The Weak Interactions

We present the phenomenology of the weak interactions in a historical perspective, from Fermi’s four-fermion theory to the V−A current×current interaction. The experiments of C.S. Wu, which established parity violation, and M. Goldhaber, which measured the neutrino helicity, are described. We study in turn the leptonic, semi-leptonic and non-leptonic weak interactions. We introduce the concept of the conserved vector current and the partially conserved axial current and show that the latter is the result of spontaneously broken chiral symmetry with the pion the corresponding pseudo-Goldstone boson. We study Gell–Mann’s current algebra and derive the Adler–Weisberger relation. Strangeness changing weak interactions and the Cabibbo theory are described. We present a phenomenological analysis of CP-violation in the neutral kaon system and we end with the intermediate vector boson hypothesis.

Probing effective field theory approach in the CP violating minimal linear $$\sigma $$ model

The Minimal Linear $$\sigma $$ σ Model is a useful theoretical laboratory. One can investigate in a perturbative renormalisable model the properties of the Higgs boson as a pseudo-Goldstone boson, the phenomenological effects of the radial mode of the field $$\texttt {s}$$ s which spontaneously breaks the global SO(5) symmetry and the validity of conclusions based on the Effective Field Theory approach with the field $$\texttt {s}$$ s in the spectrum, after the decoupling of heavy degrees of freedom. In this paper all those issues are discussed in the framework of the Minimal Linear $$\sigma $$ σ Model with CP violating phases leading to pseudoscalar components in the effective Standard Model Yukawa couplings. Also the character of the electroweak phase transition in the presence of the field $$\texttt {s}$$ s is investigated.

Fermion mass splitting in the technicolor coupled scenario

We discuss fermion mass generation in unified models where QCD and technicolor (or any two strongly interacting theories) have their Schwinger–Dyson equations coupled. In this case the technicolor (TC) and QCD self-energies are modified in comparison with the behavior observed in the isolated theories. In these models the pseudo-Goldstone boson masses are much higher than the ones obtained in different contexts, and phenomenological signals, except from a light scalar composite boson, will be quite difficult to be observed at present collider energies. The most noticeable fact of these models is how the mass splitting between the different ordinary fermions is generated. We discuss how a necessary horizontal (or family) symmetry can be implemented in order to generate the mass splitting between fermions of different generations; how the fermionic mass spectrum may be modified due to GUT interactions, as well as how the mass splitting within the same fermionic generation are generated due to electroweak and GUT interactions.

Fate of global symmetries in the Universe: QCD axion, quintessential axion and trans-Planckian inflaton decay constant

Pseudoscalars appearing in particle physics are reviewed systematically. From the fundamental point of view at an ultraviolet completed theory, they can be light if they are realized as pseudo-Goldstone bosons of some spontaneously broken global symmetries. The spontaneous breaking scale is parametrized by the decay constant [Formula: see text]. The global symmetry is defined by the lowest order terms allowed in the effective theory consistent with the gauge symmetry in question. Since any global symmetry is known to be broken at least by quantum gravitational effects, all pseudoscalars should be massive. The mass scale is determined by [Formula: see text] and the explicit breaking terms [Formula: see text] in the effective potential and also anomaly terms [Formula: see text] for some non-Abelian gauge groups [Formula: see text]. The well-known example by non-Abelian gauge group breaking is the potential for the “invisible” QCD axion, via the Peccei–Quinn symmetry, which constitutes a major part of this review. Even if there is no breaking terms from gauge anomalies, there can be explicit breaking terms [Formula: see text] in the potential in which case the leading term suppressed by [Formula: see text] determines the pseudoscalar mass scale. If the breaking term is extremely small and the decay constant is trans-Planckian, the corresponding pseudoscalar can be a candidate for a “quintessential axion.” In general, [Formula: see text] is considered to be smaller than [Formula: see text], and hence the pseudo-Goldstone boson mass scales are considered to be smaller than the decay constants. In such a case, the potential of the pseudo-Goldstone boson at the grand unification scale is sufficiently flat near the top of the potential that it can be a good candidate for an inflationary model, which is known as “natural inflation.” We review all these ideas in the bosonic collective motion framework.

Modified top quark condensation model with the extra heavy fermion, the 125 GeV pseudo-Goldstone boson, and the additional heavy scalar bosons

We discuss the modified top quark condensation model proposed in Ref. 54. This construction was inspired by the top-seesaw scenario, in which the extra heavy fermion [Formula: see text] that may be paired with the top quark is added. Besides, this model incorporates the ideas of the little Higgs scenario, in which the 125 GeV scalar particle appears as a pseudo-Goldstone boson. This model admits (in addition to the 125 GeV scalar boson [Formula: see text]) the heavier scalar excitation [Formula: see text]. We consider the region of parameters, where its mass is [Formula: see text], the width of [Formula: see text] is [Formula: see text], while the mass of the heavy fermion is [Formula: see text]. We find that in this model the value of the cross-section [Formula: see text] for [Formula: see text] is essentially smaller than the present experimental upper bound. Besides, we find that for the chosen values of parameters there should exist the CP-even scalar boson with mass [Formula: see text] and very small width. In addition, the model predicts the existence of the extra neutral CP-even scalar boson and the charged scalar boson with masses of the order of 1 TeV.

Electroweak scale invariant models with small cosmological constant

We consider scale invariant models where the classical scale invariance is broken perturbatively by radiative corrections at the electroweak scale. These models potentially offer an elegant and simple solution to the hierarchy problem. If we further require the cosmological constant to be small then such models are also highly predictive. Indeed, the minimal such model, comprizing a Higgs doublet and a real singlet, has the same number of parameters as the standard model. Although this minimal model is disfavored by recent LHC data, we show that two specific extensions incorporating neutrino masses and dark matter are fully realistic. That is, consistent with all experiments and observations. These models predict a light pseudo-Goldstone boson, h, with mass around 10 GeV or less. A fermionic-bosonic mass relation is also predicted. The specific models considered, as well as more generic scale invariant models, can be probed at the LHC.