Neutronβ−decay as a laboratory for testing the standard model

Abstract

We analyse the sensitivity of all experimentally observable asymmetries and energy distributions for the neutron β − -decay with a polarized neutron and unpolarised decay proton and electron and the lifetime of the neutron to contributions of order 10 −4 of interactions beyond the Standard model (SM). Since the asymmetries and energy distributions are expressed in terms of the correlation coefficients of the neutron β − -decay, in order to obtain a theoretical background for the analysis of contributions beyond the SM we revise the calculation of the correlation coefficients within the SM. We take into account a complete set of contributions, induced to next-to-leading order in the large proton mass expansion by the "weak magnetism" and the proton recoil, and the radiative corrections of order (α/π), calculated to leading order in the large proton mass expansion. We confirm the results, obtained in literature. The contributions of interactions beyond the SM we analyse in the linear approximation with respect to the Herczeg phenomenological coupling constants, introduced at the hadronic level. Such an approximation is good enough for the analysis of contributions of order 10 −4 of interactions beyond the SM. We show that in such an approximation the correlation coefficients depend only on the axial coupling constant, which absorbs the contributions of the Herczeg left-left and left-right lepton-nucleon current-current interactions (vector and axial-vector interactions beyond the SM), and the Herczeg scalar and tensor coupling constants. In the lifetime of the neutron in addition to the axial coupling constant the contributions of the Herczeg left-left and left-right lepton-nucleon current-current interactions (vector and axial-vector interactions beyond the SM) are absorbed by the Cabibbo-Kobayashi-Maskawa (CKM) matrix element.

Precision experiments with cold and ultra-cold neutrons

“…The authors showed that the account for the contributions of the proton photon correlations in the radiative corrections to the neutron beta decay does not contradict the description of the radiative corrections to the lifetime of the neutron and the proton recoil spectrum in terms of the standard radiative corrections but makes the proton recoil asymmetry C symmetric with respect to change of correlation coefficients A -B. They showed that the Standard Model describes well the lifetime of the neutron τ = 880.1(1.1)s with the theoretical value τ = 879.6(1.1)s, for the axial coupling constant ratio λ = −1.2750(9) and CKM matrix elements V ud obtained from the 0 + → 0 + transitions and the unitarity condition, respectively [30].…”

“…This was done in [30] within the standard quantum field theory at the rest frame of the neutron and in the non-relativistic approximation for the proton by taking into account the radiative corrections to order alpha, the proton recoil correction and the weak magnetism to order 1/M, where M is the average mass [31]. The authors showed that the account for the contributions of the proton photon correlations in the radiative corrections to the neutron beta decay does not contradict the description of the radiative corrections to the lifetime of the neutron and the proton recoil spectrum in terms of the standard radiative corrections but makes the proton recoil asymmetry C symmetric with respect to change of correlation coefficients A -B.…”

Limits on tensor coupling from neutronβdecay

“…We note, however, that our limits are comparable to those obtained from fits to the entire beta decay set when similar assumptions are made (no right-handed neutrinos). This brief report was inspired by comments in Bhattacharya et al [3] and begun as a part of thesis research [4]; however, we note that additional details have subsequently been published by Ivanov, Pitschmann, and Troitskaya [5].…”

Cold and Ultra-cold Neutrons as Probes of New Physics

“…Not least, new physics searches with 10 −4 sensitivity need adequate input from theory: the existing analysis of correlation coefficients a, A, B, C, and D [134] must be extended to order 10 −5 , and completed with non-standard correlation coefficients G, N, Q, R [135], and L to order 10 −3 .…”