无中微子双β衰变（0νββ）有效场论方法中的长程标量相互作用

中文摘要 AI 辅助

作为一种轻子数破坏过程，无中微子双β衰变（0νββ）的观测将证实中微子的马约拉纳（Majorana）属性，是超出标准模型新物理的重要低能核探针。有效场论（EFT）提供了通用、模型无关的描述，而有效机制间的干涉对解析它们对总衰变率的贡献至关重要。本研究聚焦于0νββ的EFT方法中长程拉格朗日的标量型项，同时保留两类标量相互作用：涉及共同(S+P)轻子流，分别耦合到(S-P)或(S+P)强子流的情形。它们的相干贡献会产生两类标量机制间的相互干涉，由耦合的相对复相位控制，此外还包含它们与标准质量机制的单独干涉。研究给出了紧凑的半衰期表达式、标量-标量干涉系数的显式形式（以标量核矩阵元比值和相空间积分因子表示），以及该系数的正定性边界。计算采用闭合近似和单核子冲量近似，保留了主导的标量反冲子集，并包含出射电子的s₁/₂和p₁/₂库仑波。该量纲明确的公式为两类标量系数的关联分析提供了基础。

英文摘要

As a lepton-number-violating process whose observation would establish the Majorana nature of neutrinos, neutrinoless double-beta decay ($0νββ$) is an important low-energy nuclear probe of beyond-the-Standard-Model physics. Effective field theory (EFT) provides a general, model-independent description, and interference among effective mechanisms is essential for disentangling their contributions to the total decay rate. We focus on scalar-type terms of the long-range Lagrangian in the EFT approach to $0νββ$. We simultaneously retain the two scalar interactions involving a common $(S+P)$ leptonic current coupled either to an $(S-P)$ or an $(S+P)$ hadronic current. Their coherent contribution produces mutual interference between the two scalar mechanisms, controlled by the relative complex phase of their couplings, in addition to their separate interference with the standard mass mechanism. We give a compact half-life expression, the explicit scalar--scalar interference coefficient in terms of scalar nuclear-matrix-element ratios and integrated phase-space factors, and a positivity bound on that coefficient. The calculation uses the closure and single-nucleon impulse approximations, retains the dominant scalar recoil subset, and includes the $s_{1/2}$ and $p_{1/2}$ Coulomb waves of the outgoing electrons. The resulting dimensionally explicit formulation provides a basis for correlated analyses of the two scalar coefficients.

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29 pages, 1 figure