QCD resummation for light-particle jets

TL;DR

The authors develop a QCD resummation framework to study light-quark and gluon jets, deriving evolution equations for jet and energy functions in Mellin space to resum double and single logarithms. By incorporating a phenomenological nonperturbative term, they obtain jet-mass distributions that agree with Tevatron data and demonstrate scaling with $RP_T$ and gluon-vs-quark differences due to color factors. They further predict jet energy profiles, finding light-quark jets to be narrower than gluon jets and achieving good agreement with Tevatron and LHC measurements, with energy profiles largely insensitive to nonperturbative effects. The work offers a perturbative, data-titted route to jet substructure observables and lays groundwork for applying the formalism to highly boosted heavy-particle jets at the LHC. It also highlights potential connections to PDFs and new-physics searches through jet substructure analyses.

Abstract

We construct an evolution equation for the invariant-mass distribution of light-quark and gluon jets in the framework of QCD resummation. The solution of the evolution equation exhibits a behavior consistent with Tevatron CDF data: the jet distribution vanishes in the small invariant-mass limit, and its peak moves toward the high invariant-mass region with the jet energy. We also construct an evolution equation for the energy profile of the light-quark and gluon jets in the similar framework. The solution shows that the energy accumulates faster within a light-quark jet cone than within a gluon jet cone. The jet energy profile convoluted with hard scattering and parton distribution functions matches well with the Tevatron CDF and the large-hadron-collider (LHC) CMS data. Moreover, comparison with the CDF and CMS data implies that jets with large (small) transverse momentum are mainly composed of the light-quark (gluon) jets. At last, we discuss the application of the above solutions for the light-particle jets to the identification of highly-boosted heavy particles produced at LHC.

Figures (13)

• Figure 1: Diagram for the light-quark jet function with a special vertex at the outermost end of the Wilson line. The factorization gives the LO virtual soft kernel.
• Figure 2: Factorization of the LO real soft kernel.
• Figure 3: Diagram for the light-quark jet function with a special vertex at the innermost end of the Wilson line. The factorization gives the LO hard kernel.
• Figure 4: Quark (left) and gluon (right) jet mass distributions with $S^{\rm NP}$ (solid lines) and without $S^{\rm NP}$ (dotted lines) for $P_T=600$ GeV and $R=0.7$.
• Figure 5: Resummation results for the light-quark (upper) and gluon (lower) jet mass distributions as functions of $M_J/(RP_T)$ including the nonperturbative contributions for $R=0.4$, $0.5$, $0.6$ and $0.7$ with $RP_T=280$ GeV. The ratios relative to the predictions for $R=0.7$ are also shown.