precise determination of |v cb |, |v ub |, and the b-quark mass from inclusive b decays |v cb | at...

Precise Determination of |Vcb|, |Vub|, and the b-quark mass from

inclusive B decays

• |Vcb| at the ~1% level - The new BABAR result as an example•Towards a ~5% measurement of |Vub| - what can we lean from bcl and bs•bs and its senitivity to „new physics“- how tight are the constraints really?

• |Vcb| at the ~1% level - The new BABAR result as an example•Towards a ~5% measurement of |Vub| - what can we lean from bcl and bs•bs and its senitivity to „new physics“- how tight are the constraints really?DESY TUESDAY SEMINAR

21/09/2004

Oliver Buchmüller CERN

2 Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004

CP Violation in the Standard Model(SM)

CKM Matrix

Unitarität

The elements of the CKM matrix

are the only source of CP violationin the SM

The area of the triangle is proportionalto the CP violation in the SM

Measurements of the angles and sides of the triangleMeasurements of the angles and sides of the trianglerepresent a fundamental test of the SM!represent a fundamental test of the SM!

N(q)/N(anti-q) ~ 10N(q)/N(anti-q) ~ 10-20-20

much to small!much to small!

The expected size of CP violation in the SM is much too small The expected size of CP violation in the SM is much too small to explain N(q)/N(anti-q)~10to explain N(q)/N(anti-q)~10-9-9


The sides of the triangleThe sides of the triangle

ikjkijVV δ=*

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛=

tbtstd

cbcscd

ubusud

CKM

VVV

VVV

VVV

V

0*** =++ tbtdcbcdubud VVVVVV

01*

*

*

*

=++cbcd

tbtd

cbcd

ubud

VVVV

VVVV

|Vub/Vcb| describes a circle in the (,) plane

A measurement of a length of a triangle is as good as a measurement of A measurement of a length of a triangle is as good as a measurement of an angle!an angle!


The Trinagle Today

sin2sin2 has become a has become aprecision measurement precision measurement

and is now the best know and is now the best know quantity of the triangle!quantity of the triangle!

If we want to sufficiently over constrain the triangle we need to improveIf we want to sufficiently over constrain the triangle we need to improvethe other measurements as well!the other measurements as well!

|Vcb| and |Vub|


|Vcb| und |Vub| from semilleptonic B decays

Why semileptonic B decyas?

BXl mit l=e,bcl

No „colour activity“between

W l and c quark

b

cW

1. For |Vxb| we need to have a bx transition (trivial)2. Need a precise theoretical framework to translate the measurements on “meson level” into “quark level” (not trivial)

semileptonic decays are theoretical semileptonic decays are theoretical necessity! necessity!


The Inclusive ApproachThe Inclusive ApproachThe advantage of being inclusive! QCD«mb : inclusive decays admit systematic expansion in QCD/mb Non-pert corrections are generally small and can be controlled

Hadronization probability =1, approximately insensitive to details of meson structure as QCD«mb (at least far from perturbative

singularities)

02

2

dqdqdE

d

l

Γ can be expressed as double series in s s and and QCD/mb

(OPE) with parton model as leading term No 1/mb

correction!


The Heavy Quark Expansion (HQE)The Heavy Quark Expansion (HQE)

•Short-distance physics encoded in coefficients of operator products(to some order in s). Calculable!

•Long-distance physics encoded in exp. values of products of quark operators (to some order in 1/mb). NOT calculable! Must be determined empirically.

Need to get access to the not very well know HQE parameters!Need to get access to the not very well know HQE parameters!


Access to the HQE ParameterThe HQE not only predicts the inclusive decay rates but also inclusive

differential decay distributions for semileptonic decays (e.g. moments of the lepton energy spectrum).

Measure (a lot) moments of inclusive kinematic distributions

Extract HQE parameters (e.g. mb) from a fit to all moments

Compare predicted inclusive decay rate with its measurement Γsl = Γsl (B, BRsl)

|Vcb|


Pioneering Work

M1(Mx) M2(Mx) M3(Mx)

