We present a simple set of power counting rules which allows us to easily estimate calculable instanton effects up to \( \mathcal{O} \)(1) factors. We apply the resulting Instanton NDA to examine the effects of small instantons on various axion models. We confirm that mechanisms that increase the axion mass via small instantons generically also lead to an enhancement of misaligned instanton contributions to the axion potential, deepening the axion quality problem. For generic models, new sources of CP violation in the UV must be absent in order to raise the axion mass above the QCD prediction. However, we find that Z_N and composite axions are UV-safe against these misalignment effects. Axion GUT models are also insensitive to UV contributions at the GUT scale, unless a very large number of extra states are introduced below this scale.

我们提出了一组简单的功率计数规则，使我们能够轻松估计高达\( \mathcal{O} \) (1) 个因子的可计算瞬子效应。我们应用由此产生的瞬子 NDA 来检查小瞬子对各种轴子模型的影响。我们确认，通过小瞬子增加轴子质量的机制通常也会导致轴子势的错位瞬子贡献增强，从而加深轴子质量问题。对于通用模型，必须不存在 UV 中 CP 破坏的新来源，以便将轴子质量提高到 QCD 预测之上。然而，我们发现 Z _N和复合轴子对于这些错位效应是紫外线安全的。 Axion GUT 模型对 GUT 尺度上的 UV 贡献也不敏感，除非在该尺度以下引入大量额外状态。