We calculate the contributions of weak magnetism and proton recoil of order $O(E_e^2∕m_N^2)\sim 10^{-5}$, i.e. to next-to-next-to-leading order in the large nucleon mass expansion, to the neutron lifetime and correlation coefficients of the neutron beta decay, where $E_e$ and $m_N$ are the electron energy and the nucleon mass, respectively. We analyze the electron-energy and angular distribution for the neutron beta decay with a polarized neutron, a polarized electron and an unpolarized proton. Together with Wilkinson’s corrections (Wilkinson, 1982; and radiative corrections of order $O(\alpha E_e∕m_N)\sim 10^{-5}$ Ivanov et al., 2019), calculated as next-to-leading order corrections in the large nucleon mass $m_N$ expansion to Sirlin’s corrections of order $O(\alpha ∕\pi )$ (Sirlin, 1967), the corrections of order $O(E_e^2∕m_N^2)\sim 10^{-5}$ provide an improved level of precision of the theoretical background of the neutron beta decay, calculated in the Standard Model, for experimental searches of contributions of interactions beyond the Standard Model.

我们计算弱磁性和有序质子反冲的贡献 $Ø（{Ë}_{Ë}^2∕{米}_{ñ}^2）〜\mathrm{1个}{0}^{-5}$，即在大的核子质量膨胀中，其次至前次顺序是中子寿命和中子β衰变的相关系数，其中 ${Ë}_{Ë}$ 和 ${米}_{ñ}$是电子能量和核子质量。我们用极化中子，极化电子和非极化质子分析中子β衰变的电子能量和角分布。连同威尔金森的修正（威尔金森，1982年；以及阶的辐射修正$Ø（\alpha {Ë}_{Ë}∕{米}_{ñ}）〜\mathrm{1个}{0}^{-5}$ （Ivanov等人，2019），计算为大核子质量中的次先校正 ${米}_{ñ}$ 扩展到Sirlin的订单更正 $Ø（\alpha ∕\pi ）$ （Sirlin，1967年），对命令的更正 $Ø（{Ë}_{Ë}^2∕{米}_{ñ}^2）〜\mathrm{1个}{0}^{-5}$ 提供了在标准模型中计算得出的中子β衰变理论背景的精确度提高水平，用于实验搜索标准模型以外的相互作用。