Recoil contributions in neutron β− decay and their corrections to the correlation coefficients

In this work, we evaluate the recoil corrections to the correlation coefficients in the neutron β^- decay with polarized neutron and polarized electron, up to order O(mₙ^-2), where mₙ represents the mass of neutron. In our calculations, we express the mass of proton mₚ in terms of mₙ and other small quantities to ensure that only one larger parameter, mₙ, remains in the differential cross section. Subsequently, we expand the differential cross section on mₙ^-1, and finally integrate the solid angles of the antineutrino to obtain the analytic expressions for the angular correlation coefficients. Comparing the analytic results to those in a previous study [Ivanov, Hollwieser, Troitskaya, Wellenzohn, and Berdnikov, Phys. Rev. C 95, 055502 (2017); Phys. Rev. C 104, 069901(E) (2021)], we find that, at order O(mₙ^-1), three of the results are consistent, while two differ slightly. In addition, the contributions at order O(mₙ^-2) are presented when considering a general form of $Wnp$ interactions. Numerical results show that contributions from order O(mₙ^-2) and additional form factors of $Wnp$ interactions are required to achieve a precision of 10^-5.