Perturbative QCD

Schematic view of top quark production at the TevatronSince the current generation of high-energy experiments use colliding beams of protons, it is especially important to understand the sector of the SM that accounts for the strong interaction, the theory of Quantum Chromodynamics (QCD).  This theory describes strongly-interacting particles such as protons in terms of the elementary quarks and gluons of which they are composed.  Although this theory cannot be solved exactly, it is possible to develop approximate predictions in the form of perturbative expansions.

Summary of measurements of the strong coupling, alpha-s


The expansion is in terms of the strong coupling (αs) which is approximately 0.12 at energies in which we are interested. Each successive term in the expansion is suppressed by one power of αs. Many calculations have been performed using the simplest predictions from the first, or lowest order, term in this series. Since the strong coupling is quite large (much larger than the corresponding electromagnetic coupling, which is about 1/137), such calculations have only limited accuracy.

In order to produce accurate theoretical predictions to compare with experimental results, it is preferable to calculate higher order terms in the perturbative series. These calculations do not just provide more accurate predictions of cross sections and event rates. They also begin to model more accurately the sub-structure of the colliding hadrons and the production of jets of particles observed in the detectors. Unfortunately, performing such calculations is a difficult task and these predictions only exist in a limited number of cases.

Research at Glasgow

In collaboration with other theorists around the world, researchers at Glasgow are developing these more sophisticated predictions from perturbative QCD. With them, we can investigate the phenomenology of particle collisions in more detail and help to understand the many types of events that we will observe at the LHC.

Soft Gluons

A particular focus is the behaviour of QCD radiation as the momenta of emitted gluons becomes very low (so-called "soft gluons"). This regime is known to lead to unstable results in standard calculations, and methods must be used to work out the effects of any number of soft gluons (that is, to all orders in the perturbation expansion). Recently, new mathematical structures have been discovered in QCD which describe soft gluons to higher accuracy, and in processes with many particles in the initial and final states. Current research involves working out the implications of these results in collider physics, and there are also applications in theories other than QCD (such as quantum gravity or N=4 Super-Yang-Mills theory).

Researchers at Glasgow have also been involved in so-called Monte Carlo event generators, which are large computer programs for simulating what happens inside a particle accelerator. In particular, we have developed software for describing in detail what happens when top quarks are made alongside a W or charged Higgs boson.


  • Factorization Properties of Soft Graviton Amplitudes; C. D. White; arXiv:1103.2981; Abstract, Postscript, Citations.
  • General properties of multiparton webs: Proofs from combinatorics; E. Gardi and C. D. White; JHEP 1103:079,2011; arXiv:1102.0756; Abstract, Postscript, Citations.
  • Next-to-eikonal corrections to soft gluon radiation: a diagrammatic approach; E. Laenen, L. Magnea, G. Stavenga, and C. D. White; JHEP 1101:141,2011; arXiv:1010.1860; Abstract, Postscript, Citations.
  • The MC@NLO 4.0 Event Generator; S. Frixione, F. Stoeckli, P. Torrielli, B. R. Webber, and C. D. White; arXiv:1010.0819; Abstract, Postscript, Citations.
  • Webs in multiparton scattering using the replica trick; E. Gardi, E. Laenen, G. Stavenga, and C. D. White; JHEP 1011:155, 2010; arXiv:1008.0098; Abstract, Postscript, Citations