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