M1(E) M2(E) M3(E)

mb,kin(GeV= 4.58 +0.06fit+0.05sys

GeVmc,kin(GeV= 1.15 +0.09fit+0.08sys

GeV

2 (GeV= 0.41 +0.04fit+0.04sys GeV2

D3 (GeV= 0.05 +0.02fit+0.01sys

GeV3

Input constraints: mb= 4.57 0.10 GeV mc= 1.05 0.30 GeV

DELPHI CLEO

Multi parameter fits to moments but sensitivity was limited …

10

Oliver Buchmüller CERN - DESY TUESDAY SEMINAR 21/09/2004

The B Factory BABAR and PEPII

LINAC

BABAR

SLD

11


BABAR AND PEPII

9 GeV

3.1 GeV

e+e- 4s(10.58 GeV) BB (96%, 4% non-BB)

4s(10.58 GeV)

BB production threshold

12


A Tough Race

RUNI

RUNII

RUNIII

RUNIV

Competition is important:Both B factories perform very well (15/06/2004) BABAR 227 fb-1

BELLE 275 fb-1 500 fb-1

Better than expectedand gives hope for the future.

(ca. 550 Mio BB events)

BABAR results of this talk are based on 82 fb-1

ca. 90 Mio BB events

13


Semileptonic B Events: Access to Vcb and Vub

A theoretical necessity …A theoretical necessity …

Vcb

b c

W

(Vub)

“Tree Level”“Detector Level”

No color interaction between W and c-quark

“CKM Matrix”

… … but an experimental challenge!but an experimental challenge!

DD**

ll

ee--

ee++

BBrecoreco

BBrecoilrecoil

XXcc

νν

Need to fully reconstruct the Need to fully reconstruct the semileptonic B Event in ordersemileptonic B Event in order to get access to the kinematicto get access to the kinematic

information of the signal B decayinformation of the signal B decay“Neutrino Reconstruction”

14


Kinematic of Semileptonic B Events

Reco. B:4 measured quantities

X-System4 gemessene

Größen(e.g. Mx )

Lepton3 measured quantities(e.g. El)

Energy and Momentum ConservationEnergy and Momentum Conservation

Ebreco + EX + El + E - EPEPII = 0

Pbreco + PX + Pl + P - PPEPII = 0

4 Constraints

+ Mass Constraint+ Mass Constraint

M(Breco)=M(X,l,)

+ 1 Constraint

Neutrino3 unmeasured quantities

5 Constarints – 3 unmeasured quantities =

2 times overconstraint System„2C kinematic fit“

Use fulll reconstructed B sample:„Tag“ B is full reconstructed and

the signal B is identified via the lepton.

Pe-Pe+

Incomming momentum of the two beams are well measured

(EPEPII ,PPEPII) bekannt!

full reconstruction of the entire semileptonic event (especially Mx und El)

15


1. Fully reconstructed hadronic B-decay2. Semileptonic decay of other B

o Identify Lepton (e or )o reaming tracks and neutral objects define the X-System

3. Mx determined by 2C kinematic fit

4. Sideband subtraction of the combinatoral B background

.

Hadron Moments <Mxn>

,e

,e

(*)D

K

2/350)( cMeVMx ≈σ

signalbackgroundK

5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 mES[GeV/c2]

225020001750150012501000750500250

0

Eve

nts

/ 1.8

MeV

/c2

SLBrecBBABAR Y(4S)

24 recBs

ES pm −=

7114 signal events,2102 combinatoral bg.

Out of 90 Mio BB events!

HX

high mass final states

Mx2[GeV2/c4]

16


Lepton Moments <ELn>

BABAR

eesigsig

ee--

ee++

BBtagtag

BBsigsig

νν

eetagtag

“e+e-” unlike sign

“e±e” like sign

“double lepton tag”

Subtract irreducible bg. and unfoldthe number of primary electrons from the

two samples (“ARGUS method”).

Select events withtwo identified electrons:

e+e- and e±e

Unfolded primary electron spectrum for BXl

17


<Mx> (ELCUT) and

<EL>(ELCUT)

Measure moments over a large rage in phase space

as function of a cut in the lepton energy

A cut in the lepton energy will restrict the phase space for high mass states production (D**, D*).

Thus <Mx> (ELCUT) and <EL>(EL

CUT) will probethe underlying “decay dynamic” of BXcl events.

