Tests of the standard model in neutron $\beta$ decay with a polarized neutron and electron and an unpolarized proton

We analyze the electron-energy and angular distribution of neutron ${\beta }^{-}$ decay with a polarized neutron and electron and an unpolarized proton, calculated by Ivanov et al. [Phys. Rev. C 95, 055502 (2017)] within the standard model (SM), by taking into account the contributions of interactions beyond the SM. After the absorption of vector and axial-vector contributions by the axial coupling constant and Cabibbo-Kobayashi-Maskawa (CKM) matrix element [Bhattacharya et al., Phys. Rev. D 85, 054512 (2012) and so on] these are the contributions of scalar and tensor interactions only. The neutron lifetime, correlation coefficients and their averaged values, and asymmetries of neutron ${\beta }^{-}$ decay with a polarized neutron and electron are adapted to the analysis of experimental data in search of contributions of interactions beyond the SM. Using the obtained results we propose some estimates of the values of the scalar and tensor coupling constants of interactions beyond the SM. We use the estimate of the Fierz interference term $b=-0.0028\pm 0.0026$ by Hardy and Towner [Phys. Rev. C 91, 025501 (2015)], the neutron lifetime ${\tau }_n=880.2\left(1.0\right)\mathrm{s}$ [Particle Data Group, Chin. Phys. C 40, 100001 (2016)] and the experimental data $N_{exp}=0.067\pm 0.{011}_{\mathrm{stat}.}\pm 0.{004}_{\mathrm{syst}.}$ for the averaged value of the correlation coefficient of the neutron-electron spin-spin correlations, measured by Kozela et al. [Phys. Rev. C 85, 045501 (2012)]. The contributions of $G$-odd correlations are calculated and found at the level of ${10}^{-5}$ in agreement with the results obtained by Gardner and Plaster [Phys. Rev. C 87, 065504 (2013)].

Figure 1

The theoretical electron asymmetry, calculated in the SM (blue dotted curve) and with interactions beyond the SM (red dotted curve) for $b_F=-0.0002$ and (green dotted curve) for $b_F=-0.0004$.