Abstract: We present a numeric method for the analysis of the fermion mass matrices predicted in flavour models. The method does not require any previous algebraic work, it offers a chi(2) comparison test and an easy estimate of confidence intervals. It can also be used to study the stability of the results when the predictions are disturbed by small perturbations. We have applied the method to the case of two-zero neutrino mass textures using the latest available fits on neutrino oscillations, derived the available parameter space for each texture and compared them. Textures A(1) and A(2) seem favoured because they give a small chi(2), allow for large regions in parameter space and give neutrino masses compatible with Cosmology limits. The other “allowed” textures remain allowed although with a very constrained parameter space, which, in some cases, could be in conflict with Cosmology. We have also revisited the “forbidden” textures and studied the stability of the results when the texture zeroes are not exact. Most of the forbidden textures remain forbidden, but textures F-1 and F-3 are particularly sensitive to small perturbations and could become allowed.

Abstract: Scatterings of galactic dark matter (DM) particles with the constituents of celestial bodies could result in their accumulation within these objects. Nevertheless, the finite temperature of the medium sets a minimum mass, the evaporation mass, that DM particles must have in order to remain trapped. DM particles below this mass are very likely to scatter to speeds higher than the escape velocity, so they would be kicked out of the capturing object and escape. Here, we compute the DM evaporation mass for all spherical celestial bodies in hydrostatic equilibrium, spanning the mass range [10(-)(10) – 10(2)] M-circle dot, for constant scattering cross sections and s-wave annihilations. We illustrate the critical importance of the exponential tail of the evaporation rate, which has not always been appreciated in recent literature, and obtain a robust result: for the geometric value of the scattering cross section and for interactions with nucleons, at the local galactic position, the DM evaporation mass for all spherical celestial bodies in hydrostatic equilibrium is approximately given by E-c/T-chi similar to 30, where E-c is the escape energy of DM particles at the core of the object and T-chi is their temperature. In that case, the minimum value of the DM evaporation mass is obtained for super-Jupiters and brown dwarfs, m(ev)(ap) similar or equal to 0.7 GeV. For other values of the scattering cross section, the DM evaporation mass only varies by a factor smaller than three within the range 10(-41) cm(2) <= sigma(p) <= 10(-31) cm(2), where sigma(p) is the spin-independent DM-nucleon scattering cross section. Its dependence on parameters such as the galactic DM density and velocity, or the scattering and annihilation cross sections is only logarithmic, and details on the density and temperature profiles of celestial bodies have also a small impact.

Abstract: Using lattice configurations for quantum chromodynamics (QCD) generated with three domain-wall fermions at a physical pion mass, we obtain a parameter-free prediction of QCD 's renormalisation-group-invariant process-independent effective charge, (alpha) over cap (k(2)). Owing to the dynamical breaking of scale invariance, evident in the emergence of a gluon mass-scale, m(0) = 0.43(1) GeV, this coupling saturates at infrared momenta: (alpha) over cap/pi = 0.97(4). Amongst other things: (alpha) over cap (k(2)) is almost identical to the process-dependent (PD) effective charge defined via the Bjorken sum rule; and also that PD charge which, employed in the one-loop evolution equations, delivers agreement between pion parton distribution functions computed at the hadronic scale and experiment. The diversity of unifying roles played by (alpha) over cap (k(2)) suggests that it is a strong candidate for that object which represents the interaction strength in QCD at any given momentum scale; and its properties support a conclusion that QCD is a mathematically well-defined quantum field theory in four dimensions.