On the correlation coefficient T(E_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 (Ee), which was introduced by Ebel and Feldman (Nucl. Phys. 4, 213 (1957)). The correlation coefficient T (Ee) is induced by the correlation structure ( ξn • kν )( ke • ξe)/EeEν, where ξn,e are unit spin-polarization vectors of the neutron and electron, and (Ee,ν , ke,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 + 3g 2 A ) = −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.

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

“…An independence of the radiative corrections to the correlation coefficients S(E e ) and U (E e ) of an infrared cut-off should mean that such correlation coefficients either do not get contributions from the neutron radiative beta decay or the contributions of the neutron radiative beta decay do not depend on an infrared cut-off. We would like to remind that, according to [37][38][39][40][41] (see also [12, 14-16, 18, 19] and [3]). for cancellation of a dependence of the contributions of one-virtual photon exchanges to the neutron lifetime and correlation coefficients one has to take into account the corresponding contributions of the neutron radiative beta decay.…”

“…This paper is addressed to the analysis of the structure of the correlation coefficients S(E e ) and U (E e ), introduced by Ebel and Feldman [2]. As has been shown in [3] these correlation coefficients do not survive to leading order in the large nucleon mass m N expansion in contrast to the correlation coefficient T (E e ).…”

“…The analysis of the distribution in Eq. ( 1) within the standard effective V − A theory of low-energy weak interactions [4][5][6][7] (i.e within the Standard Model (SM)), carried out to leading order in the large nucleon mass m N expansion [3], has shown that correlation coefficients a(E e ), A(E e ), B(E e ), G(E e ), H(E e ), N (E e ), Q e (E e ) and K e (E e ) of the electron-energy and angular distribution by Jackson et al [1] and the correlation coefficient T (E e ), introduced by Ebel and Feldman [2], survive and depend on the axial coupling constant g A only [8][9][10], which appears in the effective V − A theory of low-energy weak interactions by renormalization of the hadronic axial-vector current by strong lowenergy interactions [5,11]. The function ζ(E e ) defines the neutron lifetime.…”

“…[12][13][14][15] (see also [16]) the radiative corrections of order O(α/π) (or so-called outer model-independent radiative corrections [17]) were calculated to leading order in the large nucleon mass m N expansion to the neutron lifetime and correlation coefficients a(E e ), caused by electron-antineutron 3-momentum correlations, A(E e ) and B(E e ), defining the electron-and antineutrino asymmetries, respectively. In turn, the outer radiative corrections of order O(α/π) were calculated to leading order in the large nucleon mass m N expansion to the correlation coefficients G(E e ), H(E e ), N (E e ), Q e (E e ), and K e (E e ) in [18,19] and to the correlation coefficient T (E e ) in [3]. These correlation coefficients are induced by correlations of the electron spin with a neutron spin and 3-momenta of the electron and antineutrino.…”

“…These correlation coefficients are induced by correlations of the electron spin with a neutron spin and 3-momenta of the electron and antineutrino. The corrections of order O(E e /m N ), caused by weak magnetism and proton recoil, were calculated i) to the neutron lifetime and correlation coefficients a(E e ), A(E e ) and B(E e ) in [20,21] (see also [15,16]), ii) to the correlation coefficients G(E e ), H(E e ), N (E e ), Q e (E e ) and K e (E e ) in [18,19] and iii) to the correlation coefficient T (E e ) in [3]. The correlation coefficients D(E e ), R(E e ) and L(E e ), characterizing the strength of violation of time reversal invariance (T-odd effect) [22], are induced by the distortion of the Dirac wave function of the decay electron in the Coulomb field of the decay proton [23][24][25][26] (see also [19]).…”