Scattering of glue by glue on the light-cone worldsheet. II. Helicityconserving amplitudes
- Institute for Fundamental Theory Department of Physics, Universityof Florida, Gainesville, Florida 32611 (United States)
This is the second of a pair of articles on scattering of glue by glue,in which we give the light-cone gauge calculation of the one-loop on-shellhelicity conserving scattering amplitudes for gluon-gluon scattering (neglectingquark loops). The 1/p{sup +} factors in the gluon propagatorare regulated by replacing p{sup +} integrals with discretized sums omitting the p{sup +}=0 terms in each sum. We alsoemploy a novel ultraviolet regulator that is convenient for the light-coneworldsheet description of planar Feynman diagrams. The helicity conservingscattering amplitudes are divergent in the infrared. The infrared divergencesin the elastic one-loop amplitude are shown to cancel, in their contributionto cross sections, against ones in the cross section for unseen bremsstrahlunggluons. We include here the explicit calculation of the latter, because itassumes an unfamiliar form due to the peculiar way discretization of p{sup +} regulates infrared divergences. In resolving the infrareddivergences we employ a covariant definition of jets, which allows a transparentdemonstration of the Lorentz invariance of our final results. Because we usean explicit cutoff of the ultraviolet divergences in exactly four spacetimedimensions, we must introduce explicit counterterms to achieve this finalcovariant result. These counterterms are polynomials in the external momentaof the precise order dictated by power counting. We discuss the modificationsthey entail for the light-cone worldsheet action that reproduces the bareplanar diagrams of the gluonic sector of QCD. The simplest way to do thisis to interpret the QCD string as moving in six spacetime dimensions.
- OSTI ID:
- 20871036
- Journal Information:
- Physical Review. D, Particles Fields, Vol. 74, Issue 4; Other Information: DOI: 10.1103/PhysRevD.74.045018; (c) 2006 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA); ISSN 0556-2821
- Country of Publication:
- United States
- Language:
- English
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