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 ^- decay with polarized neutron and polarized electron, up to order O (m₍^-2), where m₍ represents the mass of neutron. In our calculations, we express the mass of proton m₏ in terms of m₍ and other small quantities to ensure that only one larger parameter, m₍, remains in the differential cross section. Subsequently, we expand the differential cross section on m₍^-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 (m₍^-1), three of the results are consistent, while two differ slightly. In addition, the contributions at order O (m₍^-2) are presented when considering a general form of Wnp interactions. Numerical results show that contributions from order O (m₍^-2) and additional form factors of Wnp interactions are required to achieve a precision of 10^-5.