Gauge properties of hadronic structure of nucleon in neutron radiative beta decay to order O(α/π) in standard V − A effective theory with QED and linear sigma model of strong low-energy interactions

Abstract

Within the standard V − A theory of weak interactions, Quantum Electrodynamics (QED) and the linear σ-model (LσM) of strong low-energy hadronic interactions we analyse gauge properties of hadronic structure of the neutron and proton in the neutron radiative β − -decay. We show that the Feynman diagrams, describing contributions of hadronic structure to the amplitude of the neutron radiative β − -decay in the tree-approximation for strong low-energy interactions in the LσM, are gauge invariant. In turn, the complete set of Feynman diagrams, describing the contributions of hadron-photon interactions in the one-hadron-loop approximation, is not gauge invariant. In the infinite limit of the scalar σ-meson, reproducing the current algebra results (Weinberg, Phys. Rev. Lett. 18, 188 (1967)), and to leading order in the large nucleon mass expansion the Feynman diagrams, violating gauge invariance, do not contribute to the amplitude of the neutron radiative β − -decay in agreement with Sirlin's analysis of strong low-energy interactions in neutron β − decays. We assert that the problem of appearance of gauge non-invariant Feynman diagrams of hadronic structure of the neutron and proton is related to the following. The vertex of the effective V − A weak interactions does not belong to the combined quantum field theory including the LσM and QED. We argue that gauge invariant set of Feynman diagrams of hadrons, coupled to real and virtual photons in neutron β − decays, can be obtained within the combined quantum field theory including the Standard Electroweak Model (SEM) and the LσM, where the effective V − A vertex of weak interactions is a result of the W − -electroweak boson exchange.

Neutron dark matter decays and correlation coefficients of neutron β−-decays

“…This agrees well with Weinberg's assertion about important role of strong low-energy interactions in decay processes [74]. A procedure for the calculation of these radiative corrections to the neutron β − -decays with a consistent account for contributions of strong low-energy interactions, leading to gauge invariant observable expressions dependent on the electron energy E e determined at the confidence level of Sirlin's radiative corrections [56], has been proposed in [72,73].…”

“…Our analysis of the rate of the neutron decay modes n → p + anything, measured in beam experiments, and the correlation coefficients of the neutron β − -decay, taking into account the complete set of corrections of order 10 −3 , caused by the weak magnetism and proton recoil of order O(E e /M ) and radiative corrections of order O(α/π), and the tensor coupling constants C T = −C T = 1.11 × 10 −2 and the Fierz interference term b = −1.44 × 10 −2 , does diminish an important role of the SM corrections of order 10 −5 , which has been pointed out in [52,55,72,73]. As has been shown in [55] the SM corrections of order 10 −5 concern i) Wilkinson's corrections [54], i.e.…”

“…As has been shown in [55] the SM corrections of order 10 −5 concern i) Wilkinson's corrections [54], i.e. the higher order corrections caused by 1) the proton recoil in the Coulomb electron-proton final-state interaction, 2) the finite proton radius, 3) the proton-lepton convolution and 4) the higher-order outer radiative corrections, and then ii) the higher order corrections defined by 1) the radiative corrections of order O(α 2 /π 2 ), calculated to leading order in the large nucleon mass expansion, 2) the radiative corrections of order O(αE e /M ), calculated to next-to-leading order in the large nucleon mass expansion, which depend strongly on contributions of hadronic structure of the nucleon [72,73], and 3) the corrections of the weak magnetism and proton recoil of order O(E 2 e /M 2 ), calculated to next-to-nextto-leading order in the large nucleon mass expansion [52,72]. These theoretical corrections should provide for the analysis of experimental data of "discovery" experiments the required 5σ level of experimental uncertainties of a few parts in 10 −5 [55].…”

Precision analysis of pseudoscalar interactions in neutron beta decays

“…As a result, taking into account the constraints on the scalar interaction [37] and [31] the contributions of interactions beyond the SM to the neutron β − -decay can be induced only by a tensor nucleon current [43,44]. This paper is addressed to the analysis of contributions of the one-pion-pole exchanges, caused by strong lowenergy interactions [14,35,38], and pseudoscalar interaction beyond the SM introduced in [19]- [24] to the neutron lifetime and correlation coefficients of the neutron β − -decays with different polarizations of massive fermions. For the first time, the contribution of the pseudoscalar interaction beyond the SM to the electron-energy spectrum of the neutron β − -decay with unpolarized neutron, electron and proton has been taken into account by González-Alonzo and Camalich [45].…”

Gauge and infrared properties of hadronic structure of nucleon in neutron beta decay to order O(α/π) in standard V − A effective theory with QED and linear sigma model of strong low-energy interactions

“…The infrared divergent contribution of hadronic structure of the nucleon, observed in [2], arises the problem of its necessary cancellation by the infrared divergent contribution of virtual photon exchanges to the rate of the neutron β − -decay. Following [1] we may have doubts that such a cancellation can be observed in the standard V − A effective theory of weak interactions with QED and the LσM. This is because the vertex of the effective V − A hadron-lepton current-current interaction is not a vertex of the combined quantum field theory including QED and the LσM.…”