Theoretical description of the neutron beta decay in the standard model at the level of 10^{-5}

Abstract

In the framework of the Standard Model (SM) a theoretical description of the neutron beta decay is given 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 of order O(αEe/mN ) ∼ 10 −5 to Sirlin's outer and inner radiative corrections of order O(α/π), ii) the corrections of order O(E 2 e /m 2 N ) ∼ 10 −5 , caused by weak magnetism and proton recoil, where α, Ee and mN are the fine-structure constant, the electron energy and the nucleon mass, respectively, and iii) Wilkinson's corrections of order 10 −5 (Wilkinson, Nucl. Phys. A 377, 474 (1982)). These corrections define the SM background of the theoretical description of the neutron beta decay at the level of 10 −5 , which is required by experimental searches of interactions beyond the SM with experimental uncertainties of a few parts of 10 −5 .

Radiative corrections of order O(αEe/mN) to Sirlin’s radiative corrections of order O<

“…As has been shown in [81], the inner O(αE e /m N ) RC Eq. ( 7) provide the SM theoretical description of the neutron beta decay at the level of 10 −5 −10 −4 together with i) the O(αE e /m N ) RC, calculated in [10], ii) the O(E 2 e /m 2 N ) ∼ 10 −5 corrections, caused by weak magnetism and proton recoil [82], and iii) Wilkinson's corrections [72] (see also [8,83,84]).…”

“…( 7) provide the SM theoretical description of the neutron beta decay at the level of 10 −5 −10 −4 together with i) the O(αE e /m N ) RC, calculated in [10], ii) the O(E 2 e /m 2 N ) ∼ 10 −5 corrections, caused by weak magnetism and proton recoil [82], and iii) Wilkinson's corrections [72] (see also [8,83,84]). The theoretical accuracy of these corrections is of a few parts of 10 −6 [81]. Such a SM theoretical background of the neutron beta decay should be very important for experimental searches of interactions beyond the SM [85][86][87] with experimental uncertainties of a few part of 10 −5 and even better.…”

Radiative corrections to neutron and nuclear β-decays: a serious kinematics problem in the literature

“…We would like to emphasize that, in spite of our serious critics about the handling of the bremsstrahlung integrations, we appreciate very much the authors of the neutrinotype radiative correction publications [18][19][20][21][22][23][56][57][58][59][60][61][62][63], because these papers contain a lot of precious and useful scientific merits; e.g. we have made many comparisons of our results with these publications, and in most cases we have found good agreement.…”

“…[46][47][48][49][50][51][52][53][54][55]) have been using the correct recoil-type integration methods (this list of radiative correction publications is far from complete). Unfortunately, the situation is different in the case of neutron decay: in the past two decades, most of the radiative correction calculation publications [56][57][58][59][60][61][62][63] used the incorrect neutrino-type integration method. One has to emphasize here that these radiative correction results are inappropriate only for those neutron decay experiments where the proton is detected (like measurements of the electron-neutrino correlation or neutrino asymmetry parameter).…”

“…We mention that in the case of the neutrino-type radiative correction calculations [18][19][20][21][22][23][56][57][58][59][60][61][62][63] one uses 3-body kinematics to get the connection between the neutrino and recoil particle parameters, and therefore one cannot find there any information about the region OUT of the Dalitz plot, which is present only with 4-body bremsstrahlung photon kinematics. Of course, the largest change of the 4-body kinematics relative to the 3-body kinematics on the region IN is the presence of the green trapezoid region of figure 3a.…”