Dynamical Symmetry Breaking Research Articles

Drawing insights from pion parton distributions * * Supported by the Chinese Government's Thousand Talents Plan for Young Professionals; Jiangsu Province Hundred Talents Plan for Professionals; and Forschungszentrum Jülich GmbH

A symmetry-preserving continuum approach to the two valence-body bound-state problem is used to calculate the valence, glue and sea distributions within the pion; unifying them with, inter alia, electromagnetic pion elastic and transition form factors. The analysis reveals the following momentum fractions at the scale , , ; and despite hardening induced by the emergent phenomenon of dynamical chiral symmetry breaking, the valence-quark distribution function, , exhibits the behaviour predicted by quantum chromodynamics (QCD). After evolution to , the prediction for matches that obtained using lattice-regularised QCD. This confluence should both stimulate improved analyses of existing data and aid in planning efforts to obtain new data on the pion distribution functions.

Finite volume effects on chiral phase transition and pseudoscalar mesons properties from the Polyakov-Nambu-Jona-Lasinio model

Within the framework of Polyakov-Nambu-Jona-Lasinio model and by means of Multiple Reflection Expansion, we study the finite volume effects on chiral phase transition, especially its influence on the location of the possible critical end point (CEP) and masses of mesons. Our result shows that as the radius of the sphere decreases, the location of CEP shifts toward smaller temperature while remains almost a constant in chemical potential. As for the finite volume effects on the masses of mesons, the masses of π and K increase with decreasing volume, while for σ, η and η′ the situation is the opposite. Especially, the masses of chiral parters π and σ get closer as the volume decreases, indicating that the dynamical chiral symmetry breaking effect reduces with decreasing volume.

On the Variety of Cognitive Temperatures and Their Symmetry-Breaking Dynamics

The asymptotic limit theorems of information and control theories permit exploration of a surprising number of temperature-like measures and symmetry-breaking dynamics associated with cognition. Each of several markedly different perspectives produces a distinct temperature-analog, capturing a rich and highly-punctuated behavioral landscape across the complex, hierarchical cognitive phenomena that characterize life at every scale and level of organization. Theories of cognition may be confronted by canonical conundrums similar to those plaguing the study of consciousness and its regulation. In short, there may be a spectrum of interacting cognitive 'temperatures' for organisms, social structures, institutions, information processing machines, and their composite entities, that varies across different systems, and between similar systems having undergone different individual developmental trajectories. The complexities of cognitive failure-leading to a vast array of pathologies-may be far stranger than generally recognized.

Novel solutions of general and reverse space-time nonlocal coupled integrable dispersionless systems

In this paper, we have studied a general coupled integrable dispersionless (CID) system and obtained nontrivial solutions in terms of the ratio of determinants by using matrix Darboux transformation. We obtain symmetry non-preserving oscillating solutions of the general CID system in zero background. By using suitable reduction conditions we obtain symmetry preserving unstable soliton solutions for reverse space-time nonlocal CID system. We also recovered stable soliton solutions for the classical CID system under local symmetry reduction condition. Furthermore, the dynamics of symmetry breaking and symmetry preserving first- and second-order nontrivial solutions for generalized, reverse space-time nonlocal and classical CID systems have been presented.

Effective locality and chiral symmetry breaking in QCD

A few years ago, the use of standard functional manipulations was demonstrated to imply an unexpected property satisfied by the fermionic Green’s functions of QCD, and called effective locality. This feature of QCD is non-perturbative as it results from a full integration of the gluonic degrees of freedom. In this paper, at eikonal and quenching approximation at least, the relation of effective locality to dynamical chiral symmetry breaking is examined.

Improving Center Vortex Detection by Usage of Center Regions as Guidance for the Direct Maximal Center Gauge

The center vortex model of quantum chromodynamic states that vortices, a closed color-magnetic flux, percolate the vacuum. Vortices are seen as the relevant excitations of the vacuum, causing confinement and dynamical chiral symmetry breaking. In an appropriate gauge, as direct maximal center gauge, vortices are detected by projecting onto the center degrees of freedom. Such gauges suffer from Gribov copy problems: different local maxima of the corresponding gauge functional can result in different predictions of the string tension. By using nontrivial center regions—that is, regions whose boundary evaluates to a nontrivial center element—a resolution of this issue seems possible. We use such nontrivial center regions to guide simulated annealing procedures, preventing an underestimation of the string tension in order to resolve the Gribov copy problem.

