freedom (MB ~ mb + )

O(1/M2)1 -momentum squared of b quark

2 hyperfine splitting (known from B/B* and D/D* M)

O(1/M3) ~(.5 GeV)3 from dimensional considerations

sl = |Vcb|2 (A(s,,os2)+B(s)/MB+ C1/MB

2+…)

1 combined with the sl measurements better |Vcb|2

)1

()(),(32

22

12

22

MO

ME

MD

MC

MBAObservable sss

Semileptonic Decay Width

sl (B Meson Semileptonic Decay Width) – Calculated from B meson branching fraction and lifetime

measurements (CLEO, CDF, BaBar, Belle …)– It is the first approximation to the b quarks decay width

)]/1(474.7185.3946.0648.11[192

||)3689.0()( 3

22

21

2

2

3

522

BBBBB

BcbFcs MO

MMMM

MVGlXB

Free quarkdecay width

b quark motion –increased b lifetime

M hyperfine splitting

)]/1(2

9

21[

192

||)( 3

22

21

3

522

Bbb

bubFus MOradiative

mm

mVGlXB

Observables

B Xs : 1st and 2nd moments of Photon energy

B Xc : 1st and 2nd moments of hadronic recoil mass

B Xc : lepton energy moments

Moments dxxfxMomentth )(0 0

How much is there? (area)

dxxfdxxfx

Momentnd)()(

22

How wide is it? (width)

dxxfdxxfx

Momentst)()(

11

Where is it? (mean)

b s Moments

)

1(

94

33

12

3313))(175.1954.01()(620.0385.01

2 47

222

34321

3212

02

0M

OCMM

C

MMM

mE

BBDBB

ss

B

ssb

)

1(

12

3

12

32))(05412.005083.0()(01024.000815.0

12 4321

3212

02

02

122

MO

MMMMMEE

BBB

ss

B

ss

BB

u, c, t

b s Moments

)

1(

94

33

12

3313))(175.1954.01()(620.0385.01

2 47

222

34321

3212

02

0M

OCMM

C

MMM

ME

BBDBB

ss

B

ssB

)

1(

12

3

12

32))(05412.005083.0()(01024.000815.0

12 4321

3212

02

02

122

MO

MMMMMEE

BBB

ss

B

ss

BB

u, c, t

b s Moments

)

1(

94

33

12

3313))(175.1954.01()(620.0385.01

2 47

222

34321

3212

02

0M

OCMM

C

MMM

ME

BBDBB

ss

B

ssB

)

1(

12

3

12

32))(05412.005083.0()(01024.000815.0

12 4321

3212

02

02

122

MO

MMMMMEE

BBB

ss

B

ss

BB

radiative tail

u, c, t

Hadronic Mass Moments

)( 22

MM DX

Monte Carlo model shown

Measure moments of recoil mass

D and D* well measured

Need to determine contribution to moments from high mass components

Details of resonances not included in parton level calculation

2

B D

B D*

B D** B D

B Xc

Strategy

At least two inclusive measurements needed in addition to the B branching fraction and B lifetime in order to extract Vcb.

Measure: 1st and 2nd moments of Photon energy (b s) 1st and 2nd moments of hadronic recoil mass (B Xc ) lepton energy moments (B Xc )

Many measurements are needed to verifyConvergence of ExpressionsQuark-Hadron Duality

CESR/CLEO

LEPP

Cornell Electron-positron Storage Ring

~ ¾ km circumference

e+e- collisions

Ebeam: 1.5-5.6 GeV

Most data collected near (4S) resonance.