Mx

Mx

High mass states

18


<Mx> (ELCUT) and

<EL>(ELCUT)

)( eXBBr c→ ( )2ee EE − ( )3ee EE −eE

Incr

ease

of t

he m

ean

Decrease of truncated BR

BABAR BABAR BABAR BABAR

EcutEcut EcutEcut

Phys.Rev.D69:111103,2004

Phys.Rev.D69:111104,2004

Reduction of high mass final states

19


HQE Fit

=/)( 00 EM l )( eXBBr c→B/= 3322

DLSGcb mm ),,,,,,( 0E)( eXBBr c→ lΓf

2|| cbV

),( 0EEeXBBr lc >→ i-th central El moment for El>E0:

i-th Mx moment and El>E0 :

|Vcb| „master“ formula : : l

0f3322DLSGcb mm ),,,,,,( 0E

)4..1()(

)3..1()(

0

0

==

==

iEM

iEMXi

il l

ifX

if

3322DLSGcb mm ),,,,,,( 0E3322DLSGcb mm ),,,,,,( 0E

Use dedicated HQE for every measured observable:Γclv (BR, lifetime)Hadron Mass Moments <Mx

n>(Ecut)Lepton Energy Moments <El

n>(Ecut)(Fit parameters are in red)

i-th E moment and E>E0 : l

0f3322DLSGcb mm ),,,,,,( 0E From BXs

Extract the HQE parameter mb,mc,2,G

2, D3, LS

3 and |Vcb| as well as BRclv from a simultaneous fit to all moment measurements (27+1*).

Experimental and theoretical errors and their correlations are all accounted for in the fit.* Only external input to the fit is:

B lifetime B+B0 =1.6080012 ps

20


Combined Fit to Ee and Mx

Moments =/)( 00 EM l )( eXBBr c→

B/= 3322DLSGcb mm ),,,,,,( 0E)( eXBBr c→ l

Γf2|| cbV

),( 0EEeXBBr lc >→ i-th central El moment for El>E0:

i-th Mx moment and El>E0 :

|Vcb| „master“ formula : : l

0f3322DLSGcb mm ),,,,,,( 0E

)4..1()(

)3..1()(

0

0

==

==

iEM

iEMXi

il l

ifX

if

3322DLSGcb mm ),,,,,,( 0E3322DLSGcb mm ),,,,,,( 0E

Calculations taken from Gambino and Uraltsev, hep/ph 0401063

xf1xf2

xf3 xf4

SLBf ×l0

l1f

l2f

l3f

high correlationbetweenmeasurements : this fit uses solid points only

)20ndof(0.152 ==χ

21


Fit Results

Strong correlation between mb and mc:

mb(1 GeV) – mc(1 GeV) = (3.44±0.03exp±0.02HQE±0.01αs

) GeVkine

tic

mas

s sc

hem

e

GeVGeVm

GeVGeVm

eXBBr

V

c

b

c

cb s

)02.006.007.018.1()1(

)02.004.005.061.4()1(

)%06.016.061.10()(

10)6.02.04.04.04.41(||

s

s

SL

HQEexp

HQEexp

HQEexp

3HQEexp

±±±=±±±=

±±=→×±±±±= −

Γ

Phys. Rev. Lett.93:011803,2004hep-ex/0404017

BABAR BABAR

χ2=1 ellipses

2D projections of the fit result:

BABAR

22


|Vcb| and BR(BXl)

But comparison is not on “equal footing”because the input (e.g. B lifetime and BR ) as well as the theoretical error assumption

are not the same job of HFAG

A better comparison is the total semileptonic BR.

The from the HQE Fit extracted BRis roughly 30% more accurate than

the HFAG average.sets roughly the scale of improvement

23


b-quark and c-quark mass

Conversion from kinetic mass scheme to MS scheme with hep-ph/9708372, hep-ph/0302262

See also report from CKM WS hep-ph/0304132

mc(mc) = 1.33 ± 0.10 GeVmb(mb) = 4.22 ± 0.06 GeV BABAR

24


New Moment Measurements

ICHEP04 has surprised us with a lot more moment measurementsfrom various collaborations:

BABAR:•hep-ex/0403031 (Phys.Rev.D69,2004) Hadron Moments from semileptonic B decays•hep-ex/0403030 (Phys.Rev.D69,2004) Lepton Moments from semileptonic B decays

BELLE:•hep-ex/0408139 (preliminary) Hadron Moments from semileptonic B decays•hep-ex/0409015 (preliminary) Lepton Moments from semileptonic B decays•hep-ex/0403004 (Phys.Rev.Lett.93,2004) Photon Energy Moments from BBXXss decays decays

CDF:•http://www-cdf.fnal.gov/physics/new/bottom/040428.blessed-bhadr-moments/ Hadron Moments from semileptonic B decays