Chiral vortices and pseudoscalar condensation due to rotation

We investigate the influence of rotation on the dynamical chiral symmetry breaking in strongly interacting matter. We develop a self-consistent Bogoliubov-de Gennes-like theoretical framework to study the inhomogeneous chiral condensate and the possible chiral vortex state in rotating finite-size matter in four-fermion interacting theories. We show that for sufficiently rapid rotation in $2+1$ dimensions, the ground state can be a chiral vortex state, a type of topological defect in analogy to superfluids and superconductors. The vortex state exhibits pion condensation, providing a new mechanism to realize pseudoscalar condensation in strongly interacting matter.

Spontaneous isotropy breaking for vortices in nonlinear left-handed metamaterials

We explore numerically and analytically the pattern formation and symmetry breaking of beams propagating through left-handed (negative) nonlinear metamaterials. When the input beam is a vortex with topological charge (winding number) $Q$, the initially circular (isotropic) beam acquires the symmetry of a polygon with $Q$, $2Q$, or $3Q$ sides, depending on the details of the response functions of the material. Within an effective field-theory model, this phenomenon turns out to be a case of spontaneous dynamical symmetry breaking described by a Landau-Ginzburg functional. Complex nonlinear dependence of the magnetic permittivity on the magnetic field of the beam plays a central role, as it introduces branch cuts in the mean-field solution, and permutations among different branches give rise to discrete symmetries of the patterns. By considering loop corrections in the effective Landau-Ginzburg field theory we obtain reasonably accurate predictions of the numerical results.

Crawling technicolor

We analyze the Callan-Symanzik equations when scale invariance at a nontrivial infrared (IR) fixed point $\alpha^{}_{\mathrm{IR}}$ is realized in the Nambu-Goldstone (NG) mode. As a result, Green's functions at $\alpha^{}_{\mathrm{IR}}$ do not scale in the same way as for the conventional Wigner-Weyl (WW) mode. This allows us to propose a new mechanism for dynamical electroweak symmetry breaking where the running coupling $\alpha$ "crawls" towards (but does not pass) $\alpha^{}_{\mathrm{IR}}$ in the exact IR limit. The NG mechanism at $\alpha^{}_{\mathrm{IR}}$ implies the existence of a massless dilaton $\sigma$, which becomes massive for IR expansions in $\epsilon \equiv \alpha^{}_{\mathrm{IR}} - \alpha$ and is identified with the Higgs boson. Unlike "dilatons" that are close to a WW-mode fixed point or associated with a Coleman-Weinberg potential, our NG-mode dilaton is genuine and hence naturally light. Its (mass)$^2$ is proportional to $\epsilon \beta'(4+\beta')F_\sigma^{-2} \langle\hat{G}^2\rangle_{\text{vac}}$, where $\beta'$ is the (positive) slope of the beta function at $\alpha^{}_{\mathrm{IR}}$, $F_\sigma$ is the dilaton decay constant and $\langle\hat{G}^2\rangle_{\text{vac}}$ is the technigluon condensate. Our effective field theory for this works because it respects Zumino's consistency condition for dilaton Lagrangians. We find a closed form of the Higgs potential with $\beta'$-dependent deviations from that of the Standard Model. Flavor-changing neutral currents are suppressed if the crawling region $\alpha \lesssim \alpha^{}_{\mathrm{IR}}$ includes a sufficiently large range of energies above the TeV scale. In Appendix A, we observe that, contrary to folklore, condensates protect fields from decoupling in the IR limit.

