1. Measurement of b-quark mass effects for multi-jet events at LEP Juan A. Fuster Verdú EPS-2003 Aachen, 17-23 July 2003

2. 19 July 2003J. Fuster2 Introduction (I)  Over recent years mass effects in multi-jet event topologies were observed and confirmed at LEP and SLC by various experiments (ALEPH, DELPHI, OPAL, SLD).  The availability of new massive NLO calculations for three-jet event observables (G. Rodrigo et al., W. Bernreuther et al., P. Nason et al.) and improved b-tagging techniques enabled the understanding of these effects in terms of QCD and allowed for:  Determinations of the b-quark mass at M Z (~17% precision)  Flavour independence tests of  S  S b /  S  ( ~1%precision)  More precise determination of  S (2%-3% impact for some observables)

3. 19 July 2003J. Fuster3 Some Previous Experimental Results LEP: DELPHI (1998)  ~ 0.5 GeV/c 2 ALEPH (2000)  ~ 0.5 GeV/c 2 OPAL (2001)  ~ 0.4 GeV/c 2 SLC: Bradenburg et al. SLD (1999)  ~ 1 GeV/c 2 m b (M Z ) Flavour Independence of  S LEP: DELPHI (1998)  ~ 1% ALEPH (2000)  ~ 1% OPAL (1999)  ~ 1% SLC: SLD (1999)  ~ 5%

4. 19 July 2003J. Fuster4 Introduction (II) Relevant results achieved..but.., still some interesting questions remained to be answered !!  Can precision be improved ?  Role of the quark masses parameter in the QCD generators  Can these studies be extended to other multi-jet topologies ?  Mass scheme dependence: pole mass (M b ) and running mass m b (M Z ) in  Could one single experiment cover more than one energy point for m b (  )? MS  Use of new observables  Better understand of fragmentation  Tagging for b- and l-quarks  Gluon splitting

5. 19 July 2003J. Fuster5 Prior step of the analysis: The quark mass definition Quarks are not observed as free particles in nature. Confined inside hadrons  NOT A TRIVIAL DEFINITION! Theoretical convention is needed to define quark masses (mandatory at NLO) The two most commonly used mass definitions are: Pole mass: M q Pole of the renormalized quark propagator i p-m-i  (p,m) p2=Mq2p2=Mq2 = 0  (p,m) = quark self energy Gauge and scheme independent Non-perturbative corrections give an ambiguity of order  QCD Infrared renormalon Running mass: m q (  ) renormalized mass in the MS scheme. Scheme and scale dependent.

6. 19 July 2003J. Fuster6 Definition of the observable and theoretical calculations Jet clustering algorithms: DURHAM CAMBRIDGE …New… Cancel hadronization and detector corrections Cancel EW corrections Event flavour (b, = uds) is defined by the quarks coupled to the Z 0 G.Rodrigo et al., Phys.Lett.B79 (1997) 193 M. Bilenky et al.,Phys.Rev.D60 (1999) 114006 Z. Nagy, Z, Trocsanyi, Phys.Rev.D59 (1999) 014020 F. Krauss, G. Rodrigo CERN-TH-2003-42 LO, NLO and NLL calculations for R 3,4 with massive and massless quarks b In terms of the pole mass: R 3,4  (M b ) In terms of the running mass: R 3,4  (m b (  )) b b b Extract M b and m b (M Z ) Extract  s b /  s Test prediction: Th-Exp

7. 19 July 2003J. Fuster7 Raw Data Hadron Selection Hadronic Sample: Z 0  qq b-Sample Tagging -Sample Jet reconstruction R n b (detector) Detector and Fragmentation corrections R n b (parton) Flavour Identification Experimental Process (Delphi) Data well understood Corrections small and stable

8. 19 July 2003J. Fuster8 No Generator describes particularly well data for all multijet topologies R n b at Hadron Level: Data vs. Generators Pythia Herwig Ariadne Cambridge Delphi

9. 19 July 2003J. Fuster9 Fragmentation Models Considered: (Last versions with mass effects improved) String+Peterson (Pythia) String+Bowler (Pythia) Cluster (Herwig) Tuning Hadron Correction (3-jets mainly) Fragmentation model Restrict the phase space region x E b (jet)>0.55 b mass parameter uncertainty Which mass and which value of M b should be used in the generator ? M b = 4.98  0.13 GeV/c 2 M. Eidemüller, Phys. Rev. D67 (2003) 113002 It should be the pole mass:

10. 19 July 2003J. Fuster10 R 3,4 corrected at parton level b 3-jet analysis Calculations LO: Leading Order massive NLO: Next to Leading Order Massive 4-jet analysis Calculations LO: Leading Order Massive NLO: Leading Order Massive + Next to Leading Order massless NLL: Next to Leading Log Masive approximation (on going..)

11. 19 July 2003J. Fuster11 Extracting QCD parameters  s universality m b (M Z ) m b (M Z ) or M b  s b /  s l 12 R 3 (parton) from Theory b R 3 (parton) from Data b Only for R 3 b as NLO calculation exist.

12. 19 July 2003J. Fuster12 1 b-quark mass determination Durham Cambridge y c selected to minimize overall errors, hadron correction stable (C had) and small 4-jet contamination. Result is independent of y c. Theoretical Uncertainty Durham Cambridge

13. 19 July 2003J. Fuster13 Universality of  s :  s b /  s l 2 m b (m b ) = 4.24  0.11 GeV/c 2 From NLO calculation Experimental result Durham Cambridge

14. 19 July 2003J. Fuster14  Mass effects for R 4 b only at LO  NLO approximation for R 4 b : LO massive + NLO massless Consistency: R 4 b  vs. R 3 b LO Massive Pole: M b =4.98 GeV/c 2 Running: m b (M Z ) = 2.91 GeV/c 2 3-jets: M b = m b (M Z ) =3.29 GeV/c 2 Good agreement ! LO Massive + NLO Massless m b (M Z ) MbMb Reasonable agreement ! (calculations are not comparable)

15. 19 July 2003J. Fuster15 Comparison with DELPHI analysis at threshold Measurement of moments of inclusive spectra in Semileptonic B-decays in DELPHI (EPS contribution): m b (m b ) = 4.21  0.14 GeV/c 2 First time one single experiment measures m b  at two different energy regimes To understand data as a whole and at the same time, the evolution of m b  needs to be as predicted by the RGE in the MS-scheme

16. 19 July 2003J. Fuster16 Summary A new analysis for R 3 b  is being presented with considerably improved understanding of the systematic uncertainties of previous analyses. A consistent picture of R 4 b  with respect to  R 3 b  is observed but the lack of appropriate theoretical calculations limits the results. For the first time one single experiment can measure m b (  ) at two different energy scales Running Mass: (Cambridge) Pole Mass: (Durham) () m b (M Z ) = 2.96  0.32 GeV/c 2 ( ) g g