Strong CP problem in the quantum rotor

Abstract

Recent studies have claimed that the strong $CP$ problem does not occur in QCD, proposing a new order of limits in volume and topological sectors when studying observables on the lattice. In order to shed light on this issue, we study the effect of the topological $\theta$-term on a simple quantum mechanical rotor that allows a lattice description. The topological susceptibility and the $\theta$-dependence of the energy spectrum are both computed using local lattice correlation functions. The sign problem is overcome by considering Taylor expansions in $\theta$ exploiting automatic differentiation methods for Monte Carlo processes. Our findings confirm the conventional wisdom on the strong $CP$ problem.

11 pages, 6 figures. v2: edit to match published version

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Cited by in corpus (2)

• Scaling flow-based approaches for topology sampling in $\mathrm{SU}(3)$ gauge theory
• The $\theta$-vacuum from functional renormalisation