Abstract
Asymptotically nonlocal field theories represent a sequence of higher-derivative theories whose limit point is a ghost-free, infinite-derivative theory. Here we extend this framework, developed previously in a theory of real scalar fields, to gauge theories. We focus primarily on asymptotically nonlocal scalar electrodynamics, first identifying equivalent gauge-invariant formulations of the Lagrangian, one with higher-derivative terms and the other with auxiliary fields instead. We then study mass renormalization of the complex scalar field in each formulation, showing that an emergent nonlocal scale (i.e., one that does not appear as a fundamental parameter in the Lagrangian of the finite-derivative theories) regulates loop integrals as the limiting theory is approached, so that quadratic divergences can be hierarchically smaller than the lightest Lee-Wick partner. We conclude by making preliminary remarks on the generalization of our approach to non-Abelian theories, including an asymptotically nonlocal standard model.
Highlights
Theories involving a small, finite number of higher-derivative quadratic terms, such as the Lee-Wick Standard Model (LWSM), and ghost-free theories with an infinite number of derivatives [3–6,9–14] have been studied in the literature
II, we review the framework for constructing asymptotically nonlocal theories that was illustrated in a theory of real scalar fields in Ref. [1], and summarize the main results of that work
III, we show how the same construction can be generalized to scalar quantum electrodynamics (QED), an Abelian gauge theory
Summary
Quantum field theories involving higher-derivative quadratic terms have been of substantial interest due to the improvement in the short-distance behavior of amplitudes [1–14]. We demonstrate that the theory is free of a hierarchy problem, with corrections to the squared mass of the complex scalar field set by an emergent nonlocal scale that is hierarchically smaller than the lightest Lee-Wick partner as the limiting theory is approached. III, we show how the same construction can be generalized to scalar QED, an Abelian gauge theory We show how this theory can be written in higher-derivative and in Lee-Wick form (i.e., a form with distinct fields corresponding to each propagator pole, but no higherderivative terms), and introduce a coupling to a complex scalar field of unit charge. As an additional nontrivial consistency check, we provide Appendix in which we show by direct calculation that the conclusions of Ref. [1] remain unchanged when two-loop effects are taken into account
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