Probabilistic Jet Algorithms

Conventional jet algorithms are based on a deterministic view of the underlying hard scattering process. Each outgoing parton from the hard scattering is associated with a hard, well separated jet. This approach is very successful because it allows quantitative predictions using lowest order perturbation theory. However, beyond leading order in the coupling constant, when quantum fluctuations are included, deterministic jet algorithms will become problematic precisely because they attempt to describe an inherently stochastic quantum process using deterministic, classical language. This demands a shift in the way we view jet algorithms. We make a first attempt at constructing more probabilistic jet algorithms that reflect the properties of the underlying hard scattering and explore the basic properties and problems of such an approach. In high momentum transfer scattering processes, the concept of jets makes a connection between the hadron-level observations and the underlying partonic theory. For “good” observables the theory is perturbatively calculable and, at lowest order (LO) in the coupling constant, the predictions are deterministic due to the absence of quantum fluctuations. Each parton is associated with a high momentum jet. After “hadronizing” the parton, one ends up with a collimated shower of hadrons. Often color strings of hadrons between the partons are introduced to model the energy flows better. However, the underlying hard scattering in such an approach is still classical. Conventional jet algorithms are based on these models. Their main purpose is to “invert” the hadronization and identify the underlying hard scattering parton structure. Within the classical approach this is perfectly legitimate. In fact, jet algorithms are often compared by how well they reconstruct the underlying partonic structure. Moreover, experimenters use shower models such as HERWIG [1] to estimate their theory/experimental uncertainties by hadronizing a parton in the detector simulation. Here the jet algorithm is applied to estimate the mismeasurement of the original parton energy and direction. One then uses such models to either “correct back” to the parton level or to absorb these effects into the systematic uncertainties. This philosophy is acceptable as long as quantum fluctuations can be neglected. The degree to which this approximation can be applied depends on both the experimental accuracy and on the kinematics of the event (i.e. well separated hard jets are, for all practical purposes, classical.). However, when one counts jets using the classical jet algorithms, the majority of the cross section in multi-jet events comes from the region where the jet clusters