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

2. Eli Ben-Haim b-fragmentation HEP2003, Aachen2 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.

3. Eli Ben-Haim b-fragmentation HEP2003, Aachen3 Measured Fragmentation Function 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) New average (preliminary) 0.715  0.003 Definition: Bin contents are correlated Systematics dominate

4. Eli Ben-Haim b-fragmentation HEP2003, Aachen4 Perturbative and non-perturbative components perturbativenon-perturbative Typically: gluon radiation. Calculable. Different approaches: Monte Carlo. Theoretical QCD. Typically: hadronisation. Non calculable. Contains all the contributions that are not included in the perturbative component. Usually taken as a model.

5. Eli Ben-Haim b-fragmentation HEP2003, Aachen5 = =  folding perturbative non-perturbative NO MODEL Mellin transform: X-Distributions moments Non-perturbative Part: New Approach. hep-ph/0302157 perturbative (theoretical QCD, Monte Carlo) non-perturbative (usually models) Inverse Mellin- transform Non perturbative function: directly extracted, not model dependent     

6. Eli Ben-Haim b-fragmentation HEP2003, Aachen6 Results of the New Method: General 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. 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. D NP (x) Extracted non- perturbative distributions

7. Eli Ben-Haim b-fragmentation HEP2003, Aachen7 Results of the New Method: JETSET 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). D pert (x) D NP (x) Perturbative & non-perturbative components Comparison ALEPH-OPAL D NP (x) Comparison to hadronisation models: Extracted non-perturbative distribution: D NP (x)

8. Eli Ben-Haim b-fragmentation HEP2003, Aachen8 Results of the New Method: NLL QCD Folding a physical model with the unphysical NLL QCD  not meaningful. Our extracted non-pert. QCD distribution solves this problem. Solves this Not 0 for x>1 NLL Break down Cacciari and Catani Nucl.Phys. B617 (2001) 253-290. Comparison to hadronisation models: Extracted non-perturbative distribution: D NP (x) D predicted (x) D pert (x) D NP (x) new Don’t fold NLL QCD with models !

9. Eli Ben-Haim b-fragmentation HEP2003, Aachen9 Fitting the x-distribution and moments 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. fraction of contribution from each bin to the moments moment order fraction 19 18 17 1 19 18 17 ALEPH

10. Eli Ben-Haim b-fragmentation HEP2003, Aachen10 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.