On the correlation coefficient T(Ee) of the neutron beta decay, caused by the correlation structure invariant under discrete P, C and T symmetries

Abstract

We analyze the correlation coefficient T(Ee), which was introduced by Ebel and Feldman (1957) [64]. The correlation coefficient T(Ee) is induced by the correlation structure (ξ→n⋅k→ν¯)(k→e⋅ξ→e)/EeEν¯, where ξ→n,e are unit spin-polarization vectors of the neutron and electron, and (Ee,ν¯,k→e,ν¯) are energies and 3–momenta of the electron and antineutrino. Such a correlation structure is invariant under discrete P, C and T symmetries. The correlation coefficient T(Ee), calculated to leading order in the large nucleon mass mN expansion, is equal to T(Ee)=−2gA(1+gA)/(1+3gA2)=−B0, i.e. of order |T(Ee)|∼1, where gA is the axial coupling constant. Within the Standard Model (SM) we describe the correlation coefficient T(Ee) at the level of 10−3 by taking into the radiative corrections of order O(α/π) or the outer model-independent radiative corrections, where α is the fine-structure constant, and the corrections of order O(Ee/mN), caused by weak magnetism and proton recoil. We calculate also the contributions of interactions beyond the SM, including the contributions of the second class currents.