Abstract
In his series of lectures on QCD, C.H. Llewellyn-Smith indicated the central role played by the factorization “theorems” in any perturbative analysis1. He also alluded to some possible loopholes in the theorems due to the effects of initial state hadronic interactions. In this talk I will present the results of some work done in collaboration with S.J. Brodsky and G.P. Lepage in which we investigated the effects of initial state interactions in the Drell-Yan process2.
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References
H.D. Politzer, Nucl. Phys. B129, 301 (1977). R.K. Ellis, H. Georgi, M. Machacek, H.D. Politzer and G.G. Ross, Nucl. Phys. B152, 285 (1979). S. Gupta and A.H. Mueller, Phys. Rev. D20, 118 (1979). A discussion of final state interactions and factorization for the Drell-Yan processes is given in J.C. Collins and D.E. Soper, Proceedings of the Moriond Workshop, Les Arcs, France (1981).
S.D. Drell and T.M. Yan, Phys. Rev. Lett. 25, 316 (1970). Possible complications in the parton model prediction due to “wee parton” exchange were discussed in this paper.
See, for example, G.P. Lepage and S.J. Brodsky, Phys. Rev. D22, 2157 (1980).
J.L. Cardy and G.A. Winbow, Phys. Lett. 52B, 95 (1974), and C. E. DeTar, S.D. Ellis and P.V. Landshoff, Nucl. Phys. B87 176 (1975). Possible nuclear effects on transverse momentum have also been considered by C. Michael and G. Wilk, University of Liverpool preprint LTH64 (March 1981) (to be published in Zeit. Phys. C). See also T. Jaroszewicz, M. Jezabek, Zeit. Phys. C. Particles and Fields 4, 277 U980), and A. Bialas and E. Bialas, Phys. Rev. D21, 675 (1980).
This type of cancellation renders all graphs finite in the Abelian case. However, in a non-Abelian theory, the can-cellation is, in general, spoiled because of the different color factors associated with the potentially cancelling graphs.
Indeed, for two-dimensional QCD, in which the hadrons have no transverse size, the initial state interactions do cancel, and one obtains the parton model result [J. Kripfganz and M.G. Schmidt, Nucl. Phys. B125, 323 (1977)]. For a further discussion of this point in the context of two-dimensional QCD see J.H. Weis, Acta Phys. Polon. B9, 1501 (1978).
See, for example, R.P. Feynman and R.D. Field, Phys. Rev. B15, 2590 (1977).
G.E. Hogan, Ph.D. Dissertation, Princeton University (1979).
J. Badier et al., CERN preprint CERN-EP/81-63 (June 1981).
The lowest order initial state amplitude is pure imaginary, so there is no 0(αs) contribution.
See, for example. Hung Cheng and Tai Tsun Wu, Phys. Rev. D1, 2775 (1970).
A.H. Mueller, Columbia University preprint CU-TP-213 (October 1981).
This argument is very similar to the discussion of a “formation zone” for radiation due to a classical current given by L. Landau and I. Pomeranchuk, Doklady Academii Nauk USSR 92, 535 (1953). We thank L. Stodolsky for bringing this work to our attention.
For example, any elastic or inelastic interaction with an amplitude T ∼ sf (t), where tf(t)→0 for t large, leads to our results.
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© 1983 Plenum Press, New York
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Bodwin, G.T. (1983). Initial State Interactions, Factorization, and the Drell-Yan Process. In: Capri, A.Z., Kamal, A.N. (eds) Particles and Fields 2. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-3593-1_12
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DOI: https://doi.org/10.1007/978-1-4613-3593-1_12
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