Abstract
The formation and evolution of leading jets can be described by jet functions which satisfy non-linear DGLAP-type evolution equations. Different than for inclusive jets, the leading jet functions constitute normalized probability densities for the leading jet to carry a longitudinal momentum fraction relative to the initial fragmenting parton. We present a parton shower algorithm which allows for the calculation of leading-jet cross sections where logarithms of the jet radius and threshold logarithms are resummed to next-to-leading logarithmic (NLL′) accuracy. By calculating the mean of the leading jet distribution, we are able to quantify the average out-of-jet radiation, the so-called jet energy loss. When an additional reference scale is measured, we are able to determine the energy loss of leading jets at the cross section level which is identical to parton energy loss at leading-logarithmic accuracy. We identify several suitable cross sections for an extraction of the jet energy loss and we present numerical results for leading subjets at the LHC. In addition, we consider hemisphere and event-wide leading jets in electron-positron annihilation similar to measurements performed at LEP. Besides the average energy loss, we also consider its variance and other statistical quantities such as the KL divergence which quantifies the difference between quark and gluon jet energy loss. We expect that our results will be particularly relevant for quantifying the energy loss of quark and gluon jets that propagate through hot or cold nuclear matter.
Highlights
Energetic jets play a major role at high-energy collider experiments such as the Large Hadron Collider (LHC) and the Relativistic Heavy Ion Collider (RHIC), as well as the future Electron-Ion Collider (EIC) [1]
We start with an next-to-leading order (NLO) computation of the average momentum fraction which is contained in the leading jet at the jet function level
The formation and evolution of leading jets is described by jet functions with non-linear DGLAP-type evolution equations
Summary
Energetic jets play a major role at high-energy collider experiments such as the Large Hadron Collider (LHC) and the Relativistic Heavy Ion Collider (RHIC), as well as the future Electron-Ion Collider (EIC) [1]. Given that leading jets form a well-defined object distributed probabilistically by the fragmentation process, they allow for a well-defined notion of jet energy loss at the jet function and cross section level. One of the main novelties of our work is the development of a Monte Carlo parton shower framework which solves the non-linear DGLAP-type evolution equations of leading jets, while including the complete next-to-leading logarithmic (NLL ) threshold resummed hard-scattering and jet functions. We discuss how nonperturbative effects can be included in the threshold limit which is phenomenologically relevant for leading jets and present numerical results for both processes at the cross section level. We present numerical results for the mean and variance of the leading jet/energy loss distribution and focus in particular on quark/gluon differences. We refer to ref. [23] where these relations were proposed in the context of statistical properties of randomly broken objects and spin glasses
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