Abstract
Within the framework of Soft Collinear Effective Theory, we present calculations of semi-inclusive jet functions and fragmenting jet functions at next-to-leading order (NLO) for both quark- and gluon-initiated jets, for jet algorithms of $J_{E_T}^{(I)}$ and $J_{E_T}^{(II)}$ where one maximizes a suitable jet function. We demonstrate the consistency of the obtained results with the standard perturbative QCD calculations for $J_{E_T}^{(I)}$ algorithm, while the results for fragmenting jet functions with the $J_{E_T}^{(II)}$ algorithm are new. The renormalization group (RG) equation for both semi-inclusive jet functions and fragmenting jet functions are derived and shown to follow the time-like DGLAP evolution equations, independent of specific jet algorithms. The RG equation can be used to resum single logarithms of the jet size parameter $\beta$ for highly collimated jets in these algorithms where $\beta \gg 1$.
Highlights
In high-energy proton-proton and nucleus-nucleus collisions, a tremendous number of collimated jets of hadrons are produced and measured at the Large Hadron Collider (LHC)
There have been calculations with the standard perturbative quantum chromodynamics (QCD) techniques for JðEITÞ algorithm [27,38], we demonstrate that there are interesting advantages in performing the calculations directly from the operator definitions of semi-inclusive jet functions (SIJFs) and semi-inclusive fragmenting jet functions (SIFJFs) within soft collinear effective theory (SCET), and we compare our results with the standard perturbative QCD calculations
Note that we focus on fully analytical calculations of the SIJFs and SIFJFs at next-toleading order (NLO) in the current work, and we leave phenomenological implementations of these results in pp and AA collisions for future publications
Summary
In high-energy proton-proton and nucleus-nucleus collisions, a tremendous number of collimated jets of hadrons are produced and measured at the Large Hadron Collider (LHC). This algorithm was subsequently improved by Bai, Han, and Lu [37] by using the total transverse energy instead of the energy in the fixed function, which is more appropriate for hadronic collisions such as those at the LHC, because transverse energies are boost invariant This type of algorithm has been implemented into the standard perturbative QCD (pQCD) calculations at NLO for single-inclusive jet production [38] and jet fragmentation functions [27] at hadron colliders, in which infrared safety of the algorithms is established and comparisons to cone and anti-kT algorithms are presented.
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