A. OyangurenA. Oyanguren

Ph.D. thesis.Ph.D. thesis.

26/03/2004

Theory Theory

Introduction Introduction

|V|Vcbcb| from| from

Analysed data samplesAnalysed data samples

The DELPHI experimentThe DELPHI experiment

|V|Vcbcb| from inclusive decays | from inclusive decays

Summary and Conclusions Summary and Conclusions

ContentsContents

Contents 2

Eur. Phys. J. C33 (2004) 213

Phys.Lett. B556 (2003) 41DELPHI Paper 340/draft 1

The CKM matrixThe CKM matrix

Introduction

VVcbcb

q2

ccbb

Vud Vus Vub

Vcd Vcs Vcb

Vtd Vts Vtb

CKM =

3

VVcbcb is a fundamental parameter of the is a fundamental parameter of the SMSM

From tree level From tree level processesprocesses

=sinC 0.22DeterminesDetermines AA

, A, , A, , ,

PDG PDG ’02’02

5%5% accuracyaccuracy

Measurement of |VMeasurement of |Vcbcb||

Introduction 4

by means of:by means of:

Exclusive processes

Inclusive processes

Theory 5

Heavy quark expansionsHeavy quark expansions

Heavy Quark Effective Theory (HQET)

Operator Product Expansion (OPE)

Inclusive decays:

Exclusive decays:

sl sl = = |V|Vcbcb||22 f f (theory)(theory)

Decoupling of heavy quark spin Decoupling of heavy quark spin (doublets)(doublets)Universal form factorsUniversal form factors

F(qF(q22maxmax)=1)=1

Non perturbative corrections in inverse powers Non perturbative corrections in inverse powers of mof mbbExpected small ( Expected small ( no term 1/mno term 1/mbb ))

DELPHIDELPHI

The DELPHI experiment

6

RICH

TPC

ToFmagnet

ID

HPC

Muon chambers HCAL

OD

VD

B decays B decays @@ DELPHI DELPHI

7

HPC + muon chambers

bb / hadrons 22%

EB 0.7 Ebeam 30 GeV

3mm

D0

-

B0

Fragmentationparticles

Other B

+D*+ K-

+RICH

Tracking(VD)

Missing energy

Analysed data samples

Z → qq 3.4 M

c 3mm

Event reconstructionEvent reconstruction

8Analysed data samples

Exclusive reconstruction:Exclusive reconstruction:

9|Vcb| from

|V|Vcbcb| from | from

Known function (Phase space)

Form factor of the B D* transition Normalized by HQET (mQ ) at q2

max (w= 1) (1/ mQ )n and QCD corrections

FD*(1)=1

FD*(1)= 0.91 0.04 *

* PDG ‘02

From the s.l. decay width:From the s.l. decay width:

D*D*

Selected candidatesSelected candidates

10|Vcb| from

D0 K-+ D0 K- + - + D0 K-+(0)

D*D*++ - - -- candidates candidates 1688 48

m= m(D0) -m(D0) ~ m(soft)DD0 0 softsoft

B B D* D* --

qq2 2 measurementmeasurement

11|Vcb| from

Measured

From missing energy

E, p conservation

, vertex info...

From decay products

Efficiency (q2):

q2 resolution:

(q2s) = (0.9850.026) + (0.00240.0043)q2

s

Sample compositionSample composition

12|Vcb| from

• Combinatorial background

• b D**-

D*+X

• b D*+DX- Y

• Z cc

• Events with fake leptons

• b D*+ -X

- Y

Real or fake D*+ candidates can come, apart from signal Bd→D*+

- events, from :

Main source of background

m distribution

Discriminant variables based on the event

topology

QX< 0

QX= 0

Isospin

2313

(Cascade)

(d±)

FitFit

13|Vcb| from

Event by event Event by event likelihood:likelihood:

d+d-

dN

dq2 |Vcb|2 F2(w) K(w) eff(q2)

res(q2)

F(w) as function of other form factors: R1 and R2, and the slope 2

(I. Caprini, L. Lellouch, M. Neubert, [Nucl. Phys. B530(1998)153])Fit F(1)|Vcb| and 2

meas.

q2 m

Results on real dataResults on real data

14|Vcb| from

Fitted D** Fitted D** contribution: contribution:

Systematic uncertaintiesSystematic uncertainties

15|Vcb| from

DELPHI averageDELPHI average

16|Vcb| from

DELPHI average:DELPHI average:

Goals:Goals:Increased statistics ( 4)Improvements in the reconstruction (Eb, mD*)

Control on background

Comparison with other measurementsComparison with other measurements

17|Vcb| from

World averageWorld average |Vcb|=0.0402 0.0009 0.0018

(excl.)

|V|Vcbcb| from inclusive decays | from inclusive decays

18|Vcb| from inclusive decays

Measured sl=(0.434 0.008)×10-10 MeV

Error on |VError on |Vcbcb| ~ 1 %| ~ 1 %

sl =|Vcb|2

Theory:Theory:

1+O(1/mb) 2

ci=f(mb,mc,s)

O.P.E.O.P.E.

