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In this paper, we study a class of conformal metric deformations in the quasi-radial coordinate parametrizing the three-sphere in the conformally compactified Minkowski spacetime S1 × S3. Prior to reduction of the associated Laplace–Beltrami operators to a Schrödinger form, a corresponding class of exactly solvable potentials (each one containing a scalar and a gradient term) is found. In particular, the scalar piece of these potentials can be exactly or quasi-exactly solvable, and among them we find the finite range confining trigonometric potentials of Pöschl–Teller, Scarf and Rosen–Morse. As an application of the results developed in the paper, the large compactification radius limit of the interaction described by some of these potentials is studied, and this regime is shown to be relevant to a quantum mechanical quark deconfinement mechanism. [ABSTRACT FROM AUTHOR]

The Schwinger confinement mechanism stipulates that a massless fermion and a massless antifermion are confined as a massive boson when they interact in the Abelian QED interaction in (1+1)D.If we approximate light quarks as massless and apply the Schwinger confinement mechanism to quarks, we can infer that a light quark and a light antiquark interacting in the Abelian QED interaction are confined as a QED meson in (1+1)D. Similarly, a light quark and a light antiquark interacting in the QCD interaction in the quasi-Abelian approximation will be confined as a QCD meson in (1+1)D. The QED and QCD mesons in (1+1)D can represent physical mesons in (3+1)D when the flux tube radius is properly taken into account. Such a theory leads to a reasonable description of the masses of π 0 , η , and η ′ , and its extrapolation to the unknown QED sector yields an isoscalar QED meson at about 17 MeV and an isovector QED meson at about 38 MeV. The observations of the anomalous soft photons, the hypothetical X17 particle, and the hypothetical E38 particle bear promising evidence for the possible existence of the QED mesons. Pending further confirmation, they hold important implications on the properties on the quarks and their interactions. [ABSTRACT FROM AUTHOR]

Despite the obvious progress made by the Feynman, Ravndal, and Kislinger relativistic model in describing the internal motion of a system with confinement of quarks in a nucleon, it turned out to be insufficiently realistic for a number of reasons. In particular, the model does not take into account some cornerstone properties of QCD, namely, gluon exchange between quarks, the influence of the resulting quark sea on valence quarks, and the self-interaction of colored gluons. It is these phenomena that spontaneously break the chiral symmetry of the quark system and form the bulk of the nucleon. To eliminate the above shortcomings of the model, the problem of self-organization of a three-quark dynamical system immersed in a colored quark–antiquark sea is considered within the framework of complex probabilistic processes that satisfy the stochastic differential equation of the Langevin–Kline–Gordon–Fock type. Taking into account the hidden symmetry of the internal motion of a dynamical system, a mathematically closed nonperturbative approach was developed, which makes it possible to construct the mathematical expectation of the wave function and other parameters of the nucleon in the form of multiple integral representations. It is shown that additional subspaces arising in a representation characterized by a noncommutative geometry with topological features participate in the formation of an effective interaction between valence quarks against the background of harmonic interaction between them. [ABSTRACT FROM AUTHOR]

We describe multiquark clusters in quark matter within a Beth-Uhlenbeck approach in a background gluon field coupled to the underlying chiral quark dynamics using the Polyakov gauge. An effective potential for the traced Polyakov loop is used to establish the center symmetry of the SU(3) color which suppresses colored states and its dynamical breaking as an aspect of the confinement/deconfinement transition. Quark confinement is modeled by a large quark mass in vacuum which is motivated by a confining density functional approach. A multiquark cluster containing n quarks and antiquarks is described as a binary composite of smaller subclusters n 1 and n 2 ( n 1 + n 2 = n ). It has a spectrum consisting of a bound state and a scattering state continuum. For the corresponding cluster-cluster phase shifts we use simple ansätze that capture the Mott dissociation of clusters as a function of temperature and chemical potential. We go beyond the simple "step-up-step-down" model that ignores continuum correlations and introduce an improved model that includes them in a generic form. In order to explain the model, we restrict ourselves here to the cases where the cluster size is 1 ≤ n ≤ 6 . A striking result is the suppression of the abundance of colored multiquark clusters at low temperatures by the coupling to the Polyakov loop and their importance for a quantitative description of lattice QCD thermodynamics at non-vanishing baryochemical potentials. An important ingredient are Polyakov-loop generalized distribution functions of n-quark clusters which are derived here for the first time. Within our approach we calculate thermodynamic properties such as baryon density and entropy. We demonstrate that the limits of a hadron resonance gas at low temperatures and O (g 2) perturbative QCD at high temperatures are correctly reproduced. A comparison with lattice calculations shows that our model is able to give a unified, systematic approach to describe properties of the quark-gluon-hadron system. [ABSTRACT FROM AUTHOR]

