The most non-trivial of the established microscopic theories of physics is QCD: the theory of the strong interaction. A critical link between theory and experiment is provided by the methods of perturbative QCD, notably the well-known factorization theorems. Giving an accurate account of the concepts, theorems and their justification, this book is a systematic treatment of perturbative QCD. As well as giving a mathematical treatment, the book relates the concepts to experimental data, giving strong motivations for the methods. It also examines in detail transverse-momentum-dependent parton densities, an increasingly important subject not normally treated in other books. Ideal for graduate students starting their work in high-energy physics, it will also interest experienced researchers wanting a clear account of the subject.

/pdf/foundations-of-perturbative-qcd-57f25gk1iq.pdf

Foundations of Perturbative QCD

An infinite number of physically nontrivial symmetries are found for abelian gauge theories with massless charged particles. They are generated by large U(1) gauge transformations that asymptotically approach an arbitrary function "(z, ¯ z) on the conformal sphere at future null infinity (I + ) but are independent of the retarded time. The value of " at past null infinity (I − ) is determined from that on I + by the condition that it take the same value at either end of any light ray crossing Minkowski space. The " 6 constant symmetries are spontaneously broken in the usual vacuum. The associated Goldstone modes are zero-momentum photons and comprise a U(1) boson living on the conformal sphere. The Ward identity associated with this asymptotic symmetry is shown to be the abelian soft photon theorem.

/pdf/new-symmetries-of-massless-qed-4gezzqsqhh.pdf

New Symmetries of Massless QED

http://cds.cern.ch/record/447188/files/0007142.pdf

The soft-gluon current at one-loop order

Infrared factorization, Wilson lines and the heavy quark limit

We examine the structure of infrared singularities in QCD and quantum General Relativity, from the point of view of the recently conjectured double copy property which relates scattering amplitudes in non-Abelian gauge theories with gravitational counterparts. We show that IR divergences in both theories are consistent with the double copy procedure, to all orders in perturbation theory, thus providing all loop-level evidence for the conjecture. We further comment on the relevance, or otherwise, to the so-called dipole formula, a conjecture for the complete structure of IR singularities in QCD.

BCJ duality and the double copy in the soft limit

Although the conceptual difficulties associated with infrared divergences in quantum electrodynamics have long since been resolved, a convenient technique for identifying the appropriate infrared-finite part of Feynman graphs has been lacking. Such a technique is presented here. The polarization sums for both real and virtual photons are rearranged into two parts. One of these (called the $K$-polarization sum) resembles a gauge transformation whose structure permits a simple demonstration of infrared factorization and exponentiation. It is easy to see by inspection that the residual factors (with $G$-polarization sums) are infrared free. This is done for each separate graph, in contrast to earlier treatments where contributions from sets of graphs had to be considered together. The technique is illustrated by a detailed treatment of the radiative corrections to lowest-order potential scattering, and generalizations to other processes are indicated.

G. Grammer

Papers

Improved Treatment for the Infrared-Divergence Problem in Quantum Electrodynamics