Successful Symmetry Breaking Research Articles

Molecular anatomy of emerging Xenopus left-right organizer at successive developmental stages.

Vertebrate left-right symmetry breaking is preceded by formation of left-right organizer. In Amphibian, this structure is formed by gastrocoel roof plate, which emerges from superficial suprablastoporal cells. GRP is subdivided into medial area, which generates leftward flow by rotating monocilia and lateral Nodal1 expressing areas, which are involved in sensing of the flow. After successful symmetry breaking, medial cells are incorporated into a deep layer where they contribute to the axial mesoderm, while lateral domains join somitic mesoderm. Here, we performed detailed analysis of spatial and temporal gene expression of important markers and the corresponding morphology of emerging GRP. Endodermal marker Sox17 and markers of superficial mesoderm display complementary patterns at all studied stages. At early stages, GRP forms Tekt2 positive epithelial domain clearly separated from underlying deep layers, while at later stages, this separation disappears. Marker of early somitic mesoderm MyoD1 was absent in emerging GRP and was induced together with Nodal1 during early neurulation. Decreasing morphological separation is accompanied by lateral to medial covering of GRP by endoderm. Our data supports continuous link between superficial mesoderm at the start of gastrulation and mature GRP and suggests late induction of somitic fate in lateral GRP.

Ruga mechanics of soft-orifice closure under external pressure

Here, we report the closure resistance of a soft-material bilayer orifice increases against external pressure, along with ruga-phase evolution, in contrast to the conventional predictions of the matrix-free cylindrical-shell buckling pressure. Experiments demonstrate that the generic soft-material orifice creases in a threefold symmetry at a limit-load pressure of p / μ ≈ 1.20, where μ is the shear modulus. Once the creasing initiates, the triple crease wings gradually grow as the pressure increases until the orifice completely closes at p / μ ≈ 3.0. By contrast, a stiff-surface bilayer orifice initially wrinkles with a multifold symmetry mode and subsequently develops ruga-phase evolution, progressively reducing the orifice cross-sectional area as pressure increases. The buckling-initiation mode is determined by the layer's thickness and stiffness, and the pressure by two types of the layer's instability modes—the surface-layer-wrinkling mode for a compliant and the ring-buckling mode for a stiff layer. The ring-buckling mode tends to set the twofold symmetry for the entire post-buckling closure process, while the high-frequency surface-layer-wrinkling mode evolves with successive symmetry breaking to a final closure configuration of two- or threefold symmetry. Finally, we found that the threefold symmetry mode for the entire closure process provides the orifice's strongest closure resistance, and human saphenous veins remarkably follow this threefold symmetry ruga evolution pathway.

String monopoles, string walls, vortex skyrmions, and nexus objects in the polar distorted B phase of He3

The composite cosmological objects -- Kibble-Lazarides-Shafi (KLS) walls bounded by strings and cosmic strings terminated by Nambu monopoles -- could be produced during the phase transitions in the early Universe. Recent experiments in superfluid $^3$He reproduced the formation of the KLS domain walls, which opened the new arena for the detailed study of those objects in human controlled system with different characteristic lengths. These composite defects are formed by two successive symmetry breaking phase transitions. In the first transition the strings are formed, then in the second transition the string becomes the termination line of the KLS wall. In the same manner, in the first transition monopoles are formed, and then in the second transition these monopoles become the termination points of strings. Here we show that in the vicinity of the second transition the composite defects can be described by relative homotopy groups. This is because there are two well separated length scales involved, which give rise to two different classes of the degenerate vacuum states, $R_1$ and $R_2$, and the composite objects correspond to the nontrivial elements of the group $\pi_n(R_1,R_2)$. We discuss this on example of the so-called polar distorted B phase, which is formed in the two-step phase transition in liquid $^3$He distorted by aerogel. In this system the string monopoles terminate spin vortices with even winding number, while KLS string walls terminate on half quantum vortices. In the presence of magnetic field, vortex-skyrmions are formed, and the string monopole transforms to the nexus. We also discuss the integer-valued topological invariants of those objects. Our consideration can be applied to the composite defects in other condensed matter and cosmological systems.

Vacuum stability and symmetry breaking in left-right symmetric model

We derive analytic necessary and sufficient conditions for the vacuum stability of the left-right symmetric model by using the concepts of copositivity and gauge orbit spaces. We also derive the conditions sufficient for successful symmetry breaking and the existence of a correct vacuum. We then compare results obtained from the derived conditions with those from numerical minimization of the scalar potential. Finally, we discuss the renormalization group analysis of the scalar quartic couplings through an example study that satisfies vacuum stability, perturbativity, unitarity and experimental bounds on the physical scalar masses.

Vacuum structure of the left-right symmetric model

The left-right symmetric model (LRSM), originally proposed to explain parity violation in low energy processes, has since emerged as an attractive framework for light neutrino masses via the seesaw mechanism. The scalar sector of the minimal LRSM consists of an SU(2) bi-doublet, as well as left- and right-handed weak isospin triplets, thus making the corresponding vacuum structure much more complicated than that of the Standard Model. In particular, the desired ground state of the Higgs potential should be a charge conserving, and preferably global, minimum with parity violation at low scales. We show that this is not a generic feature of the LRSM potential and happens only for a small fraction of the parameter space of the potential. We also analytically study the potential for some simplified cases and obtain sufficient conditions (though not necessary) to achieve successful symmetry breaking. We then carry out a detailed statistical analysis of the minima of the Higgs potential using numerical minimization and find that for a large fraction of the parameter space, the potential does not have a good vacuum. Imposing the analytically obtained conditions, we can readily find the small part of the parameter space with good vacua. Consequences for some scalar masses are also discussed.