Dynamical symmetry breaking in Yang–Mills geometrodynamics

We are going to analyze through a first order perturbative formulation the local loss of symmetry when a source of non-Abelian Yang-Mills and gravitational fields interacts with an external agent that perturbes the original geometry associated to the source. Then, as the symmetry in Abelian and non-Abelian field structures in four-dimensional Lorentzian spacetimes is displayed through the existence of local orthogonal planes of symmetry that we previously called blades one and two, the loss of symmetry will be manifested by the tilting of these planes under the influence of the external agent. It was found already that there is an algorithm to block diagonalize the Yang-Mills field strength isospace projections in a local gauge invariant way. Independently, it was also found an algorithm to diagonalize the Yang-Mills stress-energy tensor in a gauge invariant way. Using these results and perturbative analysis from a previous manuscript dealing with the Abelian case, we are going to demonstrate how to develop an algorithm for constructing local energy-momentum conserved currents inside both local orthogonal planes. As the interaction proceeds, the planes are going to tilt perturbatively, and in this strict sense the original local symmetries will be lost. But we will prove that the new blades at the same point will correspond after the tilting generated by perturbation, to new symmetries, with associated new local currents, both on each new local planes of symmetry. Old symmetries will be broken, new will arise. There will be a local symmetry evolution in the non-Abelian case as well.

Future Circular Colliders

After 10 years of physics at the Large Hadron Collider (LHC), the particle physics landscape has greatly evolved. Today, a staged Future Circular Collider (FCC), consisting of a luminosity-frontier highest-energy electron–positron collider (FCC-ee) followed by an energy-frontier hadron collider (FCC-hh), promises the most far-reaching physics program for the post-LHC era. FCC-ee will be a precision instrument used to study the Z, W, Higgs, and top particles, and will offer unprecedented sensitivity to signs of new physics. Most of the FCC-ee infrastructure could be reused for FCC-hh, which will provide proton–proton collisions at a center-of-mass energy of 100 TeV and could directly produce new particles with masses of up to several tens of TeV. This collider will also measure the Higgs self-coupling and explore the dynamics of electroweak symmetry breaking. Thermal dark matter candidates will be either discovered or conclusively ruled out by FCC-hh. Heavy-ion and electron–proton collisions (FCC-eh) will further contribute to the breadth of the overall FCC program. The integrated FCC infrastructure will serve the particle physics community through the end of the twenty-first century. This review combines key contents from the first three volumes of the FCC Conceptual Design Report.

Strange Stars in the Vector Interaction Enhanced Bag Model

The vector interaction enhanced Bag model (vBag) for dense quark matter extends the commonly used thermodynamic Bag model (tdBag) by incorporating effects of dynamical chiral symmetry breaking (D χ SB) and vector repulsion. Motivated by the suggestion that the stability of strange matter is in tension with chiral symmetry breaking (D χ SB) we examine the parameter space for its stability in the vBag model in this work. Assuming the chiral transition occurs at sufficiently low density, we determine the stability region of strange matter as a function of the effective Bag constant and the vector coupling. As an astrophysical application, we construct contours of maximum mass M max and radius at maximum mass R max in this region of parameter space. We also study the stability of strange stars in the vBag model with maximum mass in the 2 M ⊙ range by computing the spectrum of radial oscillations, and comparing to results from the tdBag model, find some notable differences.

Dynamical Lorentz symmetry breaking in a tensor bumblebee model

In this paper, we formulate a theory of the second-rank antisymmetric (pseudo)tensor field minimally coupled to a spinor, calculate the one-loop effective potential of the (pseudo)tensor field, and, explicitly, demonstrate that it is positively defined and possesses a continuous set of minima, both for tensor and pseudotensor cases. Therefore, our model turns out to display the dynamical Lorentz symmetry breaking. We also argue that, contrarily to the derivative coupling we use here, derivative-free couplings of the antisymmetric tensor field to a spinor do not generate the positively defined potential and thus do not allow for the dynamical Lorentz symmetry breaking.

Photoinduced Electron Transfer in Donor-Acceptor Complexes: Isotope Effect and Dynamic Symmetry Breaking.

Electron–nuclear (vibronic) coupling has emerged as an important factor in determining the efficiency of energy transfer and charge separation in natural and artificial photosynthetic systems. Here we investigate the photoinduced charge-transfer process in a hydrogen-bonded donor–acceptor molecular complex. By using real-time quantum–classical simulations based on time-dependent Kohn–Sham equations, we follow in detail the relaxation from the Franck–Condon point to the region of strong nonadiabatic coupling where electron transfer occurs. We elucidate how the charge transfer is coupled to specific vibrational modes and how it is affected by isotope substitution. The importance of resonance in nuclear and electron dynamics and the role of dynamic symmetry breaking are emphasized. Using the dipole moment as a descriptive parameter, exchange of angular momentum between nuclear and electronic subsystems in an electron–nuclear resonant process is inferred. The performed simulations support a nonadiabatic conversion via adiabatic passage process that was recently put forward. These results are relevant in deriving rational design principles for solar-to-fuel conversion devices.

