On the structure of the correlation coefficients S(E_e) and U(E_e) of the neutron beta decay

Abstract

In the standard effective V −A theory of low-energy weak interactions (i.e. in the Standard Model (SM)) we analyze the structure of the correlation coefficients S(Ee) and U (Ee), where Ee is the electron energy. These correlation coefficients were introduced to the electron-energy and angular distribution of the neutron beta decay by Ebel and Feldman ( Nucl. Phys. 4, 213 (1957)) in addition to the set of correlation coefficients proposed by Jackson et al. (Phys. Rev. 106, 517 (1957)). The correlation coefficients S(Ee) and U (Ee) are induced by simultaneous correlations of the neutron and electron spins and electron and antineutrino 3-momenta. These correlation structures do no violate discrete P, C and T symmetries. We calculate the contributions of the radiative corrections of order O(α/π), taken to leading order in the large nucleon mass mN expansion, and corrections of order O(Ee/mN ), caused by weak magnetism and proton recoil. In addition to the obtained SM contributions we calculate the contributions of interactions beyond the SM (BSM contributions) in terms of the phenomenological coupling constants of BSM interactions by Jackson et al. (Phys. Rev. 106, 517 (1957)) and the second class currents by Weinberg (Phys. Rev.112, 1375).

Theoretical description of the neutron beta decay in the standard model at the level of 10^{-5}

“…We have given a SM theoretical description of the neutron beta decay for a polarized neutron, a polarized electron and an unpolarized proton at the level of 10 −5 with a theoretical accuracy of a few parts of 10 −6 . To the well-known radiative corrections of order O(α/π) [18][19][20][21][22] (see also [10,11,13,28,29]) and corrections of order O(E e /m N ) [45] and [14,21,22] (see also [10,11,13,28,29]) we have added i) the radiative corrections of order O(αE e /m N ) ∼ 10 −5 [15,16], which are treated as next-to-leading order corrections in the large nucleon mass m N expansion to Sirlin's outer and inner radiative corrections of order O(α/π), calculated to leading order in the large nucleon mass m N , expansion, ii) the corrections of order O(E 2 e /m 2 N ) ∼ 10 −5 [23], caused by weak magnetism and proton recoil, and iii) Wilkinson's corrections [14] (see also [10,11,13]) of order 10 −5 . All of these corrections define the SM background of the theoretical description of the neutron beta decay at the level of 10 −5 .…”

“…According to [10,28,29], the electron-energy and angular distribution of the neutron beta decay for a polarized neutron, a polarized electron and an unpolarized proton in Eq. ( 1) is determined by…”

“…Taking into account the contribution of the neutron radiative beta decay [10,11,13,28,29] we transcribe the correlation function ζ(E e ) RC and the correlation coefficients ζ(E e ) RC X(E e ) RC for X = b, a, A, B, . .…”

“…where we have used the notations in Refs. [10] - [23,28,29]. Then, g A and G V are the axial and vector coupling constants, respectively, [1,2,5,6,9], the Cabibbo-Kobayashi-Maskawa (CKM) matrix element V ud is included in the defintion of the vector coupling constant G V , ξ n and ξ e are unit spin-polarization vectors of the neutron and electron [10,11,13] (see also [30]), respectively, dΩ e and dΩ ν are infinitesimal solid angles in the directions of electron k e and antineutrino k ν 3-momenta, respectively, E 0 = (m 2 n − m 2 p + m 2 e )/2m n = 1.2926 MeV is the end-point energy of the electron-energy spectrum [1,2], F (E e , Z = 1) is the relativistic Fermi function, describing the electron-proton final-state Coulomb interaction, is equal to [31](see also [14] and a discussion in [11])…”

“…We would like to notice that recently [28,29] the correlation coefficients T (E e ), S(E e ) and U (E e ) have been investigated theoretically within the SM at the level of 10 −3 by taking into account i) the outer model-independent radiative corrections of order O(α/π), calculated to leading order in the large nucleon mass m N expansion, ii) the corrections of order O(E e /m N ), caused by weak magnetism and proton recoil, and iii) the corrections, caused by interactions beyond the SM [24], including the contributions of the second class currents or the G-odd correlations (as for G-parity invariance of strong interactions, we refer to the paper by Lee and Yang [41]) by Weinberg [42] (see also [43,44] and [11][12][13]).…”