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Exploring the Modified Leading Log Approximation (MLLA) and Its Implications for Jet Fragmentation

This research investigates the Modified Leading Log Approximation (MLLA) model in jet fragmentation, focusing on infrared stability and the cut-off scale parameter ( Q_{eff} ), which can drop to approximately ( Lambda_{QCD} sim 250 text{ MeV} ) while accounting for soft partons. By considering local hadronization, we analyze the relationship between hadron and parton distributions through the Local Parton-Hadron Duality (LPHD). The findings suggest that MLLA serves as a "mostly correct" framework for understanding hadronization despite some discrepancies, allowing parameter extraction for improved predictions in future analyses.

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Exploring the Modified Leading Log Approximation (MLLA) and Its Implications for Jet Fragmentation

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  1. Finalizing MLLA comparisons Andrey Korytov Alexei Safonov

  2. Analytical results are infrared stable  cut-off scale parameter Qeff can be pushed down to QCD~250 MeV. Soft partons are accounted for! Hadronization occurs locally at the last moment  hadrons “remember” features of parton distributions. Nhadrons/Npartons=KLPHD Hadron distributions are related to Parton ones! (Bassetto et al.MLLA (Modified Leading Log Approximation) + LPHD(Ya. Azimov et al., 1985) (Local Parton-Hadron Duality) Perturbative dominance scenario. Result =Perturbative Model, which potentially may coherently describe jet fragmentation! Two parameters only - Qeff and KLPHD

  3. MLLA spectrum: • Parton level multiplicity: • Hadron momentum distribution: • Parameters: KLPHD, r, Qeff(Qeff=240±40 MeV from momentum distribution fits)

  4. Does MLLA have a chance? CDF Preliminary (each distribution fitted separately) • Reasonable qualitative agreement • Quantitative match is not perfect (excess and not exact shape)

  5. Does MLLA have a chance? • Q is not a “universal” constant (systematic errors are correlated!). Qeff=240±40 MeV

  6. Does MLLA have a chance? CDF Preliminary • K is not constant for fixed energy

  7. Does MLLA have a chance? • Obviously, we cannot talk about formal agreement between the data and theory. Do we expect one? • Simple hadronization assumption (in fact, absence of it) may be too naïve. • If the problem is in the hadronization stage, it is still possible that properties of the hadrons are mostly determined by parton distributions (perturbative dominance scenario). Qualitative agreement supports this.

  8. MLLA - “mostly correct” model Even though MLLA is not a precise model, it describes data fairly well. • Let’s consider MLLA as a “mostly correct model” with allowed minor deviations from data. • Then MLLA parameters still can be extracted and will make sense.

  9. MLLA - “mostly correct” model • K is not the same as KLPHD. We need to fit K vs fraction of gluon jets in the sample. • If MLLA - almost true, then Qeff is “almost universal”. • It is better to refit 9 distributions with 10 parameters (9 values for K(Ejet)+Qeff). • Result will be more consistent if we want to do something else further with these Ks

  10. Parameter KLPHD CDF Preliminary

  11. Fit procedure: • Chi-square: • Correlation matrix: • Coefficients  can not be precisely defined and have to be varied within reasonable range.

  12. Fit for KLPHD Separate fit Combined fit

  13. Peak Position Systematic errors are correlated!

  14. Peak Position • Same fit procedure. • 2 smaller cones added • Error comes from fit + comparison of fits for all 5 cones(Q=240-250 MeV) and for 3 larger cones only(Q=250-290 MeV).

  15. Peak Position

  16. Conclusion • MLLA is not perfect. Too naïve LPHD assumptions may be responsible • If MLLA is “mostly correct”, MLLA parameters can be extracted. • Qeff=240±40MeV. (250±40 MeV from peak position) • Indirectly measured KLPHD=0.75±0.06, ratio of multiplicities in gluon and quark jets r=1.8±0.4. • Agreement with multiplicity comparison to MLLA KLPHD=0.69±0.3±0.5, r=1.7±0.3

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