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Register a new userA new angle on an old problem: Helicity approach to neutron beta decay in the Standard Model
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We elaborate on the dichotomy between the description of the semileptonic decays of heavy hadrons on the one hand and the semileptonic decays of light hadrons such as neutron $beta$ decays on the other hand. For example, almost without exception the semileptonic decays of heavy baryons are described in cascade fashion as a sequence of two two-body decays $B_1 to B_2 + W_{rm off-shell}$ and $W_{rm off-shell} to ell + u_ell$ whereas neutron $beta$ decays are analyzed as true three-body decays $n to p + e^- +bar u_e$. Within the cascade approach it is possible to define a set of seven angular observables for polarized neutron $beta$ decays as well as the longitudinal, transverse and normal polarization of the decay electron. We determine the dependence of the observables on the usual vector and axial vector form factors. In order to be able to assess the importance of recoil corrections we expand the rate and the $q^2$ averages of the observables up to NLO and NNLO in the recoil parameter $delta=(M_n-M_p)/(M_n+M_p)= 0.689cdot 10^{-3}$. Remarkably, we find that the rate and three of the four parity conserving polarization observables that we analyze are protected from NLO recoil corrections when the second class current contributions are set to zero.
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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(alpha E_e/m_N) ~ 10^{-5} to Sirlins outer and inner radiative corrections of order O(alpha/pi), ii) the corrections of order O(E^2_e/m^2_N) ~ 10^{-5}, caused by weak magnetism and proton recoil, and iii) Wilkinsons corrections of order 10^{-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^{-5}, which is required by experimental searches of interactions beyond the SM with experimental uncertainties of a few parts of 10^{-5}.
Coherent forward neutron propagation in gas is discussed as a new approach to search for neutron-antineutron oscillations ($ n-bar{n}$), which violate both $B$ and $B-L$ conservation. We show that one can increase the probability of neutron - antineutron transitions to essentially the free neutron oscillation rate in the presence of a nonzero external magnetic field by tuning the density of an appropriate mixture of gases so that the neutron optical potential of the gas cancels that from an external magnetic field.
The interference of charge-changing interactions, weaker than the V-A Standard Model (SM) interaction and having a different Lorentz structure, with that SM interaction, can, in principle, produce effects near the end point of the Tritium beta decay spectrum which are of a different character from those produced by the purely kinematic effect of neutrino mass expected in the simplest extension of the SM. We show that the existence of more than one mass eigenstate can lead to interference effects at the end point that are stronger than those occurring over the entire spectrum. We discuss these effects both for the special case of Dirac neutrinos and the more general case of Majorana neutrinos and show that, for the present precision of the experiments, one formula should suffice to express the interference effects in all cases. Implications for sterile neutrinos are noted.
We calculate the correlation coefficients of the electron-energy and electron-antineutrino angular distribution of the neutron beta 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}, Wilkinsons corrections of order 10^{-5}$(Wilkinson, Nucl. Phys. A377, 474 (1982) and Ivanov et al., Phys. Rev. C95, 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. C87, 065504 (2013)) and Ivanov et al. (Phys. Rev. C98, 035503 (2018)).
We point out that in theories where the gravitino mass, $M_{3/2}$, is in the range (10-50)TeV, with soft-breaking scalar masses and trilinear couplings of the same order, there exists a robust region of parameter space where the conditions for electroweak symmetry breaking (EWSB) are satisfied without large imposed cancellations. Compactified string/M-theory with stabilized moduli that satisfy cosmological constraints generically require a gravitino mass greater than about 30 TeV and provide the natural explanation for this phenomenon. We find that even though scalar masses and trilinear couplings (and the soft-breaking $B$ parameter) are of order (10-50)TeV, the Higgs vev takes its expected value and the $mu$ parameter is naturally of order a TeV. The mechanism provides a natural solution to the cosmological moduli and gravitino problems with EWSB.
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