Operating Energies 2/3 data collected ON (4S)

e+e- (4S) BB ( ~ 1.0 nb) e+e- qq ( ~ 3.0 nb)

1/3 data collected OFF 60 MeV below Resonance Continuum only Almost perfect qq background sample

(4S)

CLEO

Photons: XtalCal (res=1.8%)

Electrons: XtalCal, Tracking

Muons: MuCh, Tracking

p K e : ToF+DeDx

Measurements I

Moments & Vcb

HadronicMass Moments Want from B Xc but can not

use hadronic daughters

Reconstruct mass with B, , and four-vectors

)cos(2222 BBBBX PPEEMMM

EEMMM BBX 2~ 222

2XM

Xsmall unknown

Xc

Lepton: Select events with very high lepton momentum (1.5 GeV) above lower momentum secondaries (eg D decays)

Neutrino: Use all observed energy-momentum to calculate neutrino 4-vector fakes arise from non-interacting neutrals (Klong, secondary neutrinos, neutrons)

– Fit spectrum with• B D • B D*• B

XH(various models for XH)

– Find moments of true MX

2 spectrum


0.0620.0230.251)( 22 MM DX

163.0048.0576.0)(222 MM XX

PRL 87 251808, 2001


• If we believed the second moment expansion, we could get Vcb from this

• Use first moments from b s and hadronic b cinstead...

Photon Energy Moments Always require high

energy photon 2.0 < E < 2.7 GeV |cos | < 0.7

Naïve strategy: Measure E spectrum for ON and OFF resonance and subtract

But, must suppress huge continuum background![veto is not enough] and

Three attacks: Shape analysis Pseudoreconstruction Leptons

Photon Energy Moments




Hadronic Mass and Photon Energy

011.0032.0346.2 E

0020.00066.00226.022 EE

GeV

GeV 2

0.0620.0230.251)( 22 MM DX

163.0048.0576.0)(222 MM XX

GeV 2

GeV 4

CLEO

PRL 87 251807, 2001

Vcb

In MS scheme, at order 1/MB3

and s2o

= 0.35 + 0.07 + 0.10 GeV1= -.236 + 0.071 + 0.078 GeV2

|Vcb|=(4.04 + 0.09 + 0.05 + 0.08) 10-2

sl, 1 Theory

Lepton Energy Moments in B X l

Muons Electrons

5.1

7.1

0

dEdEd

dEdEd

Rl

l

sl

ll

sl

5.1

5.1

1

dEdEd

dEdEdE

Rl

l

sl

ll

sll

Unfolded Lepton Energy Spectrum

for leptons from B X l

R0 = 0.6187+0.0014 +0.0016

R1 = 1.7810+0.0007+0.0009 GeV

CLEOMeasure lepton energy

From energy spectrum:

PR D67 072001, 2003

Consistency Among

Observables and ellipse extracted from 1st moment

of B Xs photon energy spectrum and 1st moment of hadronic mass2 distribution(B Xc l). We use the HQET equations in MS scheme at order 1/MB

3 and s2 o.

Expressions: A. Falk, M. Luke, M. Savage, Z. Ligeti, A. Manohar, M. Wise, C. Bauer

The red and black curves are derived from the new CLEO results for B X l lepton energy moments. Expressions: M.Gremm, A. Kapustin, Z. Ligeti and M.

Wise, I. Stewart and I. Bigi, N.Uraltsev, A. Vainshtein

Gray band represents total uncertainty for the 2nd moment of photon energy spectrum.

CLEO

Consistency Among

Experiments

CLEO • BABAR Preliminary• CLEO

OPE (Falk, Luke), 1 free param.

OPE (Falk, Luke), 1 using CLEOs photon energy moment.

Interpretation of Data

• BABAR Preliminary• CLEO



Expect average hadronic mass to increase with lowering lepton momentum cut

Increase observed much larger than expected

Suspects

Heavy Quark Expansion

BaBar measurement(s)

CLEO measurement(s)

Repeat BaBar’s measurement (underway)Suspect photon energy moments

Did we miss a contribution at low photon energy?Need to have missed a strange quark state with high mass. Baryon (our Neural Networks were never informed of this possibility)

Mechanism for baryon production in B decay

Internal W Emission External W Emission

Di-quark popping providing a mechanism for baryon production in B semileptonic decays will also allow for the same in B radiative decays.