CLEO:•hep-ex/0403052 (Phys.Rev.D70:,2004) Hadron Moments from semileptonic B decays•hep-ex/0403053 (Phys.Rev.D70:,2004) Lepton Moments from semileptonic B decays•hep-ex/0108032 (Phys.Rev.Lett.87,2001) Photon Energy Moments from BBXXss decays decays DELPHI:•hep-ex/0210046 Hadron Moments from semileptonic B decays•hep-ex/0210046 Lepton Moments from semileptonic B decays

More than 100 single moment measurements! perfect playground for consistency tests …

25


Include Additional Moments in the HQE Fit

BABAR moments only All Momentsχ2/NDF 0.75 0.55|Vcb|x10-3 41.390.59(0.62) 41.380.45(0.62) mb [GeV] 4.6110.067 4.6100.053mc [GeV] 1.180.09 1.170.08BRclv [%] 10.610.17 10.640.14

Very consistent results and the inclusion of the additionalVery consistent results and the inclusion of the additionalmoments leads to significant improvements of the extractedmoments leads to significant improvements of the extracted

fit parameters (e.g. mfit parameters (e.g. mbb ~25%) ~25%)

Include all moment measurements in the fit that are givenwith a full covariance matrix.

Use the extracted HQE parameters as base for the theoretical predictions!

26


Comparison: Hadron Moments

Y-a

xis:

HQ

E p

red

icti

on

- M

easu

rem

en

t

Best fit

Total Error

Exp. Error

Very good agreement!

Also the moments notincluded in the fit agree

well with the HQE predictionbased on the fit results!

27


Comparison: Lepton Moments

Y-a

xis:

HQ

E p

red

icti

on

- M

easu

rem

en

t

Very good agreementfor lepton momentsfrom BABAR, BELLE

and DELPHI.

Under investigation.Under investigation. Need to properly take into

account common systematics, all correlations, etc …

but looks like a ~3σ difference

Keep in mined that the moments are highly correlate.Typical between the two extreme values is ~50%

Best fit

Total Error

Exp. Error

But the results from CLEO fit not too well …

28


Comparison with other (independent) determinations

In hep-ph/0408002 Bauer et al. have carried out an independent |Vcb|determination based on calculations in the 1s scheme (and other schemes).

mb, mc

Leading orderdefined in different schemes

(2, G

2)

1,2

O(1/mb2)

&

(D3, LS

3)

1,2O(1/mb

3)

& Gremm,Kapustin

A simultaneous fit to all data yields: (hep-ph/0408002 - 1s scheme)

|Vcb|=41.90.6(fit)0.1(B) x10-3

mb1s =4.680.4(fit) GeV

1 =-0.230.06(fit) GeV2

(our results - kinetic scheme) |Vcb|=41.40.5(fit) [0.6(theo)] x10-3

mbkin =4.610.5(fit) GeV

2

=0.400.04(fit) GeV2

Comparison:

2 = -1 + O(s) -1 + 0.17 GeV2

translate mb into MS: mb(mb) — —

|Vcb|: 41.9 vs.. 41.4 [x10-

3] 0.4 vs. 0.4 [GeV2] 4.19 vs. 4.22 [GeV]

Leading HQE parameters are consistent but |Vcb| differs by 1.2% - - too much?

29


Inclusive |Vcb|

• Moment measurements from various experiments as well as improved theoretical calculations in the HQE framework allow the extraction of the O(1/mb

3) parameters without any external constraints. Example BABAR analysis:

GeVGeVm

GeVGeVm

eXBBr

V

c

b

c

cb s

)02.006.007.018.1()1(

)02.004.005.061.4()1(

)%06.016.061.10()(

10)6.02.04.04.04.41(||

s

s

SL

HQEexp

HQEexp

HQEexp

3HQEexp

±±±=±±±=

±±=→×±±±±= −

Γ Phys. Rev. Lett,2004hep-ex/0404017

Orhep-ph/0408002

1S scheme Bauer et al.

The determination of |Vcb| from inclusively defined moments of semileptonic kinematic distributions has entered the phase of a

precision measurement.

Still a few outstanding issues:•Consistency of CLEO lepton moments•Compatibility of extracted |Vcb| values (inconsistently applied QED corrections?!)•Uncertainty of calculations for the non-integer moment <Mx> and <Mx3>

>2% measurement of |Vcb| + extraction of all HQE parameters to O(1/mb

3)

But the general picture looks very encouraging ….

