rhul group meeting 18. dec. 03henning flächer 1 hadronic mass moments from semileptonic b meson...

RHUL Group Meeting 18. Dec. 03 Henning Flächer 1

Hadronic Mass Moments from Semileptonic B Meson Decays

at BABAR

Henning Flächer

OUTLINE

• Mass Moment Measurement• Interpretation in context of HQET• Conclusions

• Motivation• Fully reconstructed B mesons• Event selection


Motivation

CKM matrix describes quark mixing by relating the weak- to the mass- eigenstates and accommodates CP violation.

Semileptonic B decays give direct access to |Vub| and |Vcb|Allow for factorization of leptonic and hadronic currents.

Advantages of inclusive B decays: large rates OPE provide expansions for inclusive observables like:• semileptonic decay width• mean values of hadronic mass distributions• mean values of lepton momentum spectra

Precise theoretical calculations if OPE provides consistent framework ΓSL|Vcb|2 (1+corrections)


|Vcb| and |Vub| from semileptonic B decays

BXl with l=e,bc l

b c

W

No interaction between W → lν and c-quark

•When measuring |Vcb| we look for b → c transitions

•Due to the strong interaction it is only possible to measure B→Xc lν

In semileptonic B decays final state interaction is reduced to a minimum

Only then it is possible to relate b→c to B→Xc

Xc can be D, D*, D** & D(*) (n)πInvariant mass of Xc is our observable!


Non-perturbative parameters appear in the expansion which need to be measured by experiment

Theory: The way towards |Vcb|

Operator Product Expansions within the context of Heavy Quark Effective Theory provide a powerful tool to predict decay rates with very

high precision (2%)

Important assumption:Quark-Hadron Duality

Similar expansions in other variables:

Inclusive B decays: invariant mass of X-system <MX>

In b→ s γ gamma decays: photon energy <Eγ>Consis

tency

needs t

o

be test

ed and

verifi

ed!!!

}{ )π

α()

m

1()λcλcΛ(

m

c)

π

αc(1Λ

m

c

π

αc1cm

192π

VGΓ

2s

3B

27162

2B

5s4

B

3s21

5B

2

3cb

2F

sl OO


Analysis Method


Fully Reconstructed B-Mesons

Reconstruct one B candidate in the event:

A big step forward!

Reconstruction efficiency ratherlow, only ~ 0.4 % only possible at

a B-Factory like BaBar!

With a data set of 89 M BB pairs(Run1+2 only) we obtain ~ 350 000 fully reconstructed B mesons

Considering the semileptonic branching fraction we finally

obtain 350000 x 2 x 10.8% ~ 70 000 semileptonic decays.


Semiexclusive B reconstruction

)( 04

0321

(*) nKnKnnDB s

Consider the following decays:

Add π+, π0, K+, K0siteratively until:

22*2* /2.5 cGeVpEm BbeamES

EbeamB EEE 3**

Advantages:• Breco momentum• Breco Flavour• Background reduction (combinatorics)• mES sideband

Lepton required on recoil side

2,2,5 4321 nnnn

Disadvantage:• limited statistics


What is Xc?

nresoH

nresoH

resoX

resoH XXXX

DDDDX

MRMR

MRMRM

**

Decays B Xc l v:

Four resonances above D*

Four non-resonant decays

Broad mass spectrum above thetwo narrow resonances (D,D*)

D*

D

Mass spectrum on detector level:

MXdet (GeV)

i

iR 1with

Moment:

(weighted sum)


Event Topology

BB -> Breco (X,l,Pmiss)

Apply Energy and Momentum conservation

EBreco+ EX + El + E - EPEPII = 0

PBreco+ PX + Pl + P - PPEPII = 0

4 Constraints

+ Mass Constraints

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

+ 1 Constraints

X-SystemX-System(4 measured parameters)(4 measured parameters)

Lepton(3 measured parameters)

Missing Neutrino(3 unmeasured parameters)

B reco candidate(4 measured parameters)

Observable:Observable: Invariant mass of X-System Invariant mass of X-System

:= Mx:= Mx

Kinematically closed environment – reconstruction of all kinematic quantities (energies, momenta, masses) in the B meson rest frame can be

achieved!


Selection

Identification of exactly one lepton with P* > 0.9 GeV

Event quality cuts: |Emiss-pmiss| < 0.5 GeVBreco Quality: P > 40%

Event Selection:

Furthermore: Emiss > 0.5 GeV & pmiss > 0.5 GeV Total charge |ΔQ| ≤ 1 7100 signal and 2100 background events

Lepton charge consistentwith prompt B decay


Analysis Strategy

• Subtract Background from misreconstructed B mesons• Calibrate measured masses event-by-event• Subtract remaining B Background• Apply efficiency and acceptance corrections

To obtain the true meanvalue of the hadronic mass distribution we need to:

Extract <MX> as a function of the minimal lepton momentum

P*=0.9GeV

P*=1.5GeV


Effect of kinematic Fit: Resolution Functions

Kinematic Fit improves resolution of the

invariant mass MX

Almost unbiased measurement irrespective

of final state

Reduction of branchingfraction dependence


Calibration Curve

True modes:True modes:DD*D** (two narrow +two broad)

XH (4 spin dependent D(*)PI)

Large variety of different models and different final states

Mxtrue binning (example)

Define calibration curve independent of underlying model! binning in bins of Mx

true

21PMPM true

X

reco

X


Calibration Curves

Relate measured hadronic mass to true mass of X-system:• linear relation as function of true mass• irrespective of decay and underlying model

4 XHreso

4 XHnreso

D*

D

Application of calibration results in true mass irrespective of decay mode and model


If correction factor 1 and RMS small for PDF variations (i.e. dropping contributions to XH

resoand XHnreso) only a small systematic error for model

and branching fraction dependence is achieved!

Extraction Method – Full Formula

MCDATA

calib

nX

icut

NPDF

i

MCTRUE

l

nX

il

NPDF

iBG

calib

nX

data

calib

nX

TRUEnX

MR

MRFMFMM

1

1)1/(

The full formula has not only to take into account the mass bias but it must also account for lepton acceptance and efficiency differences Ri .

correction factor

Since we measure Mx we of course also can get Mxn

Calibrate the measured mass event-by-event: data

calib

n

X

datan

XMM

Subtract remaining background


Distribution of Bias Factors

P*>1.1GeV

P*>0.9GeV

RMS(P*>0.9) =0.01 GeV2

RMS(P*>1.1) =0.01 GeV2

Vary assumptions for X model:Change X composition: disregard single decay modes and combinations, i.e. drop them in pairs, triplets etc. and observe how MC correction changes Small model dependence!

<MX2> (GeV2) <MX

2> (GeV2)

Spread is small compared to other error sources:stat. error: 0.05 GeV2

det. sys. error: 0.03 GeV2

background: 0.04 GeV2


Result: First and Second Moment of MX Distribution

<MX> <MX2>

Clear P*min dependence,reflecting increasing contribution

from high mass final states.

Points are highly correlated


Crosscheck on MC

Derive calibration and background subtraction

from MC and apply to independent “MC data” sample.

Works both, for lower P*min cut and differentially

in bins of P*

Moment <MX2>

Difference to true value


Apply the complete extraction procedure tothis data sample and measure <MX> as afunction of the lepton momentum.

Crosscheck on Data – Partial Reconstruction of D*+

Select a data control sample where thetrue underlying mass is know

Use the decay B0 D*+ lν:Partially reconstruct D* decays by identifying a slow charged pion

MD*2


Consistency of Results

We split the data into statistically independent subsamplesand repeated the measurement.

Statistical Errors only!


Interpretation in Context of HQET


Reminder of Expansion

perturbative expansion in αs

non-perturbative expansion to first, second and third order

in 1/mB

Determine parameters Λ and λ1

λ2 known from B*-B andD*-D mass splitting

Λ – mass difference between B meson and b quark λ1 – negative of kinetic energy squared of b quarkλ2- chromo-magnetic coupling of b quark spin to “brown muck”

αs(2)

1/mB

1/mB2

1/mB3One e

xpansion fo

r

every

P* cut


Interpretation in context of HQET

Fit for Λ and λ1 by minimizing χ2

taking correlations between data points into account

The extracted parameters describeall hadronic mass moment

measurements

Prediction of P* dependence for <MX

2> using Λ from b s γ and <MX

2> at P*min =1.5 GeV results in less consistent description.

OPE prediction using CLEO data only<Mx2> and <E> from bs

OPE fit to

the BABAR data

Calculations from Falk and Luke (Phys.Rev.D57:424-430,1998)


Results in λ1-Λ plane

Hadronic Mass Momentsfrom all three Experimentsoverlap in same region.

Band in λ1-Λ plane from b sγ slightly offset

Experimental Errors only!

Δχ2 =1 ellipse

This fit is performed inthe MS scheme for

comparison with otherexperiments

We extract λ1 = -0.36 ± 0.09 GeV2

and Λ = 0.53 ± 0.09 GeV

CLEO: λ1= -0.24 ± 0.07 GeV2

and Λ = 0.35 ± 0.07 GeV(experimental errors only)


A more comprehensive Approach

“External Input”

Based on improved OPE calculations in the(1S) mass scheme (Phys. Rev. D67. 05012, 2003)

we can now include moment measurementsin the fit as well as SL

Simultaneous extraction of HQE parameters and |Vcb| !

(development of fit code in close collaboration with theorists)

Calculate Calculate SL SL from BABAR data only!from BABAR data only!

life time measurements and BR(BXl) have by now reached a precession that makes

SL (BABAR) very competitive!

Two possibilities:Two possibilities:1. Check consistency of the HQE calculations by

comparing hadron moments from BABAR with other moment measurements (“external input”)

2. Use the BABAR hadron moments together with SL (BABAR) to obtained an improved

determination of |Vcb|

“BABAR Input”

MeV


Consistency of the HQE: Hadron Moments vs. Lepton Moments BABAR only

Simultaneous extraction of |Vcb|, mb1S, and 1

1S

from a fit to the HQE in the 1S mass scheme(O(1/mB

3) parameters are fixed in the fit)

|Vcb| - mb1S plane 1

1S - mb1S plane

Not

e: 2

=1

con

tou

r in

clu

de

alre

ady

par

t of

th

e th

eory

err

ors.

On

ly O

(1/m

B3 )

un

cert

ain

ties

are

not

incl

ud

ed!

• Good agreement between BABAR moments and other hadron moment measurementsGood agreement between BABAR moments and other hadron moment measurements• 2=1 contour of hadron moments and lepton moments do not overlap indication for large O(1/mB

3) corrections or maybe even more …?(bear in mind that SL is common in both fits!)


|Vcb| extracted using BABAR data only

Caveat: We still have to establish the consistency of the OPE to at least the same level of accuracy we would like to achieve for |Vcb| (<1%)!

Precise measurement of |Vcb| with input from BaBar data alone (life time, branching fractions, moments)

and very competitive (3% total error)!

[previous inclusive Vcb measurement from BABAR: |Vcb| = 42.30.7(exp)2.0(theo) ~5% (Phys. Rev. D67, 2002) ]

BABAR only

MeV

*

* Contributed to EPS03in Aachen


Summary and Conclusion

• We have measured the first and second moment of the MX distribution for different P* cuts (0.9 to 1.6 GeV).• With a completely new and unique extraction approach we were able to overcome model uncertainty which leads to a significant improvement of the hadronic mass moment measurement.

• Using a simultaneous extraction of |Vcb|, mb1S, and 1

1S from a fit to the HQE calculations we obtain an improved measurement of Vcb which is based on BABAR data only!• A comparison with other hadron moment measurements from CLEO and DELPHI demonstrates good agreement.

• A consistency test of hadron and lepton moments in the framework of the OPE leads to inconclusive results and demonstrates again the importance of the determination of all the O(1/mB

3) parameters from data.

More moment measurements from differentMore moment measurements from different physics processes will be needed to test HQET+OPE to the level of <1%.physics processes will be needed to test HQET+OPE to the level of <1%.


Backup Slides


The PEP-II B-Factory

E [GeV] e+ / e- 9.0 / 3.1

I [mA] e+ / e- 1550 / 1175

Bunches 1034

L [cm-2 s-1] 6.582 x 1033

Lint [pb-1/day] 395.1

Energy asymmetric e+-e- collider

(peak performance)


PEP-II and BaBar Performance

This analysis is based on Run1+2 only (82 fb-1)

Continuous improvement in delivered and recorded luminosity!


The BABAR - Detector

Cerenkov Detector (DIRC)

144 quartz bars11000 PMTs

1.5 T Solenoid

Electromagnetic Calorimeter 6580 CsI(Tl) crystals(electrons/photons)

Drift Chamber40 layers

Instrumented Flux Returniron / RPCs (muon / neutral hadrons)

Silicon Vertex Tracker5 layers, double sided strips

e+ (3.1 GeV)

e- (9 GeV)

SVT: 97% efficiency, 15 m z hit resolution (inner layers, perp. tracks)

SVT+DCH: (pT)/pT = 0.13 % pT + 0.45 %

DIRC: K- separation 4.2 @ 3.0 GeV/c 3.0 @ 4.0 GeV/c EMC: E/E = 2.3 %E-1/4 1.9 %

http://www.slac.stanford.edu/~buchmuel/WINNT/Profiles/Vera/Vera/DOCUME~1/luth/LOCALS~1/Temp/svt.jpg


Checks on Background Subtraction

Select eventswhere lepton chargeis inconsistent with

prompt B decay

Fit MC shapes todata to obtain normalization

Charged B’s

Neutral B’s

Contribution from B0-B0 mixing_

MC scaling factorcompatible with 1

0.8<P*<1.0

0.8<P*<1.0

1.0<P*<1.4

P*>1.4

1.0<P*<1.4 P*>1.4

rhul group meeting 18. dec. 03henning flächer 1 hadronic mass moments from semileptonic b meson...

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