Limits on Baryon Production (External W Emission)

Br(BXs <3.8 x 10-5 90% CL(E>2.0 GeV , Xs containingBaryons )PR D68:011102, 2003

SemileptonicCase

RadiativeCase

Br(Bpe-X)< 5.9 x 10-4 90% CLPR D68:012004, 2003Strong Limit but not enough.

Recent Moments Results

Current standing from CLEO and BaBar. (Extrapolates well to DELPHI measurement)

Good agreement between analyses.

Tolerable agreement with theory.

Global Analysis: hep-ph/0210027 Bauer,Ligeti,Luke &

Manohar

|Vcb|=(4.08+0.09) 10-2

PR D67:054012, 2003

Measurements II

Vub

|Vub| from Lepton Endpoint (using b s )

|Vub| from b u– We measure the endpoint

yield– Large extrapolation to obtain |

Vub|

– High E cut leads to theoretical difficulties (we probe the part of spectrum most influenced by fermi momentum)

GOAL: Use b s to understand Fermi momentum and apply to b ufor improved measurement of |Vub|

Kagan-Neubert DeFazio-Neubert

Convolute with light cone shape function.

b s (parton level)

B Xs (hadron level)

B lightquark shape function, SAME (to lowest order in QCD/mb) for b s B Xs and b u l B Xu l.

b u l (parton level)

B Xu l (hadron level)

Fraction of b uspectrum above 2.2 is

0.13 ± 0.03

Method for partial inclusion of subleading corrections: Neubert

•Published

•With subleading corrections

Subleading corrections large C. Bauer, M. Luke, T. Mannel A. Leibovich, Z. Ligeti, M. Wise M.B. Voloshin

|Vub| from Lepton Endpoint (using b s )

|Vub| = (4.08 + 0.34 + 0.44 + 0.16 + 0.24)10-3

The 1st two errors are from experiment and 2nd from theory

PRL 88 231803 2002

CLEO

Summary

Summary Vcb: Bound state corrections to the semileptonic width, predicted

by HQET and measured by a number moments analyses have permitted the extraction of Vcb to a level of a few %.

The precision has a minimal impact on constrains but we can view as stringest test of HQE methods used for Vub.

Many new measurements now available (some overlapping) Recent measurements of hadronic mass moments with lower

cut on lepton momentum. More inclusive. Hints at trend that may be incompatible with theory but experimental and theoretical uncertainties are still large.

CLEO: Soon to publish lepton moments at lower lepton energy cut.

Enough data available for a global fit (with correlations properly accounted for). Need more input from theory on best method of including theory uncertainties.

Summary Vub: Important to reduce uncertainties for test of standard model

The photon energy spectrum in b s provides a

quantitative model for the bound state effects in b u l This approach has not yet reached its full potential We

expect improved measurements from B factories (in progress at CLEO).

Current work is to improve shape extraction particulalry at low photon energy

The method does require additional theoretical refinements. Can theory calculate differences in the b light quark

processes or provide reliable estimate of this difference.

Improved Photon Energy Spectrum

Original analysis optimized for Br Measurement.Motivation for improving spectrum particularly in the low photon energy region.

Backgrounds are numerous in low energy region. 0 electrons (with no track matching) anti-neutrons KLong

-More efficient 0/ veto -CC simulation of non-photon showers constrained by data

Calorimeter Lateral Shape


Repeat entire analysis without a cut on the Calorimeter cluster shape.

MC does not model data well either dueto incorrect simulation of shower shape or wrong Klong and anti-neutron rates.


Require enriched anti-neutron sample

Select events with L baryon if no anti-proton found look at “photons” in the event. The antineutron calorimeter responseis extracted from this sample.

B X l with Neutrino Reconstruction Neutrino four-momentum inferred from hermeticity of detector.

