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We review the status of the Standard Model theory of neutron beta decay. Particular emphasis is put on the recent developments in the electroweak radiative corrections. Given that some existing approaches give slightly different results, we thoroughly review the origin of discrepancies, and provide our recommended value for the radiative correction to the neutron and nuclear decay rates. The use of dispersion relation, lattice Quantum Chromodynamics, and an effective field theory framework allows for high-precision theory calculations at the level of 10−4, turning neutron beta decay into a powerful tool to search for new physics, complementary to high-energy collider experiments. We offer an outlook to the future improvements.

We review some recent progress in the theory of electroweak radiative corrections in semileptonic decay processes. The resurrection of the so-called Sirlin’s representation based on current algebra relations permits a clear separation between the perturbatively-calculable and incalculable pieces in the O(GFα) radiative corrections. The latter are expressed as compact hadronic matrix elements that allow systematic non-perturbative analysis such as dispersion relation and lattice QCD. This brings substantial improvements to the precision of the electroweak radiative corrections in semileptonic decays of pion, kaon, free neutron and JP=0+ nuclei that are important theory inputs in precision tests of the Standard Model. Unresolved issues and future prospects are discussed.

We report a theoretical derivation of the Cabibbo–Kobayashi–Maskawa (CKM) matrix parameters and the accompanying mixing angles. These results are arrived at from the exceptional Jordan algebra applied to quark states, and from expressing flavor eigenstates (i.e., left chiral states) as a superposition of mass eigenstates (i.e., the right chiral states) weighted by the square root of mass. Flavor mixing for quarks is mediated by the square root mass eigenstates, and the mass ratios used are derived from earlier work from a left–right symmetric extension of the standard model. This permits a construction of the CKM matrix from first principles. There exist only four normed division algebras, and they can be listed as follows: the real numbers R, the complex numbers C, the quaternions H and the octonions O. The first three algebras are fairly well known; however, octonions as algebra are less studied. Recent research has pointed towards the importance of octonions in the study of high-energy physics. Clifford algebras and the standard model are being studied closely. The main advantage of this approach is that the spinor representations of the fundamental fermions can be constructed easily here as the left ideals of the algebra. Also, the action of various spin groups on these representations can also be studied easily. In this work, we build on some recent advances in the field and try to determine the CKM angles from an algebraic framework. We obtain the mixing angle values as θ12=11.093∘,θ13=0.172∘,θ23=4.054∘. In comparison, the corresponding experimentally measured values for these angles are 13.04∘±0.05∘,0.201∘±0.011∘,2.38∘±0.06∘. The agreement of theory with experiment is likely to improve when the running of quark masses is taken into account.

Precise measurements of nuclear beta decays provide a unique insight into the Standard Model due to their connection to the electroweak interaction. These decays help constrain the unitarity or non-unitarity of the Cabibbo–Kobayashi–Maskawa (CKM) quark mixing matrix, and can uniquely probe the existence of exotic scalar or tensor currents. Of these decays, superallowed mixed mirror transitions have been the least well-studied, in part due to the absence of data on their Fermi to Gamow-Teller mixing ratios (ρ). At the Nuclear Science Laboratory (NSL) at the University of Notre Dame, the Superallowed Transition Beta-Neutrino Decay Ion Coincidence Trap (St. Benedict) is being constructed to determine the ρ for various mirror decays via a measurement of the beta–neutrino angular correlation parameter (aβν) to a relative precision of 0.5%. In this work, we present an overview of the St. Benedict facility and the impact it will have on various Beyond the Standard Model studies, including an expanded sensitivity study of ρ for various mirror nuclei accessible to the facility. A feasibility evaluation is also presented that indicates the measurement goals for many mirror nuclei, which are currently attainable in a week of radioactive beam delivery at the NSL.

▪ Abstract  Experiments using slow neutrons address a growing range of scientific issues spanning nuclear physics, particle physics, astrophysics, and cosmology. The field of fundamental physics using neutrons has experienced a significant increase in activity over the last two decades. This review summarizes some of the recent developments in the field and outlines some of the prospects for future research.

Usual bi-maximal neutrino mixing faces an inherent problem in lowering the solar angle below tan 2 θ 12 = 0.50 when charged lepton correction is considered. This minimum θ 12 is achievable only if charged parity violation is absent. We start with a new model which incorporates a new idea of mixing developed recently, called bi-large mixing, similar to bi-maximal mixing except that the former chooses rather θ 13 as Cabibbo angle ( θ c ) than zero. The bi-large mixing may be visualized in the framework of bi-trimaximal mixing which is related to a discrete flavour symmetry group Δ ( 96 ) . Also the motivation comes from F-Theory inspired Grand unified theory. We apply this mixing in the neutrino sector followed by a charged lepton correction with the Cabibbo–Kobayashi–Maskawa type matrix, U eL . The model marks a prediction on θ 23 to lie within the first octant. The charged-parity violating phase appearing from charged lepton sector δ 12 l dictates the prediction of all the three mixing angles. A proper choice of δ 12 l , leads to the predictions of all the three mixing angles including θ 12 , to align precisely with the experimental best-fit. This close agreement thus hoists bi-large mixing as an important and promising mixing scheme, in contrast to bi-maximal or tri-bimaximal mixing as a first approximation.

We know that our Universe is composed of only ～4.5% “known” matter; therefore, our understanding is incomplete. This can be seen directly in the case of neutrino oscillations (without even considering potential other universes). Charm quarks have had considerable impact on our understanding of known matter, and quantum chromodynamics (QCD) is the only local quantum field theory to describe strong forces. It is possible to learn novel lessons concerning strong dynamics by measuring rates around the thresholds of [ Q ¯ Q ] states with Q = b, c. Furthermore, these states provide us with gateways towards new dynamics (ND), where we must transition from “accuracy” to “precision” eras. Finally, we can make connections with τ transitions and, perhaps, with dark matter. Charm dynamics acts as a bridge between the worlds of light- and heavy-flavor hadrons (namely, beauty hadrons), and finding regional asymmetries in many-body final states may prove to be a “game changer”. There are several different approaches to achieving these goals: for example, experiments such as the Super Tau-Charm Factory, Super Beauty Factory, and the Super Z 0 Factory act as gatekeepers – and deeper thinking regarding symmetries.