Abstract: We show that, after resolving what was thought to be an ambiguity in the Higgs coupling, the FSM gives, apart from two extra terms (i) and (ii) to be specified below, an effective action in the standard sector which has the same form as the SM action, the two differing only in the values of the mass and mixing parameters of quarks and leptons which the SM takes as Finputs from experiment while the FSM obtains as a result of a fit with a few parameters. Hence, to the accuracy that these two sets of parameters agree in value, and they do to a good extent as shown in earlier work,' the FSM should give the same result as the SM in all the circumstances where the latter has been successfully applied, except for the noted modifications due to (i) and (ii). If so, it would be a big step forward for the FSM. The correction terms are: (i) a mixing between the SM's gamma – Z with a new vector boson in the hidden sector, (ii) a mixing between the standard Higgs with a new scalar boson also in the hidden sector. And these have been shown a few years back to lead to (i') an enhancement of the W mass over the SM value,(2) – and (ii') effects consistent with the g – 2 and some other anomalies,(3) precisely the two deviations from the SM reported by experiments(4,5) recently much in the news.

Abstract: This paper is aimed at studying the thermodynamic properties of quantum gases confined to a torus. To do that, we consider noninteracting gases within the grand canonical ensemble formalism. In this context, fermions and bosons are taken into account and the calculations are properly provided in both analytical and numerical manners. In particular, the system turns out to be sensitive to the topological parameter under consideration: the winding number. Furthermore, we also derive a model in order to take into account interacting quantum gases. To corroborate our results, we implement such a method for two different scenarios: a ring and a torus.

Abstract: The framed standard model (FSM), constructed to explain the empirical mass and mixing patterns (including CP phases) of quarks and leptons, in which it has done quite well, gives otherwise the same result as the standard model (SM) in almost all areas in particle physics where the SM has been successfully applied, except for a few specified deviations such as the W mass and the g-2 of muons, that is, just where experiment is showing departures from what SM predicts. It predicts further the existence of a hidden sector of particles some of which may function as dark matter. In this paper, we first note that the above results involve, surprisingly, the FSM undergoing a vacuum transition (VTR1) at a scale of around 17MeV, where the vacuum expectation values of the colour framons (framed vectors promoted into fields) which are all nonzero above that scale acquire some vanishing components below it. This implies that the metric pertaining to these vanishing components would vanish also. Important consequences should then ensue, but these occur mostly in the unknown hidden sector where empirical confirmation is hard at present to come by, but they give small reflections in the standard sector, some of which may have already been seen. However, one notes that if, going off at a tangent, one imagines colour to be embedded, Kaluza-Klein (KK) fashion, into a higher-dimensional space-time, then this VTR1 would cause 2 of the compactified dimensions to collapse. This might mean then that when the universe cooled to the corresponding temperature of 1011 K when it was about 10-3 s old, this VTR1 collapse would cause the three spatial dimensions of the universe to expand to compensate. The resultant expansion is estimated, using FSM parameters previously determined from particle physics, to be capable, when extrapolated backwards in time, of bringing the present universe back inside the then horizon, solving thus formally the horizon problem. Besides, VTR1 being a global phenomenon in the FSM, it would switch on and off automatically and simultaneously over all space, thus requiring seemingly no additional strategy for a graceful exit. However, this scenario has not been checked for consistency with other properties of the universe and is to be taken thus not as a candidate solution of the horizon problem but only as an observation from particle physics which might be of interest to cosmologists and experts in the early universe. For particle physicists also, it might serve as an indicator for how relevant this VTR1 can be, even if the KK assumption is not made.