Effective description of Nelson-Barr models and the theta parameter

Abstract

Nelson-Barr theories solve the strong CP problem with CP spontaneously broken at Λ_{CP} and transmitted to the CP conserving version of the SM through vector-like quarks (VLQs). For an arbitrary number of CP breaking scalars and VLQs, we perform the full one-loop matching calculations at Λ_{CP} up to dimension five operators and the relevant matching calculations at the VLQ scale relevant to tracking the contributions to the parameter \barθ. In the EFT after the CP breaking scalars have been integrated out, we confirm that the running of \barθ at one-loop is induced by CP violating dimension five operators and similarly by dimension six operator after matching to the SMEFT. In the latter, an additional contribution enters in the matching to \barθ at tree-level due to a dimension five operator. Analyzing the experimental constraint from \barθ for generic settings, we see that a large separation between Λ_{CP} and the VLQ scale already suppresses the one-loop contribution to \barθ sufficiently. We confirm that a simple extension based on a nonconventional CP has a vanishing one-loop contribution to \barθ. Part of our results can be also applied to generic VLQ extensions of the SM.

42 pages, 7 figures. Updated discussion on 1-loop matching to theta at VLQ scale in Sec.VI.D and few other places

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• Nelson-Barr Models with Vector-Like Quark Doublets