Separate μ- and e-lepton numbers non-conservation in the Weinberg model with two higgs doublets

It is shown that in the Weiberg-Salam model with two Higgs doublets, one is naturally led to the violation of separate μ- and e-lepton numbers. The branching ratio for μ→eγ is found to be comparable to the present experimental limit.     

Resuscitation of the three-scalar doublet model with spontaneous CP violation

We show that the three-scalar doublet model with spontaneous CP violation and natural flavor conservation can be made consistent with the recent measurements of $\text{?′}\text{?}$ provided an interesting hierarchy among the vacuum expetation values present in the model is assumed. Simultaneously ΔM(K_L?K_S), the ? parameter and the electric dipole moment of the neutron are consistent with the experimental data.     

Weak basis transformations and texture zeros in the leptonic sector

We investigate the physical meaning of some of the texture zeros which appear in most of the ansatzes on leptonic masses and their mixing. It is shown that starting from arbitrary lepton mass matrices and making suitable weak basis transformations one can obtain some of these sets of zeros, which therefore have no physical content. We then analyse four-zero texture ansatzes where the charged lepton and neutrino mass matrices have the same structure. The four texture zeros cannot be obtained simultaneously through weak basis transformations, so these ansatzes do have physical content. We show that they can be separated into four classes and study the physical implications of each class.     

Probabilistic bootstrap percolation

In bootstrap percolation, sites are occupied with probabilityp, but those with less thanm occupied first neighbors are removed. This culling process is repeated until a stable configuration (all occupied sites have at leastm occupied first neighbors or the whole lattice is empty) is achieved. Formm ₁ the transition is first order, while form<m ₁ it is second order, withm-dependent exponents. In probabilistic bootstrap percolation, sites have probabilityr or (1–r) of beingm- orm-sites, respectively (m-sites are those which need at leastm occupied first neighbors to remain occupied). We have studied the model on Bethe lattices, where an exact solution is available. Form=2 andm=3, the transition changes from second to first order atr ₁=1/2, and the exponent is different forr<1/2,r=1/2, andr>1/2. The same qualitative behavior is found form=1 andm=3. On the other hand, form=1 andm=2 the transition is always second order, with the same exponents ofm=1, for any value ofr>0. We found, form=z–1 andm=z, wherez is the coordination number of the lattice, thatp _c=1 for a value ofr which depends onz, but is always above zero. Finally, we argue that, for bootstrap percolation on real lattices, the exponents and form=2 andm=1 are equal, for dimensions below 6.On leave from Universidade Federal de Santa Catarina, Depto. de Fisica, 88049, Florianópolis, SC, Brazil     

Nearest-neighbour interaction from an Abelian symmetry and deviations from Hermiticity

We show that Nearest-Neighbour Interaction (NNI) textures for the quark mass matrices can be obtained through the introduction of an Abelian flavour symmetry. The minimal realisation requires a Z₄${\mathsf{Z}}_4$ symmetry in the context of a two Higgs doublet model. It is further shown that the NNI textures can be in agreement with all present experimental data on quark masses and mixings, provided one allows for deviations of Hermiticity in the quark mass matrices at the 20% level.     

On the enumeration of the set of saturated numerical semigroups of a given genus

In this paper we present an algorithm for computing the set of saturated numerical semigroups of a given genus. We see how the set of saturated numerical semigroups can be arranged in a tree rooted in \(\mathbb{N}\) and we describe the sons of any vertex of this tree.