One-Loop QCD Corrections



Until now our calculations have been limited for the most part to the lowest perturbative order or ‘tree’ graphs. But all processes receive higher-order contributions — usually called radiative corrections — from diagrams that contain ‘loops’, even those (such as flavor changing neutral reactions) for which the lowest-order tree amplitudes are absent. Then new effects can only arise from loops, some typical examples are the \({K^0} - {\bar K^0}\) mixing and the effective ΔS = 1 neutral current (penguin) considered in Chap. 11. Weak decays offer an excellent opportunity for the study of radiative corrections due to either QCD or electroweak interactions. An n-loop diagram has an implicit factor (ħ) n ; a tree (zero-loop) diagram has (ħ)0. The (ħ) n factor shows that the tree graphs are equivalent to classical (Born) approximation, whereas loops are synonymous with quantum effects. This chapter introduces some important concepts and basic calculational methods of quantum corrections.


Radiative Correction Anomalous Magnetic Moment Vertex Function Gluon Propagator Infrared Divergence 
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Suggestions for Further Reading

Dimensional regularization

  1. Veltman, M., Diagrammatica. Cambridge U. Press, Cambridge 1994Google Scholar

Radiative corrections; mass and field renormalization; infrared effects

  1. Aoki, K., Hioki, Z., Kawabe, R., Konuma, M. and Muta, T., Electroweak Theory. Supp. Prog. T.eor. Phys. 73 (1982) 1ADSCrossRefGoogle Scholar
  2. Weinberg, S., The Quantum Theory of Fields (Vol. I) Cambridge U. Press, Cambridge 1995Google Scholar

Phase space integrals in four-dimensions

  1. Pietschmann, H., Formulae and Results in Weak Interactions. Springer, Wien, New York 1974Google Scholar

Infrared-safe radiative corrections, using dimensional regularization

  1. Field, R., Applications of Perturbative QCD. Addison-Wesley, Redwood, CA 1989Google Scholar
  2. Guberina, B., Peccei, R. D. and Ruckl, R., Nucl. Phys. B171 (1980) 333 Marciano, W. J., Phys. Rev. D12 (1975) 3861Google Scholar

Q CD corrections to weak decays, taking full account of all fermionic masses

  1. Czarnecki, A., Jezabek, M. and Kühn, J. H., Phys. Lett. B346 (1995) 335Google Scholar
  2. Ho-Kim, Q. and Pham, Xuan-Yem, Ann. of Phys. (N.Y.) 155 (1984) 202ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  1. 1.Physics DepartmentUniversité LavalSte-FoyCanada
  2. 2.Laboratoire de Physique Théorique et Hautes EnergiesUniversités Paris VI et VIIParis Cedex 05France

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