We study the problem of the existence of the quarkyonic phase in quantum chromodynamics. This phase can exists under certain conditions in quantum chromodynamics along with the phase of free quarks and the confinement phase. As is known, the confinement phase is characterized by the presence of a linear potential between quarks, and the quarks are confined to one hadron (meson or baryon). A linear potential between quarks also exists in the quarkyonic phase; however, it is not so strong to confine quarks inside one hadron. The characteristics of the quarkyonic phase, as well as the confinement phase, can be calculated in quantum chromodynamics only in a nonperturbative framework. We interpret the previously obtained results of Wilson loop calculations in the holographic approach in terms of a phase transition to the quarkyonic phase. [ABSTRACT FROM AUTHOR]

We examine the dynamics of quarks and gauge fields in the lowest energy states in the QED and QCD interactions by combining Schwinger's longitudinal confinement in (1+1)D with Polyakov's transverse confinement in (2+1)D in a "stretch (2+1)D" flux tube model in (3+1)D. For such QED and QCD systems in the flux tube configuration with cylindrical symmetry, we separate out the transverse and longitudinal degrees of freedom, approximate the non-Abelian QCD in the quasi-Abelian approximation, and solve the derived equations to study the collective excitations. We find stable collective QED and QCD excitations showing up as confined QED and QCD mesons, in support of previous theoretical studies and recent observations of the anomalous hypothetical X17 and E38 particles. Future theoretical lattice gauge calculations of QED in (3+1)D with the inclusion of the Schwinger longitudinal confinement mechanism and experimental confirmation of the hypothetical X17 and E38 particles will shed definitive light on quark confinement in the QED interaction in (3+1)D. [ABSTRACT FROM AUTHOR]

In this paper we discuss the combined effects on nuclear matter properties of the quark confinement mechanism in nucleon and of the chiral effective potential resulting from the spontaneous breaking of the chiral symmetry in nuclear matter. One specific aim is to show that the replacement of a basic chiral potential (linear sigma model type) by the enriched Nambu–Jona-Lasinio (NJL) model potential is able to reproduce the saturation properties while strongly decreasing the tension with QCD properties. Based on this NJL prediction, it is shown that the chiral potential acquires a specific scalar field cubic dependence, which contributes to the three-body interaction. We also discuss the constraints induced by Lattice-QCD on the model parameters governing the saturation properties. We introduce the term "QCD-connected parameters" for these quantities. We demonstrate that chiral symmetry and Lattice-QCD provide coherent constraints on the in-medium nuclear interaction, suggesting a fundamental origin of the saturation mechanism. [ABSTRACT FROM AUTHOR]

In this work, we use the approach recently introduced by Barros to study hadron spectra and some quark confinement properties in a Schwarzchild-like space–time generated by a nongravitational field. As a starting point, for the nongravitational field, we make the choice of a strong Yukawa-like field whose associated potential is a generalized Yukawa-like potential, typical of strong interactions. Then, from the latter field, the energy momentum tensor is constructed, the Einstein field equations are solved and the curvature function of the Schwarzchild metric is obtained. The correspondence principle applied to the Schwarzchild metric has enable us to construct the Dirac equation in the latter space. The resolution of the coupled differential equations of Dirac made it possible to obtain the energy spectrum of the strong interaction. The latter is obtained in a more general form than in the previous investigations. Then, the energy spectrum, masses and confinement radius of few hadrons are estimated and compared with experimental data and other theoretical studies. In most considered cases, our predictions are found to be in good agreement with experimental data. The good agreement observed between our outcomes and the experiment can be attributed to the choice of our potential, which has more free parameters than in past studies with the same approach. [ABSTRACT FROM AUTHOR]

