arXiv 2012.116022020-12nucl-thhep-exhep-lathep-phnucl-ex

无中微子双$β$衰变的完整首阶预言

Towards complete leading-order predictions for neutrinoless double $β$ decay

Vincenzo Cirigliano, Wouter Dekens, Jordy de Vries, Martin Hoferichter, Emanuele Mereghetti

备注：: 7 pages, 3 figures; journal version. See arXiv:2102.03371 for an extended version
发表信息：: Phys. Rev. Lett. 126, 172002 (2021)
DOI：: 10.1103/PhysRevLett.126.172002

摘要：

双中子系统$nn\to ppe^-e^-$的无中微子双$β$（$0νββ$）衰变的振幅构成了用于大规模$0νββ$搜索的重核的核结构计算的关键构件。假设$0νββ$过程是由光-马约拉纳-中微子交换介导的，在手征有效场论中的系统分析表明，已经在首阶需要接触算子来确保重整化。在这项工作中，我们开发了一种方法来估计其系数的数值模拟的Cottingham公式和验证的结果，通过复制的电荷无关性的破坏贡献的核子-核子散射长度。我们的中心结果，而在$\overline{\text{MS}}$方案中得出的，是在重整化振幅$\mathcal{A}_ν(|\mathbf{p}|,|\mathbf{p}^\prime|)$，匹配，这将允许一个来确定在核结构计算中采用的正则化方案的接触项的贡献。因此，我们的研究结果大大减少了一个关键的不确定性，在解释搜索$0νββ$衰变。

英文摘要：

The amplitude for the neutrinoless double $β$ ($0νββ$) decay of the two-neutron system, $nn\to ppe^-e^-$, constitutes a key building block for nuclear-structure calculations of heavy nuclei employed in large-scale $0νββ$ searches. Assuming that the $0νββ$ process is mediated by a light-Majorana-neutrino exchange, a systematic analysis in chiral effective field theory shows that already at leading order a contact operator is required to ensure renormalizability. In this work, we develop a method to estimate the numerical value of its coefficient in analogy to the Cottingham formula and validate the result by reproducing the charge-independence-breaking contribution to the nucleon-nucleon scattering lengths. Our central result, while derived in the $\overline{\text{MS}}$ scheme, is given in terms of the renormalized amplitude $\mathcal{A}_ν(|\mathbf{p}|,|\mathbf{p}^\prime|)$, matching to which will allow one to determine the contact-term contribution in regularization schemes employed in nuclear-structure calculations. Our results thus greatly reduce a crucial uncertainty in the interpretation of searches for $0νββ$ decay.

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