Abstract: Presented are the measurements of two-particle momentum correlations in jets produced in p-pbar collisions at center of mass frame energy 1.96 TeV. Studies were performed for charged particles within a restricted opening angle of 0.5 rad around the jet axis and for dijet events with masses ranging from about 60 to 600 GeV. Comparison of the experimental results to the theoretical predictions obtained for partons within the framework of the resummed perturbative QCD (Next-to-leading Log Approximation) shows that the parton momentum correlations do survive the hadronization stage of jet fragmentation, thus giving further support to the hypothesis of Local Parton-Hadron Duality.
Formation and evolution of jets is driven by emission of gluons at very small transverse momenta with respect to jet axis. Detailed studies of fragmentation allow one to investigate a fuzzy boundary between domains of perturbative QCD ( pQCD ) and non-perturbative hadronization. Analytical predictions are based on Next-to-Leading-Log Approximation (NLLA) calculations supplemented with the hypothesis of Local Parton-Hadron Duality ( LPHD ). Past measurements of particle multiplicity in jets and inclusive momentum distributions of particles showed good agreement with theoretical predictions, suggesting that pQCD stage of jet formation must be dominant, and the role of non-perturbative stage is reduced to converting final partons to hadrons without significantly affecting the multiplicities and momenta. Momentum correlations, however, are a more subtle effect and must be measured in order to conclude whether they survive the hadronization process.
In addition, fragmentation studies of jets at Tevatron complement measurements from e+e- and ep experiments providing a unique test of universality of jets.
Finally, this study can be used as a test of Monte-Carlo generators in p-pbar environment. Most generators were tuned to reproduce fragmentation data at LEP. This measurement will test MC generators in Tevatron environment and, maybe, will be useful in future Monte-Carlo tunings.
The correlation function is introduced in terms of variable Xi=log(Ejet/Phadron) (Ejet-energy of a jet, Phadron-momentum of a hadron ) and is measured as a ratio of two- and one- particle inclusive momentum distribution functions, i.e.
C(Xi1,Xi2)=D(X1,Xi2)/(D(Xi1)D(Xi2))
where D(Xi)=dN/dXi and D(Xi1,Xi2)=d^2N/(dXi1 dXi2) and these functions are normalized to unity.
Inclusive momentum ditribution D(Xi) has "skewed gaussian" shape with it's peak position Xi0 depending on so called jet hardness Q=Ejet*Theta_c ( where Theta_c - is a small opening angle of a cone drawn around jet axis,in which particles are counted ).
Results of NLLA calculations performed by Fong/Webber in 1989-1990 suggested that correlation function must have ridge-like shape and analytically can be expressed as:
C(dXi1,dXi2)=C0+C1(dXi1+dXi2)+C2(dXi1-dXi2)^2 where dXi=Xi-Xi0
parameters C0,C1,C2 define strength of correlation and depend on a variable log(Q/Qeff), where Q- jet hardness and Qeff- parton shower cut-off scale used in theory. These three parameters in theory are controlled differently and, therefore, have different precision. It's pretty common and more convinient and conclusive to plot two diagonal profiles dXi1=dXi2 and dXi1=-dXi2 of correlation distribution instead of plotting 3-d distribution itself.
Results
Figures 1-7 show diagonal profiles Xi1=-Xi2 and Xi1=Xi2 of correlation distribution in data for seven dijet energy bins.
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Figures 8-14 show comparison of diagonal profiles of correlation in data with Pythia Tune A and Herwig 6.5 for seven di-jet energy bins.
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Figures 15-17 show evolution of parameters C2, C1 and C0 as a function of jet hardness Q. Each data point corresponds to the value of parameter measured in particular dijet bin. CDF data points are fit to analytical NLLA function, while parton shower cut-off scale Qeff is treated as free parameter. Theoretical curves for samples with only quark and only gluon jets in the final state are also shown.
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