The Higgs mechanism and geometrical flows for two-manifolds

Using Perelman’s approach for geometrical flows in terms of an entropy functional, the Higgs mechanism is studied dynamically along flows defined in the space of parameters and in fields space. The model corresponds to two-dimensional gravity that incorporates torsion as the gradient of a Higgs field, and with the reflection symmetry to be spontaneously broken. The results show a discrete mass spectrum and the existence of a mass gap between the Unbroken Exact Symmetry and the Spontaneously Broken Symmetry scenarios. In the latter scenario, the geometries at the degenerate vacua correspond to conformally flat manifolds without torsion; twisted two-dimensional geometries are obtained by building perturbation theory around a ground state; the tunneling quantum probability between vacua is determined along the flows.

Small 𝜃13 and solar neutrino oscillation parameters from μ − τ symmetry

Exchange [Formula: see text] symmetry in the effective Majorana neutrino mass matrix does predict a maximal mixing for atmospheric neutrino oscillations asides to a null mixing that cannot be straightforwardly identified with reactor neutrino oscillation mixing, [Formula: see text], unless a specific ordering is assumed for the mass eigenstates. Otherwise, a nonzero value for [Formula: see text] is predicted already at the level of an exact symmetry. In this case, solar neutrino mixing and scale, as well as the correct atmospheric mixing arise from the breaking of the symmetry. I present a mass matrix proposal for normal hierarchy that realizes this scenario, where the smallness of [Formula: see text] is naturally given by the parameter [Formula: see text] and the solar mixing is linked to the smallness of [Formula: see text]. The proposed matrix remains stable under renormalization effects and it also allows to account for CP violation within the expected region without further constrains.

Spinor vacuum and C, P, T inversions

We have developed the theory of Clifford reflections and extended spacetime inversions. This extended spacetime has two additional dimensions associated with the presence of internal degrees of freedom of spinors. Inversions C, P, and T contain not only reflections of the basis Clifford vectors and transformations of basis spinors, but also transformations of the components of vector and spinor quantities. The research is carried out on the basis of algebraic quantum field theory using the superalgebraic representation of spinors as well as the 8-component matrix representation of spinors. We have proved that due to the presence of internal degrees of freedom of spinors, there are two vacua, the vacuum of our Universe and an alternative vacuum. The inversion operators C and T transform the vacuum into an alternative one, and therefore cannot be operators of the exact symmetry of our Universe.

Exploring multi-Higgs models with softly broken large discrete symmetry groups

We develop methods to study the scalar sector of multi-Higgs models with large discrete symmetry groups that are softly broken. While in the exact symmetry limit, the model has very few parameters and can be studied analytically, proliferation of quadratic couplings in the most general softly broken case makes the analysis cumbersome. We identify two sets of soft breaking terms which play different roles: those which preserve the symmetric vacuum expectation value alignment, and the remaining terms which shift it. Focusing on alignment preserving terms, we check which structural features of the symmetric parent model are conserved and which are modified. We find remarkable examples of structural features which are inherited from the parent symmetric model and which persist even when no exact symmetry is left. The general procedure is illustrated with the example of the three-Higgs-doublet model with the softly broken symmetry group $$\Sigma (36)$$ Σ ( 36 ) .

Patterns of nodal spread in stage III NSCLC: importance of EBUS-TBNA and 18F-FDG PET/CT for radiotherapy target volume definition

Purpose The aim of this study was to compare the pattern of intra-patient spread of lymph-node (LN)-metastases within the mediastinum as assessed by 18F-FDG PET/CT and systematic endobronchial ultrasound-guided transbronchial-needle aspiration (EBUS-TBNA) for precise target volume definition in stage III NSCLC. Methods This is a single-center study based on our preceding investigation, including all consecutive patients with initial diagnosis of stage IIIA-C NSCLC, receiving concurrent radiochemotherapy (12/2011–06/2018). Inclusion criteria were curative treatment intent, 18F-FDG PET/CT and EBUS-TBNA prior to start of treatment. The lymphatic drainage was classified into echelon-1 (ipsilateral hilum), echelon-2 (ipsilateral LN-stations 4 and 7) and echelon-3 (rest of the mediastinum, contralateral hilum). The pattern of spread was classified according to all permutations of echelon-1, echelon-2, and echelon-3 EBUS-TBNA findings. Results In total, 180 patients were enrolled. Various patterns of LN-spread could be identified. Skip lesions with an involved echelon distal from an uninvolved one were detected in less than 10% of patients by both EBUS-TBNA and PET. The pattern with largest asymmetry was detected in cases with EBUS-TBNA- or PET-positivity at all three echelons (p < 0.0001, exact symmetry test). In a multivariable logistic model for EBUS-positivity at echelon-3, prognostic factors were PET-positivity at echelon-3 (Hazard ratio (HR) = 12.1; 95%-CI: 3.2–46.5), EBUS-TBNA positivity at echelon-2 (HR = 6.7; 95%-CI: 1.31–31.2) and left-sided tumor location (HR = 4.0; 95%-CI: 1.24–13.2). There were significantly less combined ipsilateral upper (LN-stations 2 and 4) and lower (LN-station 7) mediastinal involvements (16.8% of patients) with EBUS-TBNA than with PET (38.9%, p < 0.0001, exact symmetry test). EBUS-TBNA detected a lobe specific heterogeneity between the odds ratios of LN-positivity in the upper versus lower mediastinum (p = 0.0021, Breslow-Day test), while PET did not (p = 0.19). Conclusion Frequent patterns of LN-metastatic spread could be defined by EBUS-TBNA and PET and discrepancies in the pattern were seen between both methods. EBUS-TBNA showed more lobe and tumor laterality specific patterns of LN-metastases than PET and skipped lymph node stations were rare. These systematic relations offer the opportunity to further refine multi-parameter risk of LN-involvement models for target volume delineation based on pattern of spread by EBUS-TBNA and PET.

