Finalizing MLLA comparisons
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Finalizing MLLA comparisons Andrey Korytov Alexei Safonov
description
Finalizing MLLA comparisons. Andrey Korytov Alexei Safonov. Analytical results are infrared stable cut-off scale parameter Q eff can be pushed down to QCD ~250 MeV . Soft partons are accounted for!. - PowerPoint PPT Presentation
Transcript of Finalizing MLLA comparisons
Finalizing MLLA comparisons
Andrey Korytov
Alexei Safonov
Perturbative dominance scenario.
•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)
+
Result = Perturbative Model, which potentially may coherently describe jet fragmentation!
Two parameters only - Qeff and KLPHD
•Parton level multiplicity:
•Hadron momentum distribution:
Parameters: KLPHD, r, Qeff (Qeff=240±40 MeV from momentum distribution fits)
MLLA spectrum:
),,()(
),,())(1(1
)()(
jeteffghadron
jeteffgjetgjetgLPHDhadron
EQNKN
EQNEr
EKN
)1
log(
)()(
x
formulaanalyticalNrN quarkgluon
Does MLLA have a chance?
(each distribution fitted separately)
• Reasonable qualitative agreement
• Quantitative match is not perfect (excess and not exact shape)
CDF Preliminary
Does MLLA have a chance?
• Q is not a “universal” constant (systematic errors are correlated!). Qeff=240±40 MeV
Does MLLA have a chance?
• K is not constant for fixed energy
CDF Preliminary
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.
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.
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
K1=0.632 0.005 K2=0.638 0.006 K3=0.600 0.004 K4=0.595 0.003 K5=0.588 0.003
K6=0.581 0.003 K7=0.561 0.003 K8=0.528 0.004 K9=0.488 0.007 Q=2561 MeV
Parameter KLPHD
CDF Preliminary
Fit procedure:
• Chi-square:
• Correlation matrix:
• Coefficients can not be precisely defined and have to be varied within reasonable range.
)()( 12jjijii TheoryDataSTheoryData
ibinforkkindoferrorsystematic
jiforS
ki
kk
kj
kik
statj
statiij
4
11,
Fit for KLPHD
Separate fit
CTC=0.95, vtx.cuts=0.95
stoch.Jet E=0.95
syst.Jet E=1.0 fit range=0.
KLPHD=0.750.04
r=1.820.262/ndf=4.5/7
CTC=1.0, vtx.cuts=1.0
stoch.Jet E=1.0
syst.Jet E=1.0, fit range=0.
KLPHD=0.750.04
r=1.880.262/ndf=5.9/7
CTC=1.0, vtx.cuts=1.0
stoch.Jet E=1.0
syst.Jet E=1.0 fit range=1.0
KLPHD=0.750.03
r=1.980.252/ndf=16.2/7
CTC=1.0, vtx.cuts=1.0
stoch.Jet E=1.0
syst.Jet E=1.0, fit range=0.5
KLPHD=0.760.04
r=1.910.262/ndf=8.1/7
CTC=0.9, vtx.cuts=0.9
stoch.Jet E=0.9
syst.Jet E=0.9, fit range=0.
KLPHD=0.740.04
r=1.770.262/ndf=3.47/7
CTC=0., vtx.cuts=0.
stoch.Jet E=0.
syst.Jet E=0., fit range=0.
KLPHD=0.720.03
r=1.640.232/ndf=0.85/7
Combined fit
Peak Position
Systematic errors are correlated!
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).
Peak Position
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
