Theoretical description of the neutron beta decay in the standard model at the level of 10−5

A N Ivanov,Ya A Berdnikov,R Höllwieser,M Wellenzohn,N I Troitskaya

doi:10.1103/physrevd.104.033006

Abstract

In the framework of the Standard Model (SM) a theoretical description of the neutron beta decay is given at the level of ${10}^{\ensuremath{-}5}$. The neutron lifetime and correlation coefficients of the neutron beta decay for a polarized neutron, a polarized electron, and an unpolarized proton are calculated at the account for (i) the radiative corrections (RC) of order $O(\ensuremath{\alpha}{E}_{e}/{m}_{N})\ensuremath{\sim}{10}^{\ensuremath{-}5}$, i.e., $O(\ensuremath{\alpha}{E}_{e}/{m}_{N})$ RC, to Sirlin's outer and inner $O(\ensuremath{\alpha}/\ensuremath{\pi})$ RC, where $\ensuremath{\alpha}$ and ${E}_{e}$ are the fine-structure constant and the electron energy, respectively; (ii) the outer $O(\ensuremath{\alpha}{E}_{e}/{m}_{N})$ RC, caused by Sirlin's outer $O(\ensuremath{\alpha}/\ensuremath{\pi})$ RC and the phase-volume of the neutron beta decay, calculated to next-to-leading order in the large nucleon mass ${m}_{N}$ expansion; (iii) the corrections of order $O({E}_{e}^{2}/{m}_{N}^{2})\ensuremath{\sim}{10}^{\ensuremath{-}5}$, caused by weak magnetism and proton recoil; and (iv) Wilkinson's corrections of order ${10}^{\ensuremath{-}5}$ [Wilkinson, Nucl. Phys. A377, 474 (1982)]. These corrections define the SM background of the theoretical description of the neutron beta decay at the level of ${10}^{\ensuremath{-}5}$, which is required by experimental searches of interactions beyond the SM with experimental uncertainties of a few parts of ${10}^{\ensuremath{-}5}$.

Highlights

A contemporary level of sensitivity of about 10−4 or even better for experimental investigations of the neutron beta decay [1,2,3] with a polarized neutron and unpolarized electron and proton [4,5,6,7] and with a polarized neutron, a polarized electron, and an unpolarized proton [8] demands the theoretical description of the neutron beta decay within the Standard Model (SM) [9,10] at the level of 10−5
The neutron lifetime and correlation coefficients of the neutron beta decay for a polarized neutron, a polarized electron, and an unpolarized proton are calculated at the account for (i) the radiative corrections (RC) of order OðαEe=mNÞ ∼ 10−5, i.e., OðαEe=mNÞ RC, to Sirlin’s outer and inner Oðα=πÞ RC, where α and Ee are the fine-structure constant and the electron energy, respectively; (ii) the outer OðαEe=mNÞ RC, caused by Sirlin’s outer Oðα=πÞ RC and the phase-volume of the neutron beta decay, calculated to next-to-leading order in the large nucleon mass mN expansion; (iii) the corrections of order OðE2e=m2NÞ ∼ 10−5, caused by weak magnetism and proton recoil; and (iv) Wilkinson’s corrections of order 10−5 [Wilkinson, Nucl
Y 1⁄4 ζ, X are (i) the sum of the outer Oðα=πÞ RC, calculated to leading order (LO) in the large nucleon mass mN expansion, and OðαEe=mNÞ ∼ 10−5 RC, which are treated as next-to-leading order (NLO) corrections in the large nucleon mass mN expansion to the outer and inner Oðα=πÞ RC and denoted as YRC−NLO; (ii) the outer OðαEe=mNÞ RC, caused by the outer Oðα=πÞ RC and the phase-volume of the neutron beta decay taken to NLO in the large nucleon mass expansion; (iii) the sum of the OðEe=mNÞ and OðE2e=m2NÞ ∼ 10−5 corrections, caused by weak magnetism and proton recoil; and (iv) Wilkinson’s corrections of order 10−5

Summary

INTRODUCTION

A contemporary level of sensitivity of about 10−4 or even better for experimental investigations of the neutron beta decay [1,2,3] with a polarized neutron and unpolarized electron and proton [4,5,6,7] and with a polarized neutron, a polarized electron, and an unpolarized proton [8] demands the theoretical description of the neutron beta decay within the Standard Model (SM) [9,10] at the level of 10−5. As has been shown in [11,12,13,14] Wilkinson’s corrections [15] provide the SM contributions to the neutron lifetime and correlation coefficients of the neutron beta decay of order 10−5. Structures in Eq (1) by Jackson et al [25,26,27] and Ebel and Feldman [28]

CORRELATION FUNCTIONS AND COEFFICIENTS OF THE ELECTRON-ENERGY

DISCUSSION

Wilkinson’s corrections to the neutron beta decay

Þð1 þ a1 þ a2