Abstract:We present the first measurement of $k_{T}$ distributions for particles in jets produced in $p\bar p$ collisions at center of mass energy of 1.96 TeV. Results were obtained for charged particles within a restricted cone with opening angle of 0.5 rad around the jet axis and for dijet events with masses ranging from about 60 to 740 $GeV/c^{2}$. Comparison of the experimental data to the theoretical predictions obtained for partons within the framework of the resummed perturbative QCD (Modified Leading Log Approximation) shows good agreement in the range of $k_{T}$ where the soft approximation can be applied. Pythia Tune A and Herwig 6.5 Monte-Carlo generators are consistent with data.

Detailed studies of jet fragmentation allow one to better understand the processes occurring at the boundary between the perturbative part of parton showering and non-perturbative hadronization. Past CDF studies of inclusive distributions of particles in jets showed good agreement with theoretical predictions produced for partons, suggesting that perturbative QCD (pQCD) stage of jet formation must be dominant, and the role of non-perturbative stage is reduced to converting final partons into hadrons. In this note we discuss the measurement of $k_{T}$ distributions of particles in jets, where $k_{T}$ is transverse momentum of particle with respect to jet axis. The CDF data results are compared to analytical predictions. These predictions are based on the Modified Leading Logarithmic Approximation (MLLA) and Next-to-Modified Leading Logarithmic Approximation (NMLLA) calculations supplemented with the hypothesis of Local Parton-Hadron Duality (LPHD) . We also compare distributions in data to those produced by Pythia Tune A and Herwig 6.5 Monte-Carlo generators. This analysis is interesting not only because it is the first data vs MLLA (NMLLA) comparison of $k_{T}$ spectra, but also because it allows one to probe softer particle spectra than studies of inclusive momentum or two-particle momentum correlation distributions.

In this analysis we measure $k_{T}$ distributions of particles in jets for wide range of dijet masses. Data is compared to the analytical pQCD predictions made in the framework of MLLA and NMLLA. We also compare distributions in data to those in Monte-Carlo to verify if event generators do decent job reproducing this aspect of jet fragmentation. In theory distributions are normalized to the average number of particles in a jet $n$. The MLLA predictions for $n$ were compared to CDF data in earlier analysis, good agreement between data and theory was observed. The goal of this study is to compare the shape of $k_{T}$ distributions only, and not the absolute scale. Then, normalizing distributions to unity looks like a solution. However, the majority of particles in jets have very low $k_{T}$, in the range where neither theory nor experiment can be really trusted. The problem can be solved by normalizing distributions to number of entries in a particular bin. This bin has to be in the region where both data and theory are reliable. We normalize our to distributions to the bin with $-0.20.8$) MLLA (NMLLA) works well, as well as CDF tracking efficiency is high enough.

Overall, data and theory show similar trends even though MLLA predicts more hard particles than it is observed in data. However, one has to keep in mind that MLLA predictions are made in the limit of soft approximation. This approximation works better at high values of $Q$. Generally, estimated ($y=ln(k_{T}/Q_{Eff})$) lower and upper bound where the soft approximation is valid are: $y_{min} \sim 1$ and $y_{max}\sim ln(Q/Q_{eff}) - 2.5$. Therefore, as one goes to larger $Q$, the range of validity of soft approximation is getting larger, providing better agreement of MLLA and data. The validity range of the NMLLA predictions is larger than one for MLLA predictions. The agreement between the data and the NMLLA curves is found to be very good at all values of jet energies.