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 study the resummation of large logarithmic perturbative corrections to the partonic cross sections relevant for di-hadron production in hadronic collisions, H1 H2 -> h1 h2 X, at high invariant mass of the produced hadron pair. These corrections ar
ise near the threshold for the partonic reaction and are associated with soft-gluon emission. We perform the resummation to next-to-leading logarithmic accuracy, and show how to incorporate consistently cuts in rapidity and transverse momentum of the observed particles. We present numerical results for fixed-target and ISR regimes and find enhancements over the next-to-leading order cross section, which significantly improve the agreement between theoretical predictions and data.
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.