Tensor Renormalization Group Study of the General Spin-S Blume–Capel Model

We focus on the special situation of $D=2J$ of the general spin-S Blume-Capel model on the square lattice. Under the infinitesimal external magnetic field, the phase transition behaviors due to the thermal fluctuations are discussed by the newly developed tensor renormalization group method. For the case of the integer spin-S, the system will undergo $S$ first-order phase transitions with the successive symmetry breaking with the magnetization $M=S,S-1,...0$. For the half-integer spin-S, there are similar $S-1/2$ first order phase transition with $M=S,S-1,...1/2$ stepwise structure, in addition, there is a continuous phase transition due to the spin-flip $Z_2$ symmetry breaking. In the low temperature regions, all first-order phase transitions are accompanied by the successive disappearance of the optional spin-component pairs($s,-s$), furthermore, the critical temperature for the nth first-order phase transition is the same, independent of the value of the spin-S. In the absence of the magnetic field, the visualization parameter characterizing the intrinsic degeneracy of the different phases clearly demonstrates the phase transition process.

Effect of inlet conditions on the engulfment pattern in a T-shaped micro-mixer

The effect of the inlet flow conditions on the degree of mixing in a T-shaped micro-mixer is investigated numerically. Specifically, it is observed that if the flows at the micro-mixer confluence are not fully developed, engulfment occurs at larger Reynolds number, with a different flow pattern and with much lower mixing efficiencies, compared with the case where the inlet flows are fully developed. Thus, for a given micro-mixer geometry, two different engulfment flows may be found as the Reynolds number is increased, corresponding to successive symmetry breaking processes. This work highlights also the importance of both a fine discretization of the micro-mixer as well as of suited convergence criteria for the setting of the numerical simulations.

On Pauli’s principles of “Zweiteilung und symmetrie verminderung” in Higgs physics and non-linear dynamics

Pauli’s principle of bi-division and symmetry reduction “Zweiteilung und symmetrie verminderung” is generalized to cover maximally symmetric spaces specified by Killing’s vector fields and its successive symmetry breaking to yield the particles of the standard model of high energy physics. An analogous picture borrowed from non-linear dynamics and complexity theory will be used to illustrate the conceptual aspect of the procedure from which one could infer, the existence not only of one, but several Higgs particles, possibly three neutral and two charged Higgs with masses not that far from the presently accessible electro-weak energy scale. A tree level estimation with one Higgs to approximate the mass was found to give m H ≃ 162 Gev.

Experimental and theoretical arguments for the number and the mass of the Higgs particles

Abstract Data from relatively recent experiments with linear colliders relevant to the mass of the Higgs are used for orientation purposes to find a satisfactory theory for determining the number and the mass of these elusive particles. The proposed minimally supersymmetric extension of the standard model is based on successive symmetry breaking of higher dimensional space with a maximal number of Killing’s vectors, i.e. a maximally symmetric space. It is shown that the most likely scheme for the Higgs is that consistent with five physical Higgs particles, two charged and three neutrals. These five physical particles result from eight components that are most probably not directly observable. Important for the description of these particles is the mixing parameter tan β and the cross-section. Guided by the results obtained by fitting the scarce experimental data, the most likely range in which the mass of the Higgs particle may be found is between 160–180 GeV with 161.8 and 169.4 GeV being the most likely two values.

On Pauli’s principles of “Zweiteilung und symmetrie verminderung” in Higgs physics and non-linear dynamics

Pauli’s principle of bi-division and symmetry reduction “Zweiteilung und symmetrie verminderung” is generalized to cover maximally symmetric spaces specified by Killing’s vector fields and its successive symmetry breaking to yield the particles of the standard model of high energy physics. An analogous picture borrowed from non-linear dynamics and complexity theory will be used to illustrate the conceptual aspect of the procedure from which one could infer, the existence not only of one, but several Higgs particles, possibly three neutral and two charged Higgs with masses not that far from the presently accessible electro-weak energy scale. A tree level estimation with one Higgs to approximate the mass was found to give mH ≃ 162 Gev.

Successive symmetry breaking of a compact Lie group by a single irreducible multiplet of Higgs bosons.

Using the {210}-dimensional Higgs representation of the SO(10) group as an example, we demonstrate the possibility of having a stable successive symmetry breaking (or phase transition) of a compact Lie group by a single irreducible multiplet of the Higgs boson (or order parameter). Such a symmetry breaking, which is stable under small fluctuations, was hitherto conjectured to be impossible by a weaker form of Michel's conjecture. For example, one can use a single {210} to perform the stable, two-step symmetry breaking: SO(10)\ensuremath{\rightarrow}SU(2)\ifmmode\times\else\texttimes\fi{}SU(2)\ifmmode\times\else\texttimes\fi{}SU(3)\ifmmode\times\else\texttimes\fi{}U(1)\ifmmode\times\else\texttimes\fi{} (D)\ensuremath{\rightarrow}SU(2)\ifmmode\times\else\texttimes\fi{}SU(2)\ifmmode\times\else\texttimes\fi{}SU(3) \ifmmode\times\else\texttimes\fi{}U(1).