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We calculate the contributions of weak magnetism and proton recoil of orderO(E^2_e/m^2_N)~10^{-5}, i.e. to next-to-next-to-leading order in the largenucleon mass expansion, to the neutron lifetime and correlation coefficients ofthe neutron beta decay, where E_e and m_N are the electron energy and thenucleon mass, respectively. We analyze the electron-energy and angulardistribution for the neutron beta decay with a polarized neutron, a polarizedelectron and an unpolarized proton. Together with Wilkinson's corrections(Nucl. Phys. A 377, 474 (1982) and radiative corrections of order O(alphaE_e/m_N) ~ 10^{-5} (Phys. Rev. D 99, 093006 (2019)), calculated asnext--to--leading order corrections in the large nucleon mass $m_N$ expansionto Sirlin's corrections of order O(alpha/pi) (Phys. Rev. 164, 1767 (1967)), thecorrections of order O(E^2_e/m^2_N) ~ 10^{-5} provide an improved level ofprecision of the theoretical background of the neutron beta decay, calculatedin the Standard Model, for experimental searches of contributions ofinteractions beyond the Standard Model.

Corrections of order O(E^2_e/m^2_N), caused by weak magnetism and proton  recoil, to the neutron lifetime and correlation coefficients of the neutron  beta decay