This is a brief introduction to two of the central concepts in perturbative quantum chromodynamics, jets and factorization, which serve as windows into the short-distance behavior of quantum fields.
We consider the relativistic scattering of unequal-mass scalar particles through graviton exchange in the small-angle high-energy regime. We show the self-consistency of expansion around the eikonal limit and compute the scattering amplitude up to th
e next-to-leading power correction of the light particle energy, including gravitational effects of the same order. The first power correction is suppressed by a single power of the ratio of momentum transfer to the energy of the light particle in the rest frame of the heavy particle, independent of the heavy particle mass. We find that only gravitational corrections contribute to the exponentiated phase in impact parameter space in four dimensions. For large enough heavy-particle mass, the saddle point for the impact parameter is modified compared to the leading order by a multiple of the Schwarzschild radius determined by the mass of the heavy particle, independent of the energy of the light particle.
The perturbative treatment of high-energy fixed-angle hadron-hadron exclusive scattering is reviewed and related to the transverse structure of the proton and other hadrons.
We introduce a new class of infrared safe jet observables, which we refer to as template overlaps, designed to filter targeted highly boosted particle decays from QCD jets and other background. Template overlaps are functional measures that quantify
how well the energy flow of a physical jet matches the flow of a boosted partonic decay. Any region of the partonic phase space for the boosted decays defines a template. We will refer to the maximum functional overlap found this way as the template overlap. To illustrate the method, we test lowest-order templates designed to distinguish highly-boosted top and Higgs decays from backgrounds produced by event generators. For the functional overlap, we find good results with a simple construction based on a Gaussian in energy differences within angular regions surrounding the template partons. Although different event generators give different averages for our template overlaps, we find in each case excellent rejection power, especially when combined with cuts based on jet shapes. The template overlaps are capable of systematic improvement by including higher order corrections in the template phase space.
This talk reviewed some classic results and recent progress in the resummation of leading and nonleading enhancements in QCD cross sections and of poles in dimensionally-regularized hard-scattering amplitudes.
This is a brief review of some of the basic concepts of perturbative QCD, including infrared safety and factorization, relating them to more familiar ideas from quantum mechanics and relativity. It is intended to offer perspective on methods and term
s whose use is commonplace, but whose physical origins are sometimes obscure.
