High-energy behavior in field theory and dilatational symmetry

Banerjee, M. K. ; Kugler, M. ; Levinson, C. A. ; Muzinich, I. J. (1965) High-energy behavior in field theory and dilatational symmetry Physical Review, 137 (5B). B1280-B1290. ISSN 0031-899X

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Official URL: http://prola.aps.org/abstract/PR/v137/i5B/pB1280_1

Related URL: http://dx.doi.org/10.1103/PhysRev.137.B1280


The high-energy forward-scattering amplitude in λφ4 theory is investigated by means of the Bethe-Salpeter equation. The class of irreducible diagrams which have dilatational symmetry at high energies is considered as kernels for the Bethe-Salpeter equation. For these kernels, the equation is solved using a Mellin transform. The solution is found to contain a term which, at high energies, behaves like En0/(lnE)c. This term is caused by a branch cut in a complex four-dimensional Euclidean angular-momentum plane. A lower bound for n0 is obtained from a simple diagram. Using the upper bound on n0 which results from unitarity, an upper bound on the coupling constant is obtained: λ<(3√ 8)π2.

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