AI 中文总结
研究利用与标准模型反常\(U(1)_{B + L}\)相位场相关的弱轴子，通过特定味选择规则产生暗能量预期尺度层次，其势在中微子质量四次方阶出现，振幅接近暗能量密度，未来Hyper - K和DUNE等实验可测试。
AI 中文摘要
动态暗能量为宇宙学常数提供了一种具有独特观测特征的替代方案。然而，其小能量密度尺度、哈勃尺度质量和普朗克尺度偏移使得简单模型需要精细调节且不自然。本文表明，与标准模型反常\(U(1)_{B + L}\)的相位场相关的弱轴子版本，可产生暗能量预期的尺度层次。轴子势由明确的重子和轻子数违反源控制且辐射稳定。主要贡献来自两个不等价的温伯格算符，提出基于轻子部门自发破缺的\(S_3\)置换对称性的味选择规则。所得势首先在依赖轴子的中微子质量的四次方阶出现，其振幅与暗能量密度参数上接近。主要不确定性来自\(\delta_{\rm CP}\)和\(\theta_{23}\)，未来像Hyper - K和DUNE这样的实验可直接测试该模型。在宇宙学上，对于接近普朗克质量\(M_{pl}\)的\(f\)，该场表现为解冻型精质，直到晚期被哈勃摩擦冻结且从不进入绝热区域。
英文摘要
Dynamical dark energy offers an alternative to a cosmological constant with distinct observational signatures. However, the small energy density scale, Hubble-sized mass, and Planckian excursions make simple models fine-tuned and unnatural. In this work, we show that a weak version of the axion, identified with the phase field of the anomalous $U(1)_{B+L}$ of the Standard Model, can generate the scale hierarchies expected for dark energy. The axion potential is controlled by sources of explicit baryon and lepton number violation and is radiatively stable. We show that the leading contribution comes from two inequivalent Weinberg operators, one $B+L$-conserving and one $B+L$-violating, which generate the axion potential. We propose a flavor selection rule based on a spontaneously broken $S_3$ permutation symmetry in the lepton sector that simultaneously removes the quadratic divergence and dominant temperature-dependent contributions. The resulting potential first appears at quartic order in the axion-dependent neutrino masses and, for the observed departure from tribimaximal mixing, its amplitude is parametrically close to the dark-energy density. The dominant uncertainty comes from $δ_{\rm CP}$ and $θ_{23}$, so experiments like Hyper-K and DUNE can directly test the model in the future. Cosmologically, the field behaves as thawing quintessence for $f$ close to $M_{pl}$, stays frozen by Hubble friction until late times and never enters the adiabatic regime.
