The recent detection of the cosmic microwave background polarimeter experiment BICEP2 of tensor fluctuations in the B-mode power spectrum basically excludes all plausible axion models where its decay constant is above 10¹³ GeV. Moreover, there are strong theoretical, astrophysical, and cosmological motivations for models involving, in addition to the axion, also axion-like particles (ALPs), with decay constants in the intermediate scale range, between 10⁹ GeV and 10¹³ GeV. Here, we present a general analysis of models with an axion and further ALPs and derive bounds on the relative size of the axion and ALP photon (and electron) coupling. We discuss what we can learn from measurements of the axion and ALP photon couplings about the fundamental parameters of the underlying ultraviolet completion of the theory. For the latter we consider extensions of the Standard Model in which the axion and the ALP(s) appear as pseudo Nambu-Goldstone bosons from the breaking of global chiral U(1) (Peccei-Quinn (PQ)) symmetries, occurring accidentally as low energy remnants from exact discrete symmetries. In such models, the axion and the further ALP are protected from disastrous explicit symmetry breaking effects due to Planck-scale suppressed operators. The scenarios considered exploit heavy right handed neutrinos getting their mass via PQ symmetry breaking and thus explain the small mass of the active neutrinos via a seesaw relation between the electroweak and an intermediate PQ symmetry breaking scale. For a number of explicit models, we determine the parameters of the low-energy effective field theory describing the axion, the ALPs, and their interactions with photons and electrons, in terms of the input parameters, in particular the PQ symmetry breaking scales. We show that these models can accommodate simultaneously an axion dark matter candidate, an ALP explaining the anomalous transparency of the universe for γ-rays, and an ALP explaining the recently reported 3.55 keV gamma line from galaxies and clusters of galaxies, if the respective decay constants are of intermediate scale. Moreover, they do not suffer severely from the domain wall problem.

A generalized $CP$ symmetry for leptons is presented where $CP$ transformations are part of an $S_4$ symmetry that connects different families. We study its implications for lepton mixings in a gauge model realization of the idea using a type II seesaw for neutrino masses. The model predicts maximal atmospheric mixing, nonzero ${\theta }_{13}$ and maximal Dirac phase ${\delta }_D=\pm \frac{\pi }{2}$.

General Fierz-type identities are examined and their well-known connection with completeness relations in matrix vector spaces is shown. In particular, I derive the chiral Fierz identities in a simple and systematic way by using a chiral basis for the complex 4×4 matrices. Other completeness relations for the fundamental representations of SU(N) algebras can be extracted using the same reasoning.

An attractive feature of New Physics models with multiple Higgs fields is that they are equipped with discrete symmetry groups in the Higgs and flavour sectors. These symmetry groups are often broken at the global minimum of the Higgs potential, either completely or to a proper subgroup, with certain phenomenological consequences. Here, we systematically explore these symmetry breaking patterns in the scalar sector of the three-Higgs-doublet model (3HDM). We use the full list of discrete symmetry groups allowed in 3HDM, and for each group we find all possible ways it can break by the Higgs vacuum expectation value alignment. We also discuss the interplay between these symmetry groups and various forms of CP -violation in the scalar sector of 3HDM. Not only do our results solve the problem for 3HDM, but they also hint at several general features in multi-scalar sectors.

We classify explicitly all the possible generalized $CP$ symmetries that are definable in $\Delta (27)$ flavor models. In total, only 12 transformations are possible. We also show interesting consequences of considering some of them as residual symmetries of the neutrino sector.