30


Unitarity Triangle and |Vcb|

What have we learned … 5% vs. 2%What have we learned … 5% vs. 2%

31


|Vub| today… and its (current) limitations

|Vub| has crossed the ~10% error barrier!Already quite an accomplishment but we

want more (target ~5% error)

Error Budget|Vub| |Vub| [0.09(exp) 0.1(SF) 0.05(HQE)]

10% - experimental error:With increasing statistic BABAR and BELLE will be able to significantly improve this error!

10% - “shape function” error:Limited knowledge of the shape function leads to the largest theoretical uncertainty. Currently the shape function parameter are obtained from the BELLE photon energy spectrum from bs

5% - “HQE” error:OPE based translation of the measured Brulv

into |vub|. The limiting factor is the uncertainty of the b quark mass!

Need to work hard on the extractionNeed to work hard on the extractionof the shape function parameter and of the shape function parameter and

a better determination of ma better determination of mbb

32


Photon Energy SpectrumBesides “new physics” the radiative penguin decay bs probes also very important SM quantities such as the b-quark mass and the “Fermi motion”.

s

b

bs

<E> mb

<(E-<E>)2 > Fermi Motion (

2)

Heavy Quark Limit mb

8

<E> =mb/2 and <(E-<E>)2 >= 2/12

Probes directly mb while bcl is most sensitive to mb-mc

Gives access to the shape function (b quark distribution function) for the heavy to light quark transition

Complementary information to semileptonic decays

33


The experimental challenge

Schnitt

bsBR ~ 10-4

BBudsc

Before all cuts After almost all selection cuts

The very difficult background situation requires a lower cut on the photon energy to measure relevant quantities like BRbs or the moments of the spectrum.

How far can we go down …?

34


The Measured Spectrum BELLE 2004 CLEO 2001

E>1.8 GeV

E>2.0 GeV

Ecut=1.8 GeV: BELLE

<E> =2.292 0.043 GeV<E

2> - <E>2 =0.0305 0.0100 GeV2

Ecut=2.0 GeV: CLEO

<E> =2.346 0.034 GeV<E

2> - <E>2 =0.0226 0.0070 GeV2

35


Shape Function ParameterThe shape function from bs and bul are related and it is possible

to use the photon energy spectrum to extract the shape function parametervalid for bul decays (Caveat: 1/mb corrections)

HFAG: Use the BELLE photon energy spectrum to determinethe shape function (hep-ex/0407052)

Fit true underlying photon spectrum via a Monte Carlo simulation to the measured

spectrum (similar to an unfolding)

36


HQE Prediction for <E> and <(E-<E>)2 >

New HQE calculation from Benson, Bigi and Uraltsevin the kinetic scheme [O(1/mb

3); O()] (soon to be published)(soon to be published)

Comparable to those for clv moments.

l0f

3322DLSGcb mm ),,,,,,( 0E i-th E moment and E>E0 :

Caveat: For tight cutoffs the expansion scale QMB-2E

cut(“hardness”) becomes to small for a reliable 1/Q expansion Bias in the leading HQE parameters mb am

2

Benson et al provide alsopredictions for the bias effect

as a function of the cutoffExpected bias at 2E

cut=2.0 GeV:δmb 40 MeV ; δ

2 0.1 GeV2

In the following consider both scenarios:1. HQE prediction only2. HQE prediction & bias correction

37


Consistency between bs and b clUse extracted HQE parameters from the clv moment fit to predict the moments of the photon energy spectrum.

“HQE only” “bias corrected HQE”Moment measurements agree wellwith HQE prediction obtained from

the clv moment fit. Evidence that bias correction is

needed for moments above E>1.8 GeV

But we can do more …Use the shape function parameter

which ft the BELLE spectrum to obtainthe moments as a function of the cut.

(Test: agrees nicely at E=1.8 GeV with the

direct measurement from BELLE)

Remarkable agreement withHQE prediction

Strong evidence, especially from the second moment, that bias corrections are needed above above E>1.8 GeV.

38


What can we learn from this?

1. The HQE parameter extracted from b cl events are the same as the one obtained from b s events (e.g. mb

from clv=mbfrom s)

We can use the enormous potential of our clv momentmeasurements to predict the moments of the photon energy

spectrum and to extract the shape function parameter from it!… very important for |Vub|

2. There is compelling evidence that for E>1.8 GeV the HQE prediction have to be bias corrected

(as claimed in hep-ph/0308165)We need more moment measurements as a function of E to

to established this bias effect … but the current evidence is already strong.