The gap equation in quantum chromodynamics is solved by incorporating different gluon dressing functions, some of them derived from a quark–diquark potential that exhibits a conformal symmetry. By using the bare vertex and working in the Landau gauge, the quark mass function is found to have an infrared enhancement that smoothly transitions to an asymptotically free behavior at high momentum, which is consistent with the predictions of Schwinger–Dyson equations. Additionally, these quark propagators violate reflexion positivity, indicating that the gluon dressing provides clear evidence of quark confinement. [ABSTRACT FROM AUTHOR]

We study the role of short-range correlations, as well as pion and rho loops governing long-range RPA correlations, in nuclear matter properties and response functions. We use an adapted formulation of the Brueckner G-matrix approach to generate a pair correlation function satisfying the Beg–Agassi–Gal theorem, providing a natural cutoff to the loop integrals. We present results for the case of a relativistic chiral theory, including the effects of quark confinement and of the chirally broken vacuum in a version where parameters are directly connected to QCD observables or constrained by well-established hadron phenomenology. This provides a unified and coherent view of the nuclear matter equation of state and the effect of correlations on neutrino–nucleus scattering. [ABSTRACT FROM AUTHOR]

We discuss the emergence of a new symmetry generator in a Hamiltonian realisation of four-dimensional gauge theories in the flat space foliated by retarded (advanced) time. It generates an asymptotic symmetry that acts on the asymptotic fields in a way different from the usual large gauge transformations. The improved canonical generators, corresponding to gauge and asymptotic symmetries, form a classical Kac-Moody charge algebra with a non-trivial central extension. In particular, we describe the case of electromagnetism, where the charge algebra is the U(1) current algebra with a level proportional to the coupling constant of the theory, κ = 4π2/e2. We construct bilinear generators yielding Virasoro algebras on the null boundary. We also provide a non-Abelian generalization of the previous symmetries by analysing the evolution of Yang-Mills theory in Bondi coordinates. [ABSTRACT FROM AUTHOR]

Asymptotically nonlocal field theories interpolate between Lee-Wick theories with multiple propagator poles, and ghost-free nonlocal theories. Previous work on asymp- totically nonlocal scalar, Abelian, and non-Abelian gauge theories has demonstrated the existence of an emergent regulator scale that is hierarchically smaller than the lightest Lee-Wick partner, in a limit where the Lee-Wick spectrum becomes dense and decoupled. We generalize this construction to linearized gravity, and demonstrate the emergent regula- tor scale in three examples: by studying the resolution of the singularity (i) at the origin in the classical solution for the metric of a point particle, and (ii) in the nonrelativistic gravitational potential computed via a one-graviton exchange amplitude; (iii) we also show how this derived scale regulates the one-loop graviton contribution to the self energy of a real scalar field. We comment briefly on the generalization of our approach to the full, nonlinear theory of gravity. [ABSTRACT FROM AUTHOR]

As known, the realistic, exponential, fall-off of the rate of production of light mesons in the chromo-electric field of a quark–antiquark string, as a function of the meson mass, can be obtained from the Schwinger-formula Gaussian fall-off within a phenomenological approach which assumes a certain distribution of the string tension. This approach gets a clear meaning in the London limit of the dual superconductor, where the logarithmic increase of the chromo-electric field towards the core of the string leads precisely to the change of the Gaussian fall-off to the exponential one, thus allowing for an identification of the phenomenological distribution of the string tension. In this paper, we demonstrate that, for this distribution of the string tension, the distribution of large-size Yang–Mills instantons, which are interacting with the confining monopole background, becomes O (1 / ρ 3) , where ρ is the size of an instanton. Since such a distribution of large-size instantons is known to yield confinement, we conclude that, in the London limit of the dual-superconductor vacuum, instantons can form a confining medium, and we evaluate their contribution to the total string tension. [ABSTRACT FROM AUTHOR]

