Texture zeros and hierarchical masses from flavour (mis)alignment

We introduce an unconventional interpretation of the fermion mass matrix elements. As the full rotational freedom of the gauge-kinetic terms renders a set of infinite bases called weak bases, basis-dependent structures as mass matrices are unphysical. Matrix invariants, on the other hand, provide a set of basis-independent objects which are of more relevance. We employ one of these invariants to give a new parametrization of the mass matrices. By virtue of it, one gains control over its implicit implications on several mass matrix structures. The key element is the trace invariant which resembles the equation of a hypersphere with a radius equal to the Frobenius norm of the mass matrix. With the concepts of alignment or misalignment we can identify texture zeros with certain alignments whereas Froggatt-Nielsen structures in the matrix elements are governed by misalignment. This method allows further insights of traditional approaches to the underlying flavour geometry.Comment: 27 pages; v2 matches version accepted by NPB, discussion on Dirac CP phase for neutrinos adde

Vacuum stability conditions of the economical 3-3-1 model from copositivity

By applying copositivity criterion to the scalar potential of the economical $3-3-1$ model, we derive necessary and sufficient bounded-from-below conditions at tree level. Although these are a large number of intricate inequalities for the dimensionless parameters of the scalar potential, we present general enlightening relations in this work. Additionally, we use constraints coming from the minimization of the scalar potential by means of the orbit space method, the positivity of the squared masses of the extra scalars, the Higgs boson mass, the $Z'$ gauge boson mass and its mixing angle with the SM $Z$ boson in order to further restrict the parameter space of this model.Comment: 22 pages, 7 figures, added text and references. Matches published versio

Characterisation of the dynamical quantum state of a zero temperature Bose-Einstein condensate

We describe the quantum state of a Bose-Einstein condensate at zero temperature. By evaluating the Q-function we show that the ground state of Bose-Einstein condensate under the Hartree approximation is squeezed. We find that multimode Schroedinger cat states are generated as the condensate evolves in a ballistic expansion.Comment: 13 pages, 6 figure

A bottom-up approach to the strong CP problem

The strong CP problem is one of many puzzles in the theoretical description of elementary particle physics that still lacks an explanation. While top-down solutions to that problem usually comprise new symmetries or fields or both, we want to present a rather bottom-up perspective. The main problem seems to be how to achieve small CP violation in the strong interactions despite large CP violation in weak interactions. Observation of CP violation is exclusively through the Higgs--Yukawa interactions. In this paper, we show that with minimal assumptions on the structure of mass (Yukawa) matrices they do not contribute to the strong CP problem and thus we can provide a pathway to a solution of the strong CP problem within the structures of the Standard Model and no extension at the electroweak scale is needed. However, to address the flavor puzzle, models based on minimal SU(3) flavor groups leading to the proposed flavor matrices are favored. Though we refrain from an explicit a UV completion of the Standard Model, we provide a simple requirement those models should have to intrinsically not show a strong CP problem.Comment: 12 pages; v2: extended discussion, title changed to be more genera