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Strong CP problem in the quantum rotor

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arxiv 2402.17518 v2 pith:SA4A2MUU submitted 2024-02-27 hep-lat hep-ph

classification hep-lathep-ph
keywords problemlatticestrongthetatopologicalorderquantumrotor
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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.

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  1. Lattice techniques to investigate the strong $CP$ problem: lessons from a toy model

    hep-lat 2025-02 accept novelty 4.0 of 10

    In a quantum rotor with a topological term, the proposed order of limits predicts zero topological susceptibility, contradicting both the exact quantum mechanical result and lattice simulations.

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