Considering the formalism of symplectic quantum mechanics, we investigate a two-dimensional nonrelativistic strong interacting system, describing a bound heavy quark-antiquark state. The potential has a linear component that is analyzed in the context of generalized fractional derivatives. For this purpose, the Schrödinger equation in phase space is solved with the linear potential. The ground state solution is obtained and analyzed through the Wigner function for the meson c c ¯ . One basic and fundamental result is that the fractional quantum phase-space analysis gives rise to the confinement of quarks in the meson, consistent with experimental results. [ABSTRACT FROM AUTHOR]

In 1978, Friedberg and Lee introduced the phenomenological soliton bag model of hadrons, generalizing the MIT bag model developed in 1974 shortly after the formulation of QCD. In this model, quarks and gluons are confined due to coupling with a real scalar field ρ , which tends to zero outside some compact region S ⊂ R 3 determined dynamically from the equations of motion. The gauge coupling in the soliton bag model runs as the inverse power of ρ , already at the semiclassical level. We show that this model arises naturally as a consequence of introducing the warped product metric d s M 2 + ρ 2 d s G 2 on the principal G-bundle P (M , G) ≅ M × G with a non-Abelian group G over Minkowski space M = R 3 , 1 . Confinement of quarks and gluons in a compact domain S ⊂ R 3 is a consequence of the collapse of the bundle manifold M × G to M outside S due to shrinking of the group manifold G to a point. We describe the formation of such regions S as a dynamical process controlled by the order parameter field ρ. [ABSTRACT FROM AUTHOR]

The temperature dependence of the QCD string-breaking distance is evaluated in terms of the string tension and the rate of production of light mesons in the chromo-electric field of a flux tube. As a function of the meson mass, the mentioned rate can be falling off either as a Gaussian, as suggested by the Schwinger formula, or as an exponential, which is the case in the London limit of the dual superconductor. We find an excellent agreement of the so-evaluated temperature dependence of the string-breaking distance with the respective lattice data, for the case of the meson-production rate corresponding to the London limit. [ABSTRACT FROM AUTHOR]

The basic form of the quark condensate for arbitrary values of the quark mass, external magnetic field and temperature, is derived using the field equations with account of confinement. The resulting expression of the chiral condensate is shown to be proportional to square of the singlet ground state wave function at origin, . For light quarks without magnetic field the condensates are proportional to ( is the string tension). Numerical results are presented in 5 Tables and shown to be in good agreement with the lattice data, both for nonzero magnetic field and temperature in the range MeV, GeV . [ABSTRACT FROM AUTHOR]

A characteristic signature of quark confinement is the concentration of the chromoelectric field between a static quark–antiquark pair in a flux tube. However, the structure of this flux tube, and hence of the confining force, has not been completely understood. Here we perform new lattice measurements of field distributions on smeared Monte Carlo ensembles in SU(3) gauge theory. On the basis of these simulations we demonstrate that the confining force can be understood using the analogy with the basic principles of electromagnetism as elucidated by Maxwell. We derive a chromomagnetic Lorentz force density coupling the chromoelectric field to chromomagnetic currents and integrate this force density over the flux tube interior to obtain a Maxwell-like force that squeezes the flux tube in the transverse direction. We show that the strength of this transverse confining force is equal to the value of the string tension calculated numerically from the chromoelectric field on the midplane between the quarks, verifying the consistency of these two complementary pictures of confinement. [ABSTRACT FROM AUTHOR]

