I discuss how the axial current coupling constant $g_A$ renormalized in scale symmetric chiral EFT defined at a chiral matching scale impacts on the axial current matrix elements on beta decays in nuclei with and without neutrinos. The “quenched” $g_A$ observed in nuclear superallowed Gamow–Teller transitions, a long-standing puzzle in nuclear physics, is shown to encode the emergence of chiral-scale symmetry hidden in QCD in the vacuum. This enables one to explore how trace-anomaly-induced scale symmetry breaking enters in the renormalized $g_A$ in nuclei applicable to certain non-unique forbidden processes involved in neutrinoless double beta decays. A parallel is made between the roles of chiral-scale symmetry in quenching $g_A$ in highly dense medium and in hadron–quark continuity in the EoS of dense matter in massive compact stars. A systematic chiral-scale EFT, presently lacking in nuclear theory and potentially crucial for the future progress, is suggested as a challenge in the field.

中文翻译：

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隐藏手性尺度对称性的多种作用：“淬灭”原子核中的 gA

我讨论了轴向电流耦合常数如何 $G_{\mathrm{一种}}$在手性匹配尺度上定义的尺度对称手性 EFT 重新归一化对轴向电流矩阵元素的影响对有和没有中微子的原子核中的 β 衰变产生影响。“淬火”$G_{\mathrm{一种}}$在核超容许 Gamow-Teller 跃迁中观察到的，这是核物理学中一个长期存在的谜题，它被证明编码隐藏在真空中 QCD 中的手性尺度对称性的出现。这使人们能够探索痕量异常引起的尺度对称破坏如何进入重整化$G_{\mathrm{一种}}$在适用于涉及无中微子双β衰变的某些非唯一禁止过程的原子核中。手性尺度对称性在淬火中的作用之间存在平行关系$G_{\mathrm{一种}}$在大质量致密恒星的致密物质 EoS 中的高密度介质和强子-夸克连续性中。目前缺乏核理论并且对未来进展可能至关重要的系统手性尺度 EFT 被认为是该领域的一个挑战。