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

A variational method based on weighted graph states

In a recent article [Phys. Rev. Lett. 97 (2006), 107206], we have presented a class of states which is suitable as a variational set to find ground states in spin systems of arbitrary spatial dimension and with long-range entanglement. Here, we continue the exposition of our technique, extend from spin 1/2 to higher spins and use the boson Hubbard model as a non-trivial example to demonstrate our scheme.Comment: 36 pages, 13 figure

Collective coordinates, shape transitions and shape coexistence: a microscopic approach

We investigate a description of shape-mixing and shape-transitions using collective coordinates. To that end we apply a theory of adiabatic large-amplitude motion to a simplified nuclear shell-model, where the approximate results can be contrasted with exact diagonalisations. We find excellent agreement for different regimes, and contrast the results with those from a more standard calculation using a quadrupole constraint. We show that the method employed in this work selects diabatic (crossing) potential energy curves where these are appropriate, and discuss the implications for a microscopic study of shape coexistence.Comment: 20 pages, including 6 ps file

Confinement From The Gauge Invariant Abelian Decomposition

A common approach while considering confinement is to study the dominance of an Abelian subgroup of the SU(3) gauge Links. A good way to find the Abelian component of the field is through the Cho-Guan-De gauge invariant Abelian Decomposition, which uses a carefully chosen direction vector $n$ to split the gauge field into an Abelian restricted field and a remnant coloured field. The restricted field can be further subdivided into topological and non-topological terms. We show that there is a choice of $n$ which allows us to exactly represent the Wilson Loop of full QCD as a function of only the restricted Abelian field without requiring any path ordering or additional path integrals. We present numerical evidence showing that the topological part of the restricted field dominates the string tension. We also show that $n$ contains certain topological objects, which, if they exist, will be at least partially responsible for confinement. These leave distinctive patterns in the restricted field strength, and we search for these structures in quenched lattice QCD.Comment: Lattice 2013 (Vacuum structure), Mainz, July 2013; 7 page

Gauge Invariant Factorisation and Canonical Quantisation of Topologically Massive Gauge Theories in Any Dimension

Abelian topologically massive gauge theories (TMGT) provide a topological mechanism to generate mass for a bosonic p-tensor field in any spacetime dimension. These theories include the 2+1 dimensional Maxwell-Chern-Simons and 3+1 dimensional Cremmer-Scherk actions as particular cases. Within the Hamiltonian formulation, the embedded topological field theory (TFT) sector related to the topological mass term is not manifest in the original phase space. However through an appropriate canonical transformation, a gauge invariant factorisation of phase space into two orthogonal sectors is feasible. The first of these sectors includes canonically conjugate gauge invariant variables with free massive excitations. The second sector, which decouples from the total Hamiltonian, is equivalent to the phase space description of the associated non dynamical pure TFT. Within canonical quantisation, a likewise factorisation of quantum states thus arises for the full spectrum of TMGT in any dimension. This new factorisation scheme also enables a definition of the usual projection from TMGT onto topological quantum field theories in a most natural and transparent way. None of these results rely on any gauge fixing procedure whatsoever.Comment: 1+25 pages, no figure

Vacuum Induced CP Violation Generating a Complex CKM Matrix with Controlled Scalar FCNC

We propose a viable minimal model with spontaneous CP violation in the framework of a Two Higgs Doublet Model. The model is based on a generalised Branco-Grimus-Lavoura model with a flavoured $\mathbb{Z}_2$ symmetry, under which two of the quark families are even and the third one is odd. The lagrangian respects CP invariance, but the vacuum has a CP violating phase, which is able to generate a complex CKM matrix, with the rephasing invariant strength of CP violation compatible with experiment. The question of scalar mediated flavour changing neutral couplings is carefully studied. In particular we point out a deep connection between the generation of a complex CKM matrix from a vacuum phase and the appearance of scalar FCNC. The scalar sector is presented in detail, showing that the new scalars are necessarily lighter than 1 TeV. A complete analysis of the model including the most relevant constraints is performed, showing that it is viable and that it has definite implications for the observation of New Physics signals in, for example, flavour changing Higgs decays or the discovery of the new scalars at the LHC. We give special emphasis to processes like $t\to {\rm h} c,{\rm h} u$, as well as ${\rm h}\to bs, bd$, which are relevant for the LHC and the ILC.Comment: 36 pages, 11 figure

Hamiltonian statistical mechanics

A framework for statistical-mechanical analysis of quantum Hamiltonians is introduced. The approach is based upon a gradient flow equation in the space of Hamiltonians such that the eigenvectors of the initial Hamiltonian evolve toward those of the reference Hamiltonian. The nonlinear double-bracket equation governing the flow is such that the eigenvalues of the initial Hamiltonian remain unperturbed. The space of Hamiltonians is foliated by compact invariant subspaces, which permits the construction of statistical distributions over the Hamiltonians. In two dimensions, an explicit dynamical model is introduced, wherein the density function on the space of Hamiltonians approaches an equilibrium state characterised by the canonical ensemble. This is used to compute quenched and annealed averages of quantum observables.Comment: 8 pages, 2 figures, references adde