Corrections of order O(Ee2∕mN2), caused by weak magnetism and proton recoil, to the neutron lifetime and correlation coefficients of the neutron beta decay

Abstract

We calculate the contributions of weak magnetism and proton recoil of order O(Ee2∕mN2)∼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 Eeand mNare 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(αEe∕mN)∼10−5Ivanov et al., 2019), calculated as next-to-leading order corrections in the large nucleon mass mNexpansion to Sirlin’s corrections of order O(α∕π)(Sirlin, 1967), the corrections of order O(Ee2∕mN2)∼10−5provide 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.

Keywords

• Neutron
• Weak magnetism
• Proton recoil