Abstract
We analyse the electron--energy and angular distribution of the neutron beta decay with polarized neutron and electron and unpolarized proton, calculated in 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 the neutron beta decay with polarized neutron and electron are adapted to the analysis of experimental data on searches 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_F = - 0.0028 +/- 0.0026" by Hardy and Towner (Phys. Rev. C 91, 025501 (2015)), the neutron lifetime "tau_n = 880.2(1.0)s"(Particle Data Group, Chin. Phys. C 40, 100001 (2016)) and the experimental data "N_{\exp} = 0.067 +/- 0.011_{\rm stat.} +/- 0.004_{\rm syst.}" for the averaged value of the correlation coefficient of the neutron-electron spin-spin correlations, measured by Kozela et al. (Phys. Ref. 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)).
Highlights
[1] we calculated in the standard model (SM) the electron-energy and angular distribution of neutron β− decay with a polarized neutron and electron and an unpolarized proton by taking into account the contributions of the weak magnetism and proton recoil of order O(Ee/M ), where M is an averaged nucleon mass and energy density ρe (Ee) is the electron energy, and the radiative corrections of order O(α/π ), where α is the finestructure constant [2]
For the analysis of experimental data in search of contributions of interactions beyond the SM at the level of 10−4 and even better [5], we argue that there is an important role of the theoretical background with SM corrections of order 10−5, including Wilkinson’s corrections [1] and corrections caused by the weak magnetism and proton recoil of order O(Ee2/M2), radiative corrections of order O(αEe/M ), and radiative corrections of order O(α2/π 2) [7,8]
For the analysis of experimental data in search of interactions beyond the SM in neutron β− decay with a polarized neutron and electron, we propose to use a complete set of contributions of scalar and tensor interactions beyond the SM including linear, crossing, and quadratic terms, which are given in Eq (15)
Summary
[1] we calculated in the standard model (SM) the electron-energy and angular distribution of neutron β− decay with a polarized neutron and electron and an unpolarized proton by taking into account the contributions of the weak magnetism and proton recoil of order O(Ee/M ), where M is an averaged nucleon mass and Ee is the electron energy, and the radiative corrections of order O(α/π ), where α is the finestructure constant [2]. V we calculation the G-odd corrections to the neutron lifetime and correlation coefficients of neutron β− decay with a polarized neutron and electron and an unpolarized proton We estimate these corrections to be at the level of 10−5 and even smaller, in agreement with the results obtained by Gardner and Plaster [23]. For the analysis of experimental data in search of contributions of interactions beyond the SM at the level of 10−4 and even better [5], we argue that there is an important role of the theoretical background with SM corrections of order 10−5, including Wilkinson’s corrections [1] and corrections caused by the weak magnetism and proton recoil of order O(Ee2/M2), radiative corrections of order O(αEe/M ), and radiative corrections of order O(α2/π 2) [7,8]
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