Composite operator approach to dynamical mass generation in the (2 + 1)-dimensional Gross–Neveu model

Using a nonperturbative approach based on the Cornwall–Jackiw–Tomboulis (CJT) effective action [Formula: see text] for composite operators, the phase structure of the simplest massless [Formula: see text]-dimensional Gross–Neveu model is investigated. We have calculated [Formula: see text] in the first-order of the bare coupling constant [Formula: see text] and have shown that there exist three different specific dependences of [Formula: see text] on the cutoff parameter [Formula: see text], and in each case, the effective action and its stationarity equations have been obtained. The solutions of these equations correspond to the fact that three different masses of fermions can arise dynamically and, respectively, three different nontrivial phases can be observed in the model.

Precision test of the muon-Higgs coupling at a high-energy muon collider

We explore the sensitivity of directly testing the muon-Higgs coupling at a high-energy muon collider. This is strongly motivated if there exists new physics that is not aligned with the Standard Model Yukawa interactions which are responsible for the fermion mass generation. We illustrate a few such examples for physics beyond the Standard Model. With the accidentally small value of the muon Yukawa coupling and its subtle role in the high-energy production of multiple (vector and Higgs) bosons, we show that it is possible to measure the muon-Higgs coupling to an accuracy of ten percent for a 10 TeV muon collider and a few percent for a 30 TeV machine by utilizing the three boson production, potentially sensitive to a new physics scale about Λ ∼ 30 − 100 TeV.

Trainable generator of educational content

<p>As the main problem of the research, the possibility of creating a universal educational platform that combines the possibilities of an online generation of educational content with the interface of the training process itself was considered. The methodology of the educational platform has been developed, in which the mass generation of content is carried out at random, based on simulation models of educational objects. A matrix interface is used, which allows performing custom operations by entering a sequence of typical operators. The system forms a reference base of operators, replenishing it from user solutions, which makes it possible to train and improve the system in order to provide methodological support to student users. An active demo layout of an educational content generator was created and tested, using the example of a specific problem from school mathematics. All methodological options function in the layout. There are three interface options: administrative, training and control. It was concluded that the approach based on the simulation of educational objects makes it possible to create a unified algorithmic platform that combines the functions of content generation with educational training. The system contains a unique option to teach yourself based on its interaction with students.</p>

Symmetric Mass Generation in Lattice Gauge Theory

We construct a four-dimensional lattice gauge theory in which fermions acquire mass without breaking symmetries as a result of gauge interactions. Our model consists of reduced staggered fermions transforming in the bifundamental representation of an SU(2)×SU(2) gauge symmetry. This fermion representation ensures that single-site bilinear mass terms vanish identically. A symmetric four-fermion operator is however allowed, and we give numerical results that show that a condensate of this operator develops in the vacuum.

A modular A 4 symmetric scotogenic model for neutrino mass and dark matter

Modular symmetries have been impeccable in neutrino and quark sectors. This motivated us, to propose a variant of scotogenic model based on modular $A_4$ symmetry and realize the neutrino mass generation at one-loop level through radiative mechanism. Alongside, we discuss the lepton flavour violating processes $\mu \to e \gamma$, $\mu \to3e$ and $\mu - e $ conversion in the nucleus. The lightest Dirac fermion turns out to be potential dark matter candidate, made stable by suitable assignment of modular weights. The relic density of the same has been computed with annihilations mediated by inert scalars and new $U(1)$ gauge boson. The LEP-II and ATLAS dilepton constraints on the new gauge parameters are suitably considered to show the consistent parameter region.

Making weight: acute muscle weakness and hypokalaemia exacerbated by thyrotoxicosis factitia in a bodybuilder

