On the correlation coefficient T(E) 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 ( E e ) , which was introduced by Ebel and Feldman (1957) [64] . The correlation coefficient T ( E e ) is induced by the correlation structure ( ξ → n ⋅ k → ν ¯ ) ( k → e ⋅ ξ → e ) / E e E ν ¯ , where ξ → n , e are unit spin-polarization vectors of the neutron and electron, and ( E e , 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 ( E e ) , calculated to leading order in the large nucleon mass m N expansion, is equal to T ( E e ) = − 2 g A ( 1 + g A ) / ( 1 + 3 g A 2 ) = − B 0 , i.e. of order | T ( E e ) | ∼ 1 , where g A is the axial coupling constant. Within the Standard Model (SM) we describe the correlation coefficient T ( E e ) 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 ( E e / m N ) , 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.