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.

We give a precision analysis of the correlation coefficients of the electron-energy spectrum and angular distribution of the β − -decay and radiative β − -decay of the neutron with polarized neutron and electron to order 10 −3 . The calculation of correlation coefficients is carried out within the Standard model with contributions of order 10 −3 , caused by the weak magnetism and proton recoil, taken to next-to-leading order in the large proton mass expansion, and with radiative corrections of order α/π ∼ 10 −3 , calculated to leading order in the large proton mass expansion. The obtained results can be used for the planning of experiments on the search for contributions of order 10 −4 of interactions beyond the Standard model.

We study kaonic hydrogen, the bound K − p state A Kp . Within a quantum field theoretic and relativistic covariant approach we derive the energy level displacement of the ground state of kaonic hydrogen in terms of the amplitude of K − p scattering for arbitrary relative momenta. The amplitude of low-energy K − p scattering near threshold is defined by the contributions of three resonances Λ(1405), Λ(1800) and Σ 0 (1750) and a smooth elastic background. The amplitudes of inelastic channels of low-energy K − p scattering fit experimental data on near threshold behaviour of the cross sections and the experimental data by the DEAR Collaboration. We use the soft-pion technique (leading order in Chiral Perturbation Theory) for the calculation of the partial width of the radiative decay of pionic hydrogen A πp → n+γ and the Panofsky ratio. The theoretical prediction for the Panofsky ratio agrees well with experimental data. We apply the soft-kaon technique (leading order in Chiral Perturbation Theory) to the calculation of the partial widths of radiative decays of kaonic hydrogen A Kp → Λ 0 +γ and A Kp → Σ 0 +γ. We show that the contribution of these decays to the width of the energy level of the ground state of kaonic hydrogen is less than 1%.

The chiral perturbation theory is developed at the quark level within the extended Nambu-Jona-Lasinio model, which we used for the low-energy approximation of QCD in the leading order of the large N expansion. In terms of constituent-quark loop diagrams we analyze all of the main low-energy effects caused by the first order corrections in the current-quark-mass expansions. For the correct description of the η→3π decays we confirm the important role of the final-state interaction quoted by Gasser and Leutwyler.

We calculate the correlation coefficients of the electron-energy and electron-antineutrino angular distribution of the neutron β −-decay with polarized electron and unpolarised neutron and proton. The calculation is carried out within the standard model (SM) with the contributions, caused by the weak magnetism, proton recoil and radiative corrections of order of 10 −3 , Wilkinson's corrections of order 10 −5 [Wilkinson, Nucl. Phys. A377, 474 (1982) and Ivanov et al., Phys. Rev. C 95, 055502 (2017)] and the contributions of interactions beyond the SM. The obtained results can be used for the analysis of experimental data on searches of interactions beyond the SM at the level of 10 −4 [Abele, Hyperfine Interact. 237, 155 (2016)]. 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 [

We calculate the correlation coefficients of the electron-energy and electron-antineutrino angular distribution of the neutron β − -decay with polarized electron and unpolarised neutron and proton. The calculation is carried out within the Standard Model (SM) with the contributions, caused by the weak magnetism, proton recoil and radiative corrections of order of 10 −3 , Wilkinson's corrections of order 10 −5 (Wilkinson, Nucl. Phys. A 377, 474 (1982) and Ivanov et al., Phys. Rev. C 95, 055502 (2017)) and the contributions of interactions beyond the SM. The obtained results can be used for the analysis of experimental data on searches of interactions beyond the SM at the level of 10 −4 (Abele, Hyperfine Interact. 237, 155 (2016)). 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)) and Ivanov et al. (Phys. Rev. C 98, 035503 (2018)). PACS: 12.15.Ff, 13.15.+g, 23.40.Bw, 26.65.+t PACS numbers: I. INTRODUCTIONIn Refs.[1-3] we have calculated the neutron lifetime and correlation coefficients of the electron-energy and angular distributions of the neutron β − -decay with polarized neutron and unpolarized electron and proton, and polarized neutron and electron and unpolarized proton, respectively. The neutron lifetime and correlation coefficients are calculated at the level of 10 −3 of contributions of the weak magnetism and proton recoil of order O(E e /M ), where E e is the electron energy and M is an averaged nucleon mass, and radiative corrections of order O(α/π), where α is the fine-structure constant [4]. The radiative corrections of order O(α/π) to the neutron lifetime and correlation coefficients of the neutron β − -decay with polarized neutron and unpolarized electron and proton have been calculated by Sirlin [5] and Shann [6] (for details of these calculations we relegate a reader to [7] and [1]). In turn, the radiative corrections of order O(α/π) to the correlation coefficients of the neutron β − -decay with polarized neutron and electron, and unpolarized proton have been calculated in [2]. Then, in [1] and [3] we have taken into account the contributions of interactions beyond the Standard Model (SM) to the neutron β − -decay with polarized neutron and unpolarized electron and proton, and polarized neutron and electron, and unpolarized proton, respectively. This paper is addressed to the calculation of the correlation coefficients of the electron-energy and electronantineutrino angular distribution of the neutron β − -decay with polarized electron and unpolarized neutron and proton. We calculate a complete set of corrections of order 10 −3 defined by the corrections of order O(E e /M ), caused by the weak magnetism and proton recoil and calculated to next-to-leading order in the large nucleon mass expansion, and radiative corrections of order O(α/π), calculated to leading order in the large nucleon mass expansion. We discuss also Wilkinson's corrections of order 10 −5 [8], which ...

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We suggest an effective quark model for low-lying baryon octet and decuplet motivated by QCD with a linearly rising confinement potential incorporating the extended Nambu-Jona-Lasinio (ENJL) model with linear realization of chiral U (3) × U (3) symmetry. Baryons are considered as external heavy states coupled to local three-quark currents with fixed spinorial structure and to low-lying mesons through quark-meson interactions defined in the ENJL-model. In the constituent quark loop representation we have calculated the coupling constants of the πNN, πN∆ and γN∆ interactions and the σ πN -term. The obtained results are in reasonable agreement with experimental data and other effective field theory approaches.