Hidden quasi-symmetries stabilize non-trivial quantum oscillations in CoSi

Unlocking the exotic properties promised to occur in topologically non-trivial semi-metals currently requires significant fine-tuning. Crystalline symmetry restricts the location of topological defects to isolated points (0D) or lines (1D), as formalized by the Wigner-Von Neumann theorem. The scarcity of materials in which these anomalies occur at the chemical potential is a major obstacle towards their applications. Here we show how non-crystalline quasi-symmetries stabilize near-degeneracies of bands over extended regions in energy and in the Brillouin zone. Specifically, a quasi-symmetry is an exact symmetry of a k∙p Hamiltonian to lower-order that is broken by higher-order terms. Hence quasi-symmetric points are gapped, yet the gap is parametrically small and therefore does not influence the physical properties of the system. We demonstrate that in the eV-bandwidth semi-metal CoSi an internal quasi-symmetry stabilizes gaps in the 1-2 meV range over a large near-degenerate plane (2D). This quasi-symmetry is key to explaining the surprising simplicity of the experimentally observed quantum oscillations of four interpenetrating Fermi surfaces around the R-point. Untethered from the limitations of crystalline symmetry, quasi-symmetries eliminate the need for fine-tuning as they enforce sources of large Berry curvature to occur at the chemical potential, and thereby lead to new Wigner-Von Neumann classifications of solids. Quasi-symmetries arise from a comparable splitting of degenerate states by spin-orbit coupling and by orbital dispersion - suggesting a hidden classification framework for symmetry groups and materials in which quasi-symmetries are critical to understand the low-energy physics.

Relationship between Unstable Point Symmetries and Higher-Order Approximate Symmetries of Differential Equations with a Small Parameter

The framework of Baikov–Gazizov–Ibragimov approximate symmetries has proven useful for many examples where a small perturbation of an ordinary or partial differential equation (ODE, PDE) destroys its local exact symmetry group. For the perturbed model, some of the local symmetries of the unperturbed equation may (or may not) re-appear as approximate symmetries. Approximate symmetries are useful as a tool for systematic construction of approximate solutions. For algebraic and first-order differential equations, to every point symmetry of the unperturbed equation, there corresponds an approximate point symmetry of the perturbed equation. For second and higher-order ODEs, this is not the case: a point symmetry of the original ODE may be unstable, that is, not have an analogue in the approximate point symmetry classification of the perturbed ODE. We show that such unstable point symmetries correspond to higher-order approximate symmetries of the perturbed ODE and can be systematically computed. Multiple examples of computations of exact and approximate point and local symmetries are presented, with two detailed examples that include a fourth-order nonlinear Boussinesq equation reduction. Examples of the use of higher-order approximate symmetries and approximate integrating factors to obtain approximate solutions of higher-order ODEs are provided.

Symmetry breaking meets multisite modification

Multisite modification is a basic way of conferring functionality to proteins, and a key component of post-translational modification networks. Additional interest in multisite modification stems from its capability of acting as complex information processors. In this paper we connect two seemingly disparate themes: symmetry and multisite modification. We examine different classes of random modification networks of substrates involving separate or common enzymes. We demonstrate that under different instances of symmetry of the modification network (invoked explicitly or implicitly and discussed in the literature), the biochemistry of multisite modification can lead to the symmetry being broken. This is shown computationally and consolidated analytically, revealing parameter regions where this can (and in fact does) happen, and characteristics of the symmetry broken state. We discuss the relevance of these results in situations where exact symmetry is not present. Overall, through our study we show how symmetry breaking (i) can confer new capabilities to protein networks, including concentration robustness of different combinations of species (in conjunction with multiple steady states) (ii) could have been the basis for ordering of multisite modification, which is widely observed in cells (iii) can significantly impact information processing in multisite modification and in cell signalling networks/pathways where multisite modification is present (iv) can be a fruitful new angle for engineering in synthetic biology and chemistry. All in all, the emerging conceptual synthesis provides a new vantage point for the elucidation and the engineering of molecular systems at the junction of chemical and biological systems.

Yet another lesson on the stability conditions in multi-Higgs potentials

We discuss a rather common but often unnoticed pitfall which arises when deriving the bounded-from-below (BFB) conditions in multi-Higgs models with softly broken global symmetries. Namely, necessary and sufficient BFB conditions derived for the case with an exact symmetry can be ruined by introducing soft symmetry breaking terms. Using S4 and A4-symmetric three-Higgs-doublet models as an example, we argue that all published necessary and sufficient BFB conditions, even those which are correct for the exactly symmetric case, are no longer sufficient if soft symmetry breaking is added. Using the geometric formalism, we derive the exact necessary and sufficient BFB conditions for the 3HDM with the symmetry group S4, either exact or softly broken, and review the situation for the A4-symmetric case.