Quark fragmentation as a probe of dynamical mass generation

We address the propagation and hadronization of a struck quark by studying the gauge invariance of the color-averaged cut quark propagator, and by relating this to the single inclusive quark fragmentation correlator by means of new sum rules. Using suitable Wilson lines, we provide a gauge-invariant definition for the mass of the color-averaged dressed quark and decompose this into the sum of a current and an interaction-dependent component. The latter, which we argue is an order parameter for dynamical chiral symmetry breaking, also appears in the sum rule for the twist-3 E˜ fragmentation function, providing a specific experimental way to probe the dynamical generation of mass in Quantum Chromo Dynamics.

Finite-size and finite-time effects in large deviation functions near dynamical symmetry breaking transitions

We introduce and study a class of particle hopping models consisting of a single box coupled to a pair of reservoirs. Despite being zero-dimensional, in the limit of large particle number and long observation time, the current and activity large deviation functions of the models can exhibit symmetry-breaking dynamical phase transitions. We characterize exactly the critical properties of these transitions, showing them to be direct analogues of previously studied phase transitions in extended systems. The simplicity of the model allows us to study features of dynamical phase transitions which are not readily accessible for extended systems. In particular, we quantify finite-size and finite-time scaling exponents using both numerical and theoretical arguments. Importantly, we identify an analogue of critical slowing near symmetry breaking transitions and suggest how this can be used in the numerical studies of large deviations. All of our results are also expected to hold for extended systems.

Towards a mean-field kinetic model of electroweak baryogenesis

We explore the dynamic symmetry breaking between the mass of two annihilating species entrapped within a condensing droplet of a third phase-changing species. The symmetry breaking is induced by different diffusivities and/or diffebet source terms acting at the droplet interface. Potential implications for the problem of electroweak baryogenesis are sketched out.

Transverse Takahashi identities and their implications for gauge independent dynamical chiral symmetry breaking

In this article, we employ transverse Takahashi identities to impose valuable non-perturbative constraints on the transverse part of the fermion-photon vertex in terms of new form factors, the so called $Y_i$ functions. We show that the implementation of these identities is crucial in ensuring the correct local gauge transformation of the fermion propagator and its multiplicative renormalizability. Our construction incorporates the correct symmetry properties of the $Y_i$ under charge conjugation operation as well as their well-known one-loop expansion in the asymptotic configuration of incoming and outgoing momenta. Furthermore, we make an explicit analysis of various existing constructions of this vertex against the demands of transverse Takahashi identities and the previously established key features of quantum electrodynamics, such as gauge invariance of the critical coupling above which chiral symmetry is dynamically broken. We construct a simple example in its quenched version and compute the mass function as we vary the coupling strength and also calculate the corresponding anomalous dimensions $\gamma_m$. There is an excellent fit to the Miransky scalling law and we find $\gamma_m=1$ rather naturally in accordance with some earlier results in literature, using arguments based on Cornwall-Jackiw-Tomboulis effective potential technique. Moreover, we numerically confirm the gauge invariance of this critical coupling.

Finite-volume effects on the chiral phase transition of thermal QED3

The influence of finite-volume effects on dynamical chiral symmetry breaking of thermal ${\mathrm{QED}}_{3}$ is investigated. We show that the chiral symmetry gets restored at all temperatures when the size of system is less than some certain value ${L}_{c}^{\ensuremath{'}}=189$; the critical temperature of chiral phase transition generally increases with the size of the system and the critical temperature when the system volume tends to infinity is slightly less than that in the case of infinite volume.

Cosmic strings, deformed lattices and spontaneous symmetry breaking

External conditions have a dramatic impact on the way dynamical symmetry breaking occurs. In a curved background, the natural expectation is that curvature works toward the restoration of the internal symmetry. We show instead that, for topological defects, the competing action of the locally induced curvature and boundary conditions generated by the non-trivial topology allows configurations where symmetries can be spontaneously broken close to the core. Inspired by the effect of geometrical deformations on 2D lattices, we then propose a novel mechanism to induce a superconducting phase by triggering condensation along cosmic strings.