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

2. 15 April 2004M.J. Costa2 Contents Theoretical introduction Experimental strategy Results on the measured observables Comparison with theory Summary  Motivations of the measurement.  Quark mass definition.  Observable: R n b (n=3,4 jets)  b quark mass.   s b /  s.  R n b at hadron level.  R n at parton level. b

3. 15 April 2004M.J. Costa3 Theoretical introduction The Standard Model has a set of free parameters. QCD Lagrangian:  s = g s 2 /4  and quark masses are not predicted by the SM They need to be determined experimentally !

4. 15 April 2004M.J. Costa4 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: M q Pole of the renormalized quark propagator 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. Additional mass definitions at threshold: m b kin (  )...

5. 15 April 2004M.J. Costa5 Definition of the observable and theoretical calculations Jet clustering algorithms: DURHAM CAMBRIDGE Hadronization and detector corrections 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 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 Partial cancellation Massive NLO and NLL calculations for R 3 (massive LO and massless NLO R 4 ) b b

6. 15 April 2004M.J. Costa6 Raw Data Hadron Selection Hadronic Sample: Z 0  qq b-Sample Tagging -Sample Jet reconstruction R n b (detector) Detector corrections Flavour Identification Data well understood Corrections small and stable R n b (hadron) R n b (parton) Fragmentation corrections 3jets4jets Experimental Strategy (DELPHI) 3jets

7. 15 April 2004M.J. Costa7 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 region x E b (jet)>0.55 b mass parameter uncertainty Consistent with Pole mass (Pythia) M b = 4.99  0.13 GeV/c 2 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 m b 3jets

8. 15 April 2004M.J. Costa8 Results on the measured observables R n b No Generator describes particularly well data for all multijet topologies Delphi (preliminary) Pythia Herwig Ariadne R 3,4 at hadron level: Data vs. Generators b Cambridge

9. 15 April 2004M.J. Costa9 R 3,4 corrected at parton level b 3-jet analysis Calculation Massive NLO 4-jet analysis Calculations Massive LO + Massless NLO Data 94-95 Delphi (preliminary)

10. 15 April 2004M.J. Costa10 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 do NLO calculation exist.

11. 15 April 2004M.J. Costa11 b-quark mass determination (preliminary) Durham Cambridge Theoretical Uncertainty Durham Cambridge Running mass Pole mass mb(MZ)mb(MZ) MbMb Durham Cambridge  s universality mb()mb() MbMb

12. 15 April 2004M.J. Costa12  Only Massive LO for R 4 b  NLO approximation for R 4 b : LO massive + NLO massless Consistency: R 4 b  vs. R 3 b LO Massive Good agreement ! + NLO Massless Good agreement ! (calculations are not comparable) m b (M Z )MbMb Only experimental uncertainties at LO

13. 15 April 2004M.J. Costa13 Comparison with DELPHI analysis at threshold Measurement of moments of inclusive spectra in Semileptonic B-decays in DELPHI (preliminary): m b (m b ) = 4.26  0.13 GeV/c 2 First time one single experiment measures m b  at two different energy regimes To understand data as a whole, the evolution of m b  needs to be as predicted by the RGE in the MS-scheme m b kin (1 GeV)

14. 15 April 2004M.J. Costa14 Summary New analysis for R 3 b  : considerable improvement of syst. uncertainties Mass extraction depends on M b input in Pythia Uncertainties from R 4 b  slightly higher, mass extraction limited by theoretical calculations  400 MeV. For the first time one single experiment can measure m b (  ) at two different energy scales Running Mass: (Cambridge) () 4 jets Running observed Most of dependence on M b input in generator cancels in the difference m b (m b )-m b (M Z ) = 1.39±0.30 GeV/c 2 (4.5  )

15. 15 April 2004M.J. Costa15 Backup Slides

16. 15 April 2004M.J. Costa16 No Generator describes all multijet topologies R n q at Hadron Level: Data vs. Generators Delphi (preliminary) Cambridge - bCambridge - Pythia Herwig Ariadne

17. 15 April 2004M.J. Costa17 Theoretical uncertainty for Massless NLO True NLO Mass ambiguity Alternative expansions 3j LO pole LO running 4j Approximate calculation Uncertainty estimated as maximum spread with Massless NLO  400 MeV Conservative: test in 3-jet calculation gives 2x true uncertainty

18. 15 April 2004M.J. Costa18 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 R b, R c 2j 3j Useful cross-check of flavour tagging + equations for LIGHT quarks