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

We show that in the electron-energy and angular distribution of the neutron beta decay for a polarized neutron, a polarized electron and an unpolarized proton a new correlation coefficient appears in addition to the set of correlation coefficients introduced by Jackson et al., Phys. Rev. 106, 517 (1957). This correlation coefficient, which we denote as $Q_{\nu}(E_e)$, is induced by the correlation structure $(\vec{\xi}_n\cdot \vec{k}_{\bar{\nu}})(\vec{k}_e\cdot \vec{\xi}_e)/E_e E_{\bar{\nu}}$, where $\vec{\xi}_{n,e}$ are unit spin-polarization vectors of the neutron and electron, and $(E_{e,\bar\nu}, \vec{k}_{e,\bar\nu})$ 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 $Q_{\nu}(E_e)$, calculated to leading order in the large nucleon mass $m_N$ expansion, is equal to $Q_{\nu}(E_e) = - 2 g_A(1 + g_A)/(1 + 3 g^2_A) = - B_0$, i.e. of order $|Q_{\nu}(E_e)| \sim 1$, where $g_A$ is the axial coupling constant. Within the Standard Model (SM) we describe the correlation coefficient $Q_{\nu}(E_e)$ at the level of $10^{-3}$ by taking into the radiative corrections of order $O(\alpha/\pi)$ or the outer model-independent radiative corrections, where "alpha" 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.