Maximum likelihood fit over full three dimensional decay distribution

Contributions from B Xc l(D,D*,D**and NR) and B Xu l

|Vub| =(4.05 + 0.18 + 0.58 + 0.25 + 0.21 + 0.56) 10-3

stat syst b->c b->u theory model model

Coswl q2 MX2

MX2<2.25 GeV2 Q2>11 GeV2

CLEO CONF 02-09ICHP02 ABS933

Preliminary

MX2<2.25 GeV2

Q2>11 GeV2

Inclusive B Decays

• CLEO II&IIV

37 M hadronic 9.7 M BB Pairs 3.8 M B Xc

34 k B Xu

7 k B Xs

• Observables

E EE 2

2XM )(

222

MM XX ELepton

Fraction Branching

Consistency Across Schemes- 1S Mass v.

MS and ellipse extracted from 1st moment of B Xs photon energy spectrum and 1st moment of hadronic mass2 distribution (B Xc l). We use the HQET equations in 1S scheme at order 1/MB

3 and s2 o.

1S Expressions(recent): C. Bauer, M. Trott (hep-ph/0205039) C. Bauer, A. Manohar, Z.Ligeti and M. Luke private communication

In 1S mass scheme, at order 1/MB

3

and s2o

|Vcb|=(4.05+0.09+0.04+0.10) 10-2

(recall MS: |Vcb|=(4.04+0.09+0.05+0.08) 10-2)

Vcb Results

Vcb Results

BaBar at ICHEP

• BABAR Preliminary• CLEO



DELPHI

0.0 0.4

0.534

)( 22

MM DX

Lepton Cut (GeV)

Inclusive?CLEO moments analysis reduce background withcuts on variables of interest (but no explicit mass cut on mass moments)

semileptonic: e.g. leptons from charm decay radiative: eg: photons from 0 decay model dependence of course but even more fundamental concerns

Assumption that the average value of observable is the same at the hadron and quark level relies on a truly inclusive analysis. Must lower cuts in all analyses.

BaBar (and later CLEO) measures mass moments with various lepton momentum cuts. Lower lepton momentum correlates with higher mass hadronic state. Moments expected to increase but how much?

Preliminary results indicate larger increases than expected if one uses the HQET parameter () derived from photon energy spectrum.

Moment CLEO DELPHI(prelim)

BABAR(prelim)

<m2H - m2

D> 0.251±0.023±0.062 (El>1.5GeV) 0.534±0.041±0.074 Later<(m2

H- <m2H>)2

>.576±0.048±0.163 (El > 1.5GeV) 1.23±0.16±0.15

<(m2H- <m2

H>)3

>2.97±0.67±0.48

<E 2.3460.032 0.011

(E E)2 0.02260.00660.0020

<E 1.7810+0.0007+0.0009 (El > 1.5 GeV)

1.3830.012 0.009

(E E)2 0.192 0.005 0.010

(E E)3 0.029 0.0050.005

R0 0.6187+0.0014 +0.0016 (El > 1.5 GeV)

Global Analysis: hep-ph/0210027 Bauer,Ligeti,Luke &

Manohar

Overview

VVVVVVVVV

tbtstd

cbcscd

ubusud

Unitarity

0*** VVVVVV tbtdcbcdubudVV tbtd

*

VV cbcd*

VV ubud*

Algebra

0,0

1,0

||

||

VV

cb

ub

CP

Moments Summary

CLEO has measured six moments, two each from 1) the photon energy distribution in B Xs

2) the hadronic mass2 distribution in B Xc l

3) most recently the lepton energy spectrum in B Xc l

The allowed values for HQET parameters and 1 are in agreement for all measurements.

|Vcb| extracted at the level of 3%

Documents

Inclusive B Decays - Spectra, Moments and CKM Matrix Elements Presented by Daniel Cronin-Hennessy (CLEO Collaboration) Feb 24, 2004