Flux Mixing and CP Violation in QCD

TL;DR

This paper proposes that kinetic mixing between flux sectors in QCD can effectively shift the theta angle, leading to CP violation, with implications for the strong CP problem.

Contribution

It introduces a novel mechanism where flux sector mixing shifts the QCD theta parameter, analyzed through a 1+1D model and extended to four dimensions with a three-form field approach.

Findings

Kinetic mixing induces observable shifts in electric fluxes in a 1+1D model.

Flux mixing can shift the QCD theta parameter and induce a nonzero GG expectation value.

Implications for the robustness of axion and CP/parity solutions to the strong CP problem.

Abstract

We argue that kinetic mixing between topological flux sectors generates an effective shift of the QCD $\bar\theta$ angle, thereby inducing CP-violating effects. To demonstrate this mechanism, we analyze a $(1+1)$-dimensional $U(1)\times U(1)$ gauge theory as a controlled setting, where kinetic mixing leads to observable shifts in electric fluxes. We then extend the analysis to four dimensions using a three-form field description of QCD coupled to an additional $U(1)$ three-form gauge field. We find that hidden-sector fluxes, through kinetic mixing, shift the effective $\theta$ parameter of QCD and induce a nonzero expectation value of $\langle G\tilde{G}\rangle$. We discuss the implications for the strong CP problem and clarify under which conditions standard solutions, such as axion or CP/parity-based mechanisms, are compromised or remain robust.