Summary A 32-year-old Caucasian male presented to the emergency department with a one-day history of acute severe bilateral lower limb weakness, three days after competing in a bodybuilding competition. He consumed large quantities of carbohydrate-rich foods following the competition. His past medical history was significant for anxiety, and family history was non-contributory. Examination was normal except for reduced power and hyporeflexia in both legs, despite his muscular physique. He was noted to have severe hypokalaemia (K+= 1.9 mmol/L). His thyroid function tests were consistent with thyrotoxicosis. He reported taking thyroxine and several other agents to facilitate muscle mass generation before the bodybuilding competition. His presentation was reminiscent of thyrotoxic periodic paralysis, albeit uncommon with Caucasian ethnicity. He also had transient hyperglycaemia at presentation with concomitant hyperinsulinaemia, which could be attributed to the carbohydrate load and may have exacerbated his hypokalaemia through a transcellular shift. Urine toxicology screen subsequently ruled out the use of diuretics but confirmed the presence of a long-acting beta agonist (clenbuterol) which, along with other substances, may have aggravated the hypokalaemia further. After 12 h of i.v. replacement, the potassium level normalised and leg weakness resolved. The patient agreed to stop taking thyroxine and beta agonists and was well during the clinic visit at one month follow-up. This case highlights the potential for thyrotoxicosis factitia to exacerbate hypokalaemia and muscle weakness from other causes in bodybuilders presenting with acute severe weakness, irrespective of ethnicity. Learning points In patients presenting with muscle weakness and hypokalaemia, early consideration of thyrotoxicosis is essential, even in the absence of a past history of thyroid disease or specific symptoms of thyrotoxicosis, in order to allow prompt initiation of appropriate treatment and to prevent recurrence. Bodybuilders may constitute a uniquely ‘at-risk’ group for thyrotoxic periodic paralysis secondary to thyrotoxicosis factitia, especially where there is concomitant use of beta-adrenergic agonists, even in the absence of diuretic use. Although rare and usually described in patients of Asian or Polynesian ethnicity, this case highlights that thyrotoxic periodic paralysis secondary to thyrotoxicosis factitia can also occur in patients with Caucasian ethnicity. We speculate that consuming large quantities of carbohydrates may induce hyperinsulinaemia, which could theoretically contribute to worse hypokalaemia, though mechanistic studies would be needed to explore this further.

Two-loop mass anomalous dimension in reduced quantum electrodynamics and application to dynamical fermion mass generation

We consider reduced quantum electrodynamics ($$ {\mathrm{RQED}}_{d_{\gamma },{d}_e} $$ RQED d γ , d e ) a model describing fermions in a de-dimensional space-time and interacting via the exchange of massless bosons in dγ-dimensions (de ≤ dγ). We compute the two-loop mass anomalous dimension, γm, in general $$ {\mathrm{RQED}}_{4,{d}_e} $$ RQED 4 , d e with applications to RQED4,3 and QED4. We then proceed on studying dynamical (parity-even) fermion mass generation in $$ {\mathrm{RQED}}_{4,{d}_e} $$ RQED 4 , d e by constructing a fully gauge-invariant gap equation for $$ {\mathrm{RQED}}_{4,{d}_e} $$ RQED 4 , d e with γm as the only input. This equation allows for a straightforward analytic computation of the gauge-invariant critical coupling constant, αc, which is such that a dynamical mass is generated for αr> αc, where αr is the renormalized coupling constant, as well as the gauge-invariant critical number of fermion flavours, Nc, which is such that αc → ∞ and a dynamical mass is generated for N < Nc. For RQED4,3, our results are in perfect agreement with the more elaborate analysis based on the resolution of truncated Schwinger-Dyson equations at two-loop order. In the case of QED4, our analytical results (that use state of the art five-loop expression for γm) are in good quantitative agreement with those obtained from numerical approaches.

One colorful resolution to the neutrino mass generation, three lepton flavor universality anomalies, and the Cabibbo angle anomaly

We propose a simple model to simultaneously explain four observed flavor anomalies while generating the neutrino mass at the one-loop level. Specifically, we address the measured anomalous magnetic dipole moments of the muon, ∆aμ, and electron, ∆ae, the observed anomaly of b → sl+l− in the B-meson decays, and the Cabibbo-angle anomaly. The model consists of four colorful new degrees of freedom: three scalar leptoquarks with the Standard Model quantum numbers (3, 3, −1/3), (3, 2, 1/6), and (3, 1, 2/3), and one pair of down-quark-like vector fermion in (3, 1, −1/3). The baryon number is assumed to be conserved for simplicity.Phenomenologically viable solutions with the minimal number of real parameters can be found to accommodate all the above-mentioned anomalies and produce the approximate, close to 1σ, neutrino oscillation pattern at the same time. From general consideration, the model robustly predicts: (1) neutrino mass is of the normal hierarchy type, and (2) $$ {\mathcal{M}}_{ee}^{\nu } $$ M ee ν ≲ 3 × 10−4 MeV.The possible UV origin to explain the flavor pattern of the found viable parameter space is briefly discussed. The parameter space can be well reproduced within a simple split fermion toy model.