This paper pursues the hypothesis that the tangent bundle (TB) with the central extended little groups of the SO(3,1) group as gauge group is the underlying geometric structure for a unified theory of the fundamental physical interactions. Based on this hypothesis as a first step, I recently presented a generalized theory of electroweak interaction (including hypothetical dark matter particles) (Herrmann in Eur Phys J C 79:779, 2019). The vertical Laplacian of the tangent bundle possesses the same form as the Hamiltonian of a 2D semiconductor quantum Hall system. This explains fractional charge quantization of quarks and the existence of lepton and quark families. As will be shown, the SU(3) color symmetry for strong interactions arises in the TB as an emergent symmetry similar to Chern–Simon gauge symmetries in quantum Hall systems. This predicts a signature of quark confinement as a universal large-scale property of the Chern–Simon fields and induces a new understanding of the vacuum as the ground state occupied by a condensate of quark–antiquark pairs. The gap for quark–antiquark pairing is calculated in the mean-field approximation, which allows a numerical estimation of the characteristic parameters of the vacuum such as its chemical potential, the quark condensation parameter and the vacuum energy. Note that a gauge theoretical understanding of gravity was previously achieved by considering the translation group T(3,1) in the TB as gauge group. Therefore, the theory presented here can be considered as a new type of unified theory for all known fundamental interactions linked with the geometrization program of physics. [ABSTRACT FROM AUTHOR]

We propose a modification of standard QCD description of the color triplet of quarks by introducing a 12-component color generalization of Dirac spinor, with built-in Z 3 grading playing an important algebraic role in quark confinement. In the "color Dirac equations" the S U (3) color symmetry is entangled with the Z 3 -graded generalization of Lorentz symmetry, containing three 6-parameter sectors related by Z 3 -graded maps. The generalized Lorentz covariance requires simultaneous presence of 12 color Dirac multiplets, which lead to the description of all internal symmetries of quarks: besides S U (3) × S U (2) × U (1) , the flavor symmetries and three quark families. We also discuss the generalized gauge fields and show how the Standard Model content appears naturally due to the overall Z 3 × Z 2 × Z 2 symmetry. [ABSTRACT FROM AUTHOR]

There are two ways to unify gravitational field and gauge field. One is to represent gravitational field as principal bundle connection, and the other is to represent gauge field as affine connection. Poincaré gauge theory and metric-affine gauge theory adopt the first approach. This paper adopts the second. In this approach, (i) gauge field and gravitational field can both be represented by affine connection; they can be described by a unified spatial frame. (ii) Time can be regarded as the total metric with respect to all dimensions of internal coordinate space and external coordinate space. On-shell can be regarded as gradient direction. Quantum theory can be regarded as a geometric theory of distribution of gradient directions. Hence, gauge theory, gravitational theory, and quantum theory all reflect intrinsic geometric properties of manifold. (iii) Coupling constants, chiral asymmetry, PMNS mixing, and CKM mixing arise spontaneously as geometric properties in affine connection representation, so they are not necessary to be regarded as direct postulates in the Lagrangian anymore. (iv) The unification theory of gauge fields that are represented by affine connection can avoid the problem that a proton decays into a lepton in theories such as S U 5 . (v) There exists a geometric interpretation to the color confinement of quarks. In the affine connection representation, we can get better interpretations to the above physical properties; therefore, to represent gauge fields by affine connection is probably a necessary step towards the ultimate theory of physics. [ABSTRACT FROM AUTHOR]

There are two ways to unify gravitational field and gauge field. One is to represent gravitational field as principal bundle connection, and the other is to represent gauge field as affine connection. Poincaré gauge theory and metric-affine gauge theory adopt the first approach. This paper adopts the second. In this approach, (i) gauge field and gravitational field can both be represented by affine connection; they can be described by a unified spatial frame. (ii) Time can be regarded as the total metric with respect to all dimensions of internal coordinate space and external coordinate space. On-shell can be regarded as gradient direction. Quantum theory can be regarded as a geometric theory of distribution of gradient directions. Hence, gauge theory, gravitational theory, and quantum theory all reflect intrinsic geometric properties of manifold. (iii) Coupling constants, chiral asymmetry, PMNS mixing, and CKM mixing arise spontaneously as geometric properties in affine connection representation, so they are not necessