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 previous work on pure scalar and Abelian gauge theories to asymptotically nonlocal non-Abelian theories. In particular, we confirm that there is a limit in which the Lee-Wick spectrum can be decoupled, but where the hierarchy problem is resolved via an emergent nonlocal scale that regulates loop diagrams and that is hierarchically smaller than the lightest Lee-Wick resonance.
Highlights
A specific theory in this sequence with N propagator poles for a given field is suitable for eliminating a scalar mass hierarchy problem if the Lee-Wick partners are comparable to the scale that one wishes to keep hierarchically below the cutoff of the theory
This is the way things work in the Lee-Wick Standard Model [9], where N 1⁄4 2, as well as generalizations to N 1⁄4 3 [10] that have been discussed in the literature
What is interesting about asymptotically nonlocal theories is that there is a large N limit in which the Lee-Wick particles become heavy but where the hierarchy problem is still resolved: loop diagrams are regulated in this limit by an emergent nonlocal scale, Mnl, that is hierarchically smaller that the mass of the lightest Lee-Wick resonance, m1: m2 M2nl ∼ O N1 : ð1:1Þ
Summary
A substantial literature exists on higher-derivative theories, including those with quadratic term that are modified by an operator involving finite or infinite numbers of derivatives [1–8]. [1] that the same result is obtained numerically when one varies the assumed form of the mass spectrum at fixed N These observations suggest that the emergence of the nonlocal scale does not depend sensitively on the exponential form of the differential operator that appears in the limiting theory, Eq (1.6), but rather on the requirement that some entire function emerges that accounts for the desired ultraviolet momentum suppression in the propagator. We provide an Appendix with the Feynman rules for the pure gauge sector of the theory, which may be useful for future phenomenological studies
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