- Access by Xinjiang University
Factorization of soft and collinear divergences in QCD in the Feynman gauge via a background field gauge
Phys. Rev. D 32, 945 – Published 15 August, 1985Erratum Phys. Rev. D 34, 1235 (1986)
DOI: https://doi.org/10.1103/PhysRevD.32.945
Abstract
We prove Ward-type identities which are needed in the proof of factorization of the Drell-Yan process. Previous treatments prove them only for an axial gauge, and the proofs are diagrammatic in nature. We, on the other hand, establish the identities for the Feynman gauge and through symmetry considerations at the Lagrangian level. Our strategy is to first derive exact results in a background field gauge and then to show that to leading order in the mass divergences the background-field-gauge results can be used in the Feynman gauge.
Erratum
References (12)
- R. Tucci, Argonne Report No. ANL-HEP-PR-84-37 (unpublished).
- G. Grammer and D. Yennie, Phys. Rev. D 8, 4332 (1973).
- Omitted end note.
- J. Collins and D. Soper, Nucl. Phys. B 193, 381 (1981).
- R. Tucci, University of Wisconsin report 1983 (unpublished).
- J. Collins, D. Soper, and G. Sterman, Nucl. Phys. B 223, 381 (1983); Phys. Lett. 109 B, 388 (1982); 126 B, 275 (1983); 134 B,263 (1984); University of Oregon Report No. OITS287 (unpublished).
- G. Bodwin, Phys. Rev. D 31, 2616 (1985).
- For a clear set of lectures see L. Abbott, Acta Phys. Pol. B 13, 33 (1982). Original references cited therein.
- For the analog in one-dimensional quantum mechanics, see R. Glauber, in Lectures in Theoretical Physics, Vol. I, Boulder, 1958, edited by W. Brittin and L. Dunham (Interscience, New York, 1959).
- Our argument relating to is a trivial modification of the proof due to B. Lee and J. Zinn-Justin which shows that S-matrix elements of non-Abelian gauge theories are independent of gauge fixing. See B. Lee and J. Zinn-Justin, Phys. Rev. D 7, 1049 (1973); B. Lee, in Methods in Field Theory, 1975 Les Houches Lectures, edited by R. Balian and J. Zinn-Justin (North-Holland, Amsterdam, 1976).
- G. 't Hooft, Nucl. Phys. B 33, 173 (1971). For an excellent set of lectures on these identities, see P. Cvitanovic, Field Theory (NORDITA, Copenhagen, Denmark (1983).
- I thank G. Bodwin for suggesting this identity to me.