Abstract: We analyse the minima of scalar potentials for multi-Higgs models where the scalars are arranged as either one triplet or two triplets of the discrete symmetries A(4), S-4, Delta (27), Delta (54), as well as Delta (3n(2)) and Delta(6n2) with n > 3. The results should be useful for both multi-Higgs models involving electroweak doublets and multi-flavon models involving electroweak singlets, where in both cases the fields transform as triplets under some non-Abelian discrete symmetry.

Abstract: We impose an S-3 symmetry on the quark fields under which two of three quarks transform like a doublet and the remaining one as singlet, and use a scalar sector with the same structure of SU(2) doublets. After gauge symmetry breaking, a Z(2) subgroup of the S-3 remains unbroken. We show that this unbroken subgroup can explain the approximate block structure of the CKM matrix. By allowing soft breaking of the S-3 symmetry in the scalar sector, we show that one can generate the small elements, of quadratic or higher order in the Wolfenstein parametrization of the CKM matrix. We also predict the existence of exotic new scalars, with unconventional decay properties, which can be used to test our model experimentally.

Abstract: We address the issue of the compositeness of hadronic states and demonstrate that starting with a genuine state of nonmolecular nature, but which couples to some meson-meson component to be observable in that channel, if that state is blamed for a bound state appearing below the meson-meson threshold it gets dressed with a meson cloud and it becomes pure molecular in the limit case of zero binding. We discuss the issue of the scales, and see that if the genuine state has a mass very close to threshold, the theorem holds, but the molecular probability goes to unity in a very narrow range of energies close to threshold. The conclusion is that the value of the binding does not determine the compositeness of a state. However, in such extreme cases we see that the scattering length gets progressively smaller and the effective range grows indefinitely. In other words, the binding energy does not determine the compositeness of a state, but the additional information of the scattering length and effective range can provide an answer. We also show that the consideration of a direct attractive interaction between the mesons in addition to having a genuine component, increases the compositeness of the state. Explicit calculations are done for the Tcc(3875) state, but are easily generalized to any hadronic system.

Abstract: The basic features of quark and lepton mass matrices can be successfully explained by natural minima of a generic potential with dynamical Yukawa fields invariant under the [SU(3)] (5)xO(3) flavor symmetry. If this symmetry is gauged, in order to avoid potentially dangerous Goldstone bosons, and small perturbations are added to exactly fit the observed pattern of fermion masses, the spectrum of massive flavor gauge bosons can naturally explain the hints for new physics in b -> s l(+) l (-) transitions, including R-K. In particular, the desired pattern of the Standard Model Yukawa couplings is compatible with a gauged U(1) (q) in the quark sector, and U(1) (mu-tau) in the lepton sector spontaneously broken around the TeV scale. In order to explain the aforementioned experimental hints, the corresponding neutral gauge bosons are required to mix, yielding to potentially observable signals in dimuon resonance searches at the LHC.

Abstract: We investigate the mass range and the corresponding free-streaming length scale of dark matter produced non-thermally from decay of heavy objects which can be either dominant or sub-dominant at the moment of decay. We show that the resulting dark matter could be very light well below keV scale with a free-streaming length satisfying the Lyman-alpha constraints. We demonstrate two explicit examples for such light cold dark matter.