Analytic structure of ${\varphi }^4$ theory using light-by-light sum rules

Abstract

We apply a sum rule for the forward light-by-light scattering process within the context of the ${\varphi }^4$ quantum field theory. As a consequence of the sum rule a stringent causality criterion is presented and the resulting constraints are studied within a particular resummation of graphs. Such resummation is demonstrated to be consistent with the sum rule to all orders of perturbation theory. We furthermore show the appearance of particular non-perturbative solutions within such approximation to be a necessary requirement of the sum rule. For a range of values of the coupling constant, these solutions manifest themselves as a physical bound state and a $K$-matrix pole. For another domain however, they appear as tachyon solutions, showing the inconsistency of the approximation in this region.

12 pages, 7 figures

References in corpus (5)

• Heavy quarkonium: progress, puzzles, and opportunities
• New Charmonium States in QCD Sum Rules: a Concise Review
• Light-by-light scattering sum rules constraining meson transition form factors
• Sum rules for light-by-light scattering
• Analyticity, Unitarity and One-loop Graviton Corrections to Compton Scattering

Cited by in corpus (4)

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