Precision analysis of electron energy spectrum and angular distribution of neutron ${\beta }^{-}$ decay with polarized neutron and electron

We give a precision analysis of the correlation coefficients of the electron energy spectrum and angular distribution of the ${\beta }^{-}$ decay and radiative ${\beta }^{-}$ decay of the neutron with polarized neutron and electron to order ${10}^{-3}$. The calculation of correlation coefficients is carried out within the standard model, with contributions of order ${10}^{-3}$ caused by the weak magnetism and proton recoil taken to next-to-leading order in the large proton mass expansion, and with radiative corrections of order $\alpha /\pi \sim {10}^{-3}$ calculated to leading order in the large proton mass expansion. The obtained results can be used for the planning of experiments on the search for contributions of order ${10}^{-4}$ of interactions beyond the standard model.

Figure 1

Radiative corrections $(\alpha /\pi )f_n\left(E_e\right), (\alpha /\pi )h_n^{\left(1\right)}\left(E_e\right)$, and $(\alpha /\pi )h_n^{\left(2\right)}\left(E_e\right)$ to the correlation coefficients $G\left(E_e\right), N\left(E_e\right)$, and $Q_e\left(E_e\right)$ of the electron energy spectrum and angular distribution, Eq. (3).

Figure 2

Relative corrections to the correlation coefficients $G\left(E_e\right), N\left(E_e\right)$, and $Q_e\left(E_e\right)$ induced by the proton recoil on the Fermi function, caused by the Coulomb electron-proton final-state interaction and calculated for the experimentally observable electron energy region $0.761\le E_e\le 0.966\mathrm{MeV}$ [7].