39


Moment Predictions

Ecut=1.8 GeV:

<E> =2.312 0.024 GeV<E

2> - <E>2 =0.0329 0.0026 GeV2

Ecut=2.0 GeV:

<E> =2.341 0.025 GeV<E

2> - <E>2 =0.0222 0.0024 GeV2

Ecut=1.8 GeV: BELLE

<E> =2.292 0.043 GeV<E

2> - <E>2 =0.0305 0.0100 GeV2

Ecut=2.0 GeV: CLEO

<E> =2.346 0.034 GeV<E

2> - <E>2 =0.0226 0.0070 GeV2

Experimental ResultsPredictions for the HQE fitbased on cl moments

The HQE fit results would constrain the moments of the photonenergy spectrum by a factor ~2 better than the current experimental

measurements. Using this information for the extractionof the shape function parameters will significantly improve

the theoretical uncertainties on Vub!

|Vub| |Vub| [0.09(exp) 0.05(SF) 0.04(HQE)]

|Vub| |Vub| [0.09(exp) 0.1(SF) 0.05(HQE)]Getting much closer to a 5% theoretical error

40


Unitarity Triangle - The Future?!

Vcb ~ 1% and Vub ~5%(theo) 5% (exp)Vcb ~ 1% and Vub ~5%(theo) 5% (exp)

41


bs: very sensitive to “new physics”

b

s

“New physics” can contribute in the loop …

…and would lead to an increase of BR(bs)

Tight constraints on “new physics parameter” which are especially important for the search at the LHC/LC.

42


BR(BXs) TodaySlide from the ICHEP04 Plenary Talk of Ahmed Ali (DESY). BRHFAG=3.540.3

BRSM =3.700.3

However, a new paper (hep-ph/0408179)from M. Neubert claims that

perturbative uncertainties have beenunderestimated in the theoretical

calculations of BRSM:

BRSM0.6

100% increase of the uncertaintyfor the SM prediction!

43


Potential Impact on “New Physics” Constraints

tan

BR(bs)MH

ICHEP2004

BR(bs)

BR

(b

s)

Since the bs decay is very sensitiveto certain contributions from „new physics“

a significant incraese of thetheoretical uncertainties would softena lot of rather tight (indirect) limits on

„new physics“ processes (e.g. 2HDM).

For illustrative purpose only - the TYPEII Two Higgs Doublet Model

0.65

200

Neubert - hep/ph 0408179

44


How can we validate the prediction?

hep-ph/0408179

According to hep-ph/0408179, also the prediction of the first moment of the photon energy spectrum <E>must suffer from large perturbative uncertainties:

<E> ~0.06 GeV (mb~ 120 MeV)

The prediction from hep-ph/0408179 are compatible with the data (E=[1.6,2.0]) but the HQE prediction in the kinetic scheme from Bigi et al. describe the data over the entire

cut range much better than the claimed <E> ~0.06 GeV (mb~ 120 MeV).

Evidence that perturbative (and non-perturbative) uncertainties are under control?

In any case, the multitude of moment measurements represent a tool to scrutinize the prediction power of the theory important for bs and its sensitivity to new physics.

45


TodayToday2007?2007?

46


BACKUP - UT Fits

----------------------------------------------------------Vcb_err : 0 ( 0.2% ) | 2% | 5%----------------------------------------------------------===> Lmax (flat Likelihood)----------------------------------------------------------rho_bar : 0.21 +- 0.05eta_bar : 0.35 +- 0.02----------------------------------------------------------===> L*e^{-1/2}----------------------------------------------------------rho_bar : 0.22 +- 0.12 | 0.22 +- 0.12 | 0.21 +- 0.14eta_bar : 0.34 +- 0.05 | 0.34 +- 0.06 | 0.35 +- 0.07----------------------------------------------------------===> L*e^{-2}----------------------------------------------------------rho_bar : 0.21 +- 0.17 | 0.20 +- 0.18 | 0.19 +- 0.20eta_bar : 0.35 +- 0.08 | 0.35 +- 0.08 | 0.36 +- 0.11

---------------------------------------

47


Backup - RESULTS

mb(mb) = 4.22 ± 0.06 GeV mc(mc) = 1.33 ± 0.10 GeV

Conversion from kinetic mass scheme to MS scheme with hep-ph/9708372, hep-ph/0302262

