Gauging Away the Strong CP Problem

TL;DR

The authors address the strong CP problem by proposing an unbroken $U(1)_X$ gauged sector whose gauge boson acquires a Stueckelberg mass through coupling to a pseudoscalar $\eta$ with axion-like couplings to $F_{QCD}\tilde{F}_{QCD}$. A crucial feature is the cancellation of the resulting mixed $U(1)_X$–$SU(3)^2$ anomaly via a bosonic Wess-Zumino term, allowing all SM fermions to remain neutral under $U(1)_X$ and enabling the theta parameter to be gauged away. The mechanism is shown to arise naturally in higher-dimensional and string-theoretic contexts, where bulk $U(1)$ gauge fields, fluxes, and Chern-Simons/Wess-Zumino couplings generate the necessary terms (with explicit realizations in Type II D-brane models and M-theory). This framework provides a novel bosonic alternative to axions or massless quarks, potentially eluding current bounds while embedding the idea in a concrete extra-dimensional/string theory setting.

Abstract

We propose a new solution to the strong-CP problem. It involves the existence of an unbroken gauged $U(1)_X$ symmetry whose gauge boson gets a Stuckelberg mass term by combining with a pseudoscalar field $η(x)$. The latter has axion-like couplings to $F_{QCD}\wedge F_{QCD}$ so that the theta parameter may be gauged away by a $U(1)_X$ gauge transformation. This system leads to mixed gauge anomalies and we argue that they are cancelled by the addition of an appropriate Wess-Zumino term, so that no SM fermions need to be charged under $U(1)_X$. We discuss scenarios in which the above set of fields and couplings appear. The mechanism is quite generic, but a natural possibility is that the the $U(1)_X$ symmetry arises from bulk gauge bosons in theories with extra dimensions or string models. We show that in certain D-brane Type-II string models (with antisymmetric tensor field strength fluxes) higher dimensional Chern-Simons couplings give rise to the required D=4 Wess-Zumino terms upon compactification. In one of the possible string realizations of the mechanism the $U(1)_X$ gauge boson comes from the Kaluza-Klein reduction of the eleven-dimensional metric in M-theory.