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Eli Ben-Haim LAL Orsay LPNHE Paris

HEP2003 Europhysics Conference, Aachen, July 2003. Extraction of the x-dependence of the non-perturbative QCD b-quark fragmentation distribution component. Eli Ben-Haim LAL Orsay LPNHE Paris. Sponsored by EEC RTN HPRN-CT-00292-2002. Contents. Measured b-fragmentation function: summary.

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Eli Ben-Haim LAL Orsay LPNHE Paris

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  1. HEP2003 Europhysics Conference, Aachen, July 2003 Extraction of the x-dependence of the non-perturbative QCD b-quark fragmentation distribution component Eli Ben-Haim LAL Orsay LPNHE Paris Sponsored by EEC RTN HPRN-CT-00292-2002

  2. Contents • Measured b-fragmentation function: summary. • Perturbative and non-perturbative QCD components of the fragmentation function. • New Method for extraction of the x-dependence of the non-perturbative QCD component. • Results of the method. • A remark concerning fitting the x-distribution and its moments. Eli Ben-Haim b-fragmentation HEP2003, Aachen

  3. New average (preliminary) 0.715  0.003 Measured FragmentationFunction • Recent results from ALEPH (May 2001), SLD (May 2002), OPAL (October 2002, not published) and DELPHI (not published). • Average < 1995 (still used): 0.7020.008 • Mean values: • ALEPH: 0.716 0.006 0.006 • DELPHI:0.71530.00070.0051 • OPAL: 0.71930.00160.0034 • SLD: 0.709 0.003 0.003 • 0.002(model) Definition: Systematics dominate Bin contents are correlated Eli Ben-Haim b-fragmentation HEP2003, Aachen

  4. Perturbative and non-perturbative components perturbative • Typically: gluon radiation. • Calculable. • Different approaches: • Monte Carlo. • Theoretical QCD. non-perturbative • Typically: hadronisation. • Non calculable. • Contains all the contributions that are not included in the perturbative • component. • Usually taken as a model. Eli Ben-Haim b-fragmentation HEP2003, Aachen

  5. perturbative (theoretical QCD, Monte Carlo) non-perturbative (usually models) perturbative non-perturbative NO MODEL Non-perturbative Part: New Approach. hep-ph/0302157 folding =  X-Distributions Non perturbative function: directly extracted, not model dependent Mellin transform:    moments Inverse Mellin- transform = Eli Ben-Haim b-fragmentation HEP2003, Aachen

  6. Extracted non-perturbative distributions DNP(x) Results of the New Method: General • Extraction point by point. • 3 perturbative Approches: • Monte Carlo (JETSET 7.3). • NLL QCD, Cacciari and Catani. • NLL+DGE QCD, Cacciari and Gardi, hep-ph/0301047. • non-perturbative = F (perturbative) • Low x region indicates gluon radiation is well accounted in the perturbative components. • Higher order QCD  the non perturbative part starts at larger x. • The non-perturbative functions for JETSET and NLL QCD have similar shapes, translated. This Non perturbative functions are expected to be valid in a different environment than e+e-, only in the framework where similar perturbative assumptions are used for its extraction. Eli Ben-Haim b-fragmentation HEP2003, Aachen

  7. Dpert(x) DNP(x) Perturbative & non-perturbative components Comparison ALEPH-OPAL DNP(x) Results of the New Method: JETSET Extracted non-perturbative distribution: Comparison to hadronisation models: • Model parameters from fit to ALEPH’s data. Comparison: folding the x-distributions, by: • Lund and Bowler models favoured (as observed by OPAL and SLD). DNP(x) Eli Ben-Haim b-fragmentation HEP2003, Aachen

  8. Dpert(x) DNP(x) Not 0 for x>1 NLL Break down Results of the New Method: NLL QCD Cacciari and Catani Nucl.Phys. B617 (2001) 253-290. Extracted non-perturbative distribution: Comparison to hadronisation models: new DNP(x) Solves this • Folding a physical model with the unphysical NLL QCD  not meaningful. • Our extracted non-pert. QCD distribution solves this problem. Dpredicted(x) Don’t fold NLL QCD with models ! Eli Ben-Haim b-fragmentation HEP2003, Aachen

  9. fraction of contribution from each bin to the moments 18 19 17 fraction 1 moment order Fitting the x-distribution and moments • Typically large x  large N. • Each moment contains a weighted information from the bins. • The information measured in x-space is distributed among moments (not necessarily low order ones). • Moments are highly correlated. • Example for ALEPH (19 bins): Fitting x-space data is different from fitting moments. ALEPH 17 18 19 Eli Ben-Haim b-fragmentation HEP2003, Aachen

  10. Summary and conclusions • A model independent extraction of the x-dependence of the non-perturbative QCD component of the b-quark fragmentation function has been performed. • It depends closely on the perturbative approach. • The result differs markedly from some hadronisation models. • Perturbative=Monte-Carlo: Lund and Bowler models are favoured. • Perturbative = NLL QCD: The extracted function goes beyond x=1. Don’t use it with hadronisation models! • The non perturbative function is 0 at low x: gluon radiation is well accounted by perturbative QCD. • This Non perturbative function is expected to be valid in a different environment than e+e-, if similar perturbative assumptions are used. Eli Ben-Haim b-fragmentation HEP2003, Aachen

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