See also report from CKM WS hep-ph/0304132

48


Backup

Lepton Moment Measurement

49


Selecting B X e Decays Based on events with one high energetic electron

p* > 1.4 GeV/c , J/-veto „tag electron“ , originates predominantly from semileptonic B-decays

Look for oppositely charged electrons :

J/

Backgrounds (MC)Signal (MC)

pe[GeV/c]pe[GeV/c]

+−→ eeJ tag/ψpe[GeV/c]

B‘s at rest :

no angularcorrelation between e+ & e cut

e+ & e „back-to- back“

1.0

0.5

0.0

-0.5

-1.00 0.5 1.0 1.5 2.0 2.5

„ARGUS-Method“

−tage cX +e

e

e

Y

BcX

+e e

B −tage

cX

e

B

0 0.5 1.0 1.5 2.0 2.5

50


Raw Spectra & Backgrounds

Sizable contribution of „upper Vertex“ processes : dominant source of syst. uncertainties at low energies

e

sce

eY

DDBBXe

+

+− →←tag

e

ce

eY

KDDBBXe

+

− →← (*)(*)tag

e

ce

e

XBBXe+

+− →←tag

e

ce

e

XBBXe+

+− →←tag

%28≈BrBr

%25≈BrBr

XeB →mostly

mostlyYeXB C →→

Ele

ctro

ns

/ 50

MeV

/c

meetag±

±± eetag

14.47 −=∫ fbdtL

51


Inclusive e Spectrum Correction for electron efficiency e and B0B0

mixing

Bremsstrahlung corrections full detector simulation checked appropriate modeling

of detector material Compare Ee distribution of

ee ee events in datawith simulation

Partial branching fraction :

⎥⎦

⎤⎢⎣

⎡−

−−−

=±±±→

dp

dN

f

f

dp

dN

f

f

dp

dNeeee

cute

exb

)21()21(

111

00

00

00

00

χ

χ

χ

χ

εεν m

=>

=>→ →

tagacc

eexbe N

GeVENGeVEXeBBr

εγν ν )6.0(

)6.0),(( )%23.006.036.10( sysstat

)(eXB c→

Consistent with previous result ( Phys. Rev. D 67, 031101)

cut- cos of acceptance

))4((

parameter mixing

e,e

000

000

tag±=

→=

=

mθε

χ

cut

BBsYBrf

BB

52


Inclusive e Spectrum : Moments

Subtraction of contribution from BXu e decays Br(BXu e from BABAR-measurement ( this talk)

Correction for QED-radiative effects PHOTOS

Moments estimated from histogram small corrections due to finite binning and boost into B-

restframe

Results (Ee > Ecut) : )( eXBBr c→ eE ( )2ee EE − ( )3ee EE −

53


Backup

Hadron Moment Measurements

54


Mxn Analysis : Event

Selection Fully reconstructed hadronic B-decay

Semileptonic decay of other B lepton with : missing energy Emis & momentum pmis

completeness of XH : Emis pmis

Mx determined by 2C kinematic fit energy conservation, p2

miss = 0

HX

,e

,e

(*)D

K

2/350)( cMeVMx ≈σ

signalbackgroundK

5.22 5.23 5.24 5.25 5.26 5.27 5.28 5.29 mES[GeV/c2]

225020001750150012501000750500250

0

Eve

nts

/ 1.8

MeV

/c2

high mass final states

Mx2[GeV2/c4]

SLBrecBBABAR Y(4S)

24 recBs

ES pm −=

0)( >× lBb QQSL

7114 signal events,2102 combinatoral bg.

55


Determination of Mxn

(n=1,2,3,4)

Measured Mxn differs from true Mx

n

For each interval in Mxn, full detector

simulation delivers Mxn and Mx

n calibration curve which is applied to

data event-by-event weak dependence on decay model validated on data with decays function of multiplicity and

Event selection efficiency depends on decay mode

influence on Mxn determined with MC,

systematic error estimated by variationof individual exclusive decay modes

missmiss pEr

−

)high()low( nx

nx MM ≠

→ lDB *

0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 pmin[GeV/c]

4.5

4.4

4.3

4.2

4.1

4.0

Mx2

[G

eV2 /

c4 ]~

calibration (D,D*, D**,D(*) mix)

verification withexcl. modes

D

*D

.Resnon−

**D

3 4 5 6 7 8 9 10 11 12 Mx

2 [GeV2/c4]

