Maria Jose Costa, CERN DIS 2004

April 14th-18th 2004, Slovakia

b-mass effects in 3 and 4 jets events with the DELPHI detector at LEP

b u,d,s

15 April 2004 M.J. Costa 2

Contents

• Theoretical introduction

• Experimental strategy

• Results on the measured observables

• Comparison with theory

• Summary

Motivations of the measurement.Quark mass definition.Observable: Rn

b (n=3,4 jets)

b quark mass.s

b/s.

Rnb at hadron level.

Rn at parton level.b

15 April 2004 M.J. Costa 3

Theoretical introduction

• The Standard Model has a set of free parameters.• QCD Lagrangian:

s = gs2/4 and quark masses are not predicted by the SM

They need to be determined experimentally!

15 April 2004 M.J. Costa 4

Quark mass definitions

• Quarks are not observed as free particles in nature.

Confined inside hadrons NOT A TRIVIAL DEFINITION!

• Theoretical convention is needed to define quark masses.• The two most commonly used mass definitions are:

Pole mass: Mq Pole of the renormalized quark propagator

Gauge and scheme independent

Non-perturbative corrections give an ambiguity of order QCD Infrared renormalon

Running mass: mq ( ) Renormalized mass in the MS scheme.

Scheme and scale dependent.

• Additional mass definitions at threshold: mbkin() ...

15 April 2004 M.J. Costa 5

00

00

/)(

/)()(

)2(

)2(

Ztotc

gnZjn

bbZtotc

gnbbZjn

cbn

y

yyR

Definition of the observable and theoretical calculations

Jet clustering algorithms:DURHAM

CAMBRIDGE

Hadronization and detector corrections EW corrections

Event flavour (b, = uds) isdefined by the quarks coupled to the Z0

G.Rodrigo et al., Phys.Lett.B79 (1997) 193M. Bilenky et al.,Phys.Rev.D60 (1999) 114006Z. Nagy, Z, Trocsanyi, Phys.Rev.D59 (1999) 014020 F. Krauss, G. Rodrigo CERN-TH-2003-42

• In terms of the pole mass: R3,4(Mb)

• In terms of the running mass: R3,4(mb())

b

b

b • Extract Mb and mb (MZ )

• Extract sb/s

Partial cancellation

Massive NLO and NLL calculations for R3 (massive LO and massless NLO R4 )b b

15 April 2004 M.J. Costa 6

Raw Data

Hadron Selection

Hadronic Sample: Z0 qq

b-Sample

Tagging

-Sample

Jet reconstruction

Rnb (detector)

Detector corrections

Flavour Identification

Data well understood

Corrections small and stable

Rnb (hadron)

Rnb (parton)

Fragmentation corrections

3jets 4jets

Experimental Strategy (DELPHI)

3jets

15 April 2004 M.J. Costa 7

• Fragmentation Models considered: (Last versions with mass effects improved)

• String+Peterson (Pythia)• String+Bowler (Pythia)• Cluster (Herwig)

Tuning

Hadronization Correction (3-jets mainly)

Fragmentation model

Restrict phase space regionxE

b(jet)>0.55

b mass parameter uncertainty

Consistent with Pole mass (Pythia)

Mb = 4.99 0.13 GeV/c2

A.X.El-Khadra et al., Ann.Rev.Nucl.Part.Sci 52 (2002) 201

From low energy

measurements

Mass result depends on value, dominant uncertainty on mb

3jets

15 April 2004 M.J. Costa 8

Results on the measured observables Rnb

No Generator describes particularly well data for all multijet topologies

Delphi (preliminary)

PythiaHerwig

Ariadne

R3,4 at hadron level: Data vs. Generatorsb

Cambridge

Cambridge

15 April 2004 M.J. Costa 9

R3,4 corrected at parton levelb

3-jet analysis Calculation

Massive NLO

4-jet analysis Calculations

Massive LO +

Massless NLO

Data 94-95

Delphi (preliminary)

15 April 2004 M.J. Costa 10

Extracting QCD parameters

s universality mb (MZ )

mb(MZ) or Mb sb/ s

l

1 2

R3 (parton) from TheorybR3 (parton) from Datab

• Only for R3b do NLO calculation exist.

15 April 2004 M.J. Costa 11

b-quark mass determination (preliminary)

Durham

Cambridge

Theoretical Uncertainty

Durham

Cambridge

Running mass

Pole mass

mb(MZ)

MbDurham

Cambridge

s universality

mb()

Mb

15 April 2004 M.J. Costa 12

Only Massive LO for R4b

NLO approximation for R4b : LO massive + NLO massless

Consistency: R4bvs. R3

b

LO Massive

Good agreement !

+NLO Massless

Good agreement !(calculations are not

comparable)

mb(MZ) Mb

Only experimentaluncertainties

at LO

15 April 2004 M.J. Costa 13

Comparison with DELPHI analysis at threshold

Measurement of moments of inclusive spectra in Semileptonic B-decays in DELPHI (preliminary):

mb(mb) = 4.26 0.13 GeV/c2

First time one single experiment measures

mbat two different energy regimes

To understand data as a whole, the evolution

of mbneeds to be as predicted by the RGE

in the MS-scheme

mbkin (1 GeV)

15 April 2004 M.J. Costa 14

Summary• New analysis for R3

b: considerable improvement of syst. uncertainties

Mass extraction depends on Mb input in Pythia

• Uncertainties from R4bslightly higher, mass extraction limited by

theoretical calculations 400 MeV.

• For the first time one single experiment can measure mb() at two different energy scales

Running Mass: (Cambridge)

( )4 jets

Running observedMost of dependence on Mb input in generator cancels in the difference

mb(mb)-mb(MZ) = 1.39±0.30 GeV/c2 (4.5)

15 April 2004 M.J. Costa 15

Backup Slides

15 April 2004 M.J. Costa 16

No Generator describes all multijet topologies

Rnq at Hadron Level: Data vs. Generators

Delphi (preliminary)Cambridge - b Cambridge - PythiaHerwig

Ariadne

15 April 2004 M.J. Costa 17

Theoretical uncertainty for Massless NLO

True NLO

Mass ambiguity

Alternative expansions

3j

LO pole

LO running

4jApproximate

calculation

Uncertainty estimated as maximum spread with Massless NLO 400 MeV

Conservative: test in 3-jet calculation gives 2x true uncertainty

15 April 2004 M.J. Costa 18

Experimental Process (Delphi)

• 2-3jets: Measure double rates simultaneously (n-jet AND inclusive sample) Smaller uncertainty.

• 4-jets: Measure only 4-jet sample with double tag. Take normalization from Rb, Rc

b

BBbh

bbBB

bh

bBB

bB

bh

bbB

bh

bB

bh

bbh

b

NNN

NNN

NNN

)(

)(21

)(

444

444

444

4

4

4

N

N

N

4

44

1NN

RRR

Rb

b

cbb

2j

3j

Useful cross-checkof flavour tagging

+ equations for LIGHT quarks