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

1. b-mass effects in 3 and 4 jets events with the DELPHI detector at LEP Maria Jose Costa, CERN DIS 2004 April 14th-18th 2004, Slovakia u,d,s b

2. Rnbl at hadron level. • Rnat parton level. bl Contents • Motivations of the measurement. • Quark mass definition. • Observable: Rnbl (n=3,4 jets) • Theoretical introduction • Experimental strategy • Results on the measured observables • b quark mass. • sb/sl. • Comparison with theory • Summary 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! 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: MqPole 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() ... M.J. Costa

5. Massive NLO and NLL calculations for R3 (massive LO and massless NLO R4 ) bl bl • In terms of the pole mass: R3,4(Mb) • In terms of the running mass: R3,4(mb()) bl bl • Extract Mb and mb (MZ ) bl • Extract sb/sl Definition of the observable and theoretical calculations Jet clustering algorithms: DURHAM CAMBRIDGE Event flavour (b, l = uds) is defined by the quarks coupled to the Z0 Partial cancellation Hadronization and detector corrections EW corrections 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 M.J. Costa

6. Flavour Identification Experimental Strategy(DELPHI) Raw Data Hadron Selection Hadronic Sample: Z0 qq 3jets 4jets Tagging b-Sample l-Sample Jet reconstruction Rnbl (detector) Data well understood Detector corrections 3jets Rnbl (hadron) Fragmentation corrections Corrections small and stable Rnbl (parton) M.J. Costa

7. Fragmentation model Restrict phase space region xEb(jet)>0.55 Hadronization Correction (3-jets mainly) • String+Peterson (Pythia) • String+Bowler (Pythia) • Cluster (Herwig) • Fragmentation Models considered: • (Last versions with mass effects improved) Tuning b mass parameter uncertainty Consistent with Pole mass (Pythia) 3jets Mb = 4.99  0.13 GeV/c2 From low energy measurements A.X.El-Khadra et al., Ann.Rev.Nucl.Part.Sci 52 (2002) 201 Mass result depends on value, dominant uncertainty on mb M.J. Costa

8. R3,4at hadron level: Data vs. Generators bl Pythia Herwig Ariadne Results on the measured observables Rnbl Delphi (preliminary) Cambridge Cambridge No Generator describes particularly well data for all multijet topologies M.J. Costa

9. R3,4corrected at parton level bl Data 94-95 Delphi (preliminary) 4-jet analysis Calculations Massive LO + Massless NLO 3-jet analysis Calculation Massive NLO M.J. Costa

10. R3 (parton) from Data R3 (parton) from Theory bl bl Extracting QCD parameters • Only for R3bl do NLO calculation exist. 1 2 s universality mb (MZ ) mb(MZ) or Mb sb/ sl M.J. Costa

11. b-quark mass determination (preliminary) mb(MZ) Running mass Durham Cambridge mb(m) Pole mass Mb Durham Mb Cambridge Theoretical Uncertainty as universality Durham Cambridge M.J. Costa

12. Only experimental uncertainties at LO Consistency: R4bl vs. R3bl • Only Massive LO for R4bl • NLO approximation for R4bl: LO massive + NLO massless LO Massive Good agreement ! + NLO Massless mb(MZ) Mb Good agreement ! (calculations are not comparable) 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 mbkin (1 GeV) First time one single experiment measures mb(m) at two different energy regimes To understand data as a whole, the evolution of mb(m) needs to be as predicted by the RGE in the MS-scheme M.J. Costa

14. Running Mass: (Cambridge) 4 jets ( ) Summary • New analysis for R3bl : considerable improvement of syst. uncertainties • Mass extraction depends on Mb input in Pythia • Uncertainties from R4bl slightly higher, mass extraction limited by • theoretical calculations  400 MeV. Running observed Most of dependence on Mb input in generator cancels in the difference mb(mb)-mb(MZ) = 1.39±0.30 GeV/c2(4.5s) • For the first time one single experiment can measure mb(m) at two different • energy scales M.J. Costa

15. Backup Slides M.J. Costa

16. Rnq at Hadron Level: Data vs. Generators Delphi (preliminary) Cambridge - b Cambridge -  Pythia Herwig Ariadne No Generator describes all multijet topologies M.J. Costa

17. 4j LO running LO pole Theoretical uncertainty for Massless NLO 3j Approximate calculation True NLO Alternative expansions Mass ambiguity Uncertainty estimated as maximum spread with Massless NLO  400 MeV Conservative: test in 3-jet calculation gives 2x true uncertainty M.J. Costa

18. Experimental Process (Delphi) 2j • 2-3jets: Measure double rates simultaneously • (n-jet AND inclusive sample) • Smaller uncertainty. Useful cross-check of flavour tagging 3j • 4-jets: Measure only 4-jet sample with double tag. • Take normalization from Rb, Rc + equations for LIGHT quarks M.J. Costa