1211109876543

Mx2

[G

eV2 /

c4 ]

~

~

182 −=∫ fbdtL

56


Hadron Moments: <Mx> and <Mx3>

Bauer et al. 1s scheme (hep-ph/0408002) Our results - kinetic scheme

<Mx> <Mx2>

<Mx3> <Mx4>

Not in the fitNot in the fit Not in the fitNot in the fit

Not in the fitNot in the fit

Not in the fitNot in the fit

While the lepton energy moments lead to very similar results, especiallythe non-integer hadron mass moments <Mx> and <Mx3> are different …

57


Scale Dependence of the Kinetic SchemeCheck scale dependence on the level of the physical observables (moments)

that are supposed to be scale independent!

Valuable input fromPaolo Gambino and Nikolai Uraltsev

Vary the scale dependent HQE parameters simultaneously between =[0.5-1.5] GeV. However, to maintain the

physical meaning of the c quark mass =[0.8-1.2] GeV is a more appropriated choice for a reasonable scale variation.

Red Band:Propagated theoretical uncertainty from the extracted HQE parameters

in the BABAR analysis.

Yellow Band:10% variation of the O(1/mb

2) and O(1/mb

3) contribution. This variation corresponds to an

0.1x10-3 uncertainty in |Vcb|

58


Scale Dependence of the Kinetic Scheme

The observed scale dependence of the predicted moments in the kinetic scheme is very small and even for the large scale variation of =[0.5-1.5] GeV (default =1GeV), the observed

moment shifts are already covered by an uncertainty of the O(1/mb2)

and O(1/mb3) contributions of 10%.

Such an uncertainty would manifest itself in an error on |Vcb | of 0.1x10-3.

Following the suggestion for the theoretical error evaluation in hep-ph/0401063, the final theoretical errors of the BABAR

analysis on |Vcb| and the extracted HQE parameters fully cover the small effect of the observed scale dependence:

Example: |Vcb| (theo-BABAR) =0.7x10-3

to be compared with |Vcb| (scale) <0.1x10-3

59


BSG MOMENT PREDICTION

I------------------- Eg=1.8 EG 2.31394725 0.0183035162 VEG 0.0329645342 0.0026 RHO 0.759208181 I------------------- Eg=2.0 EG 2.34259823 0.0190865906 VEG 0.0222734452 0.0024 RHO 0.694841549

CLV + BSG BELLE + BSG CLEO + BSG BABAR

I------------------- Eg=1.8 EG 2.31247747 0.0243168435 VEG 0.0328578215 0.0026 RHO 0.845508417 I------------------- Eg=2.0 EG 2.34107022 0.0253493739 VEG 0.0221826394 0.0024 RHO 0.795027137

CLV + BSG BELLE

Ecut=1.8 GeV: BELLE

<E> =2.292 0.043 GeV<E

2> - <E>2 =0.0305 0.010 GeV2

Ecut=2.0 GeV: CLEO

<E> =2.346 0.034 GeV<E

2> - <E>2 =0.0226 0.007 GeV2

Experimental Results

60


Yet another “triangle” to be tested …

bbss, X, Xssllll

BR ~10BR ~10-4-4

mmbb

bbululBR ~10BR ~10-3-3

VVub ub

bbclclBR ~10BR ~10-1-1

VVcbcb,,

mmbb, ,

“shape function”

HQE link established? HQE link not y

et esta

blished

bbss: : Large potential for new physics but still the issue of the rather high photon energy cutoff.

bbXXssll: ll: “Flag ship analysis” forfuture b exp. (LHCB, BTEV,1035-36)

Theoretical uncertainties on Xsll will dependent on the

knowledge of the b quark massand its fermi motion in B meson.

VubVub//Vcb: Vcb: The largest uncertainty is dueto the imperfect knowledge of the b quark

mass and its fermi motion (Vub).

We need Theory and Experiment to not onlyWe need Theory and Experiment to not only establish establish the the missing linksmissing links in the “HQE triangle” but also to check its in the “HQE triangle” but also to check its consistencyconsistency! !

The measurement of the moments is one step in this direction …

61


The three requirements from Andrei Sacharow (1967):1. Baryon number violation2. C und CP violation3. Abkehr vom thermodynamischen Gleichgewicht

Somewhere here

precise determination of |v cb |, |v ub |, and the b-quark mass from inclusive b decays |v cb | at...

Documents