Inclusive s.l. decay width:Inclusive s.l. decay width:

Non-perturbative corrections 5%

Perturbative corrections 10%

OPEOPE formalism formalism

19

, , GG22 22 DD ,, LSLS 33 33

|Vcb| from inclusive decays

Kinetic massKinetic mass scheme scheme ( (=1=1 GeV)GeV)

Can be measured?

Not rely on mNot rely on mcc expansionexpansion

sl =|Vcb|2

Quark massesQuark masses

Kinetic energy of the b quark inside the Kinetic energy of the b quark inside the mesonmeson: : chromo-magnetic exp. value chromo-magnetic exp. value (MB*-MB)22GG

22

mmbb, m, mcc

Darwin term:Darwin term:

Spin-orbit term:Spin-orbit term:

33DD

33LSLS

Phys.Lett. B556 (2003) 41

Moments of the Moments of the D** D** distributiondistribution

|Vcb| from inclusive decays

Moments of the total hadronic mass distribution in bc -

Inclusive |Vcb| determination

22%

50%

28%D

D*

D**

Inclusive observables Inclusive observables O O

Known

Measurements of OPE parameters

b c -

q2

ccbb

D** properties ?

20

D** spectroscopyD** spectroscopy

D** properties 21

Ground state Broad resonances

Narrow resonances

D** decays into D and D*

possible D** D(*)

In addition to resonant states, D** includesnon resonant D(*)

(not measured)

D** signalD** signal

22D** properties

Definition of signal and background regions

23D** properties

Fit to wrong sign candidates:

signal

**, 1ary and 2ary

vertices, and other

topological info

D** production ratesD** production rates

Fit to right sign candidates:

24

D** D(*) limits:

D** properties

Results onResults on production rates production rates

Main syMain systematicstematics:s: discr. variables & cascade modelling(RS BR’s 4% each)

From wrong sign candidatesFrom wrong sign candidates

Comparison with other measurements:Comparison with other measurements:

Increased statisticsImproved systematics

D** mass distributionD** mass distribution

25D** properties

Fit to m = m(D(*)**) - m(D(*)) and R (>0.25)

From right sign candidates

Considering D** 11 parameters

(19±13)%

26

D** mass distributionD** mass distribution

D** properties

m = m(D(*)**) - m(D(*))

D0+ D+- D*+ -

D** production characteristicsD** production characteristics

27D** properties

Total D** rate:

Main systematics due to the possible D(*) contribution

Compatible results with measure-ments from B →D** decays :

CLEOCLEO

BELLEBELLE

First measurement of D* properties in B semileptonic decays

1

Moments of the mass distributionMoments of the mass distribution

28Moments

From previous results:

Combining information from momentsCombining information from moments

29Moments

Fixing Constraining+

DELPHI hadronic mass + lepton energy moments

Fit resultsFit results

30Moments

Unconstraining the b quark mass:

The c quark mass corresponds to:

G (BPS limit) 2 2

D small 0.1 GeV 3

3

|V|Vcbcb| determination | determination

31Moments

Including electroweak, (s)2 and (1/mb)3 corrections:

In the kinetic mass scheme, mqkin(1 GeV)

s (mb/2, 2mb)mb, mc, , D, G, LS

2 2 33

LEPb,

Comparison with other measurementsComparison with other measurements

32Moments

Amsterdam, Amsterdam, ICHEP ‘02ICHEP ‘02

Aachen, ICHEP ‘03Aachen, ICHEP ‘03

New theoretical calculations: hadron + lepton moments within the kinetic mass formalism.

BABAR result seems not to fit with theoretical expectations

First measurement at low p

New analysis from BABAR

Summary and conclusions Summary and conclusions

33Summary and conclusions

|Vcb| from exclusive BdD*+

Measurement of Measurement of BR(bBR(bD*D*++XX

|Vcb| from inclusive decays

D** properties, measurements of:D** properties, measurements of: -- production rates production rates -- production characteristicsproduction characteristics -- hadronic mass momentshadronic mass moments

Development of a new OPE formalism:Development of a new OPE formalism: -- measurement of non-perturbative measurement of non-perturbative

parameters parameters up to O(1/mup to O(1/mbb))

33

00

Precise |VPrecise |Vcbcb| determination| determination-- Measured Measured sl.sl. ~ 1%~ 1%

-- Theory Theory ~ 1-1.4%~ 1-1.4%-- Non-pert. parameters Non-pert. parameters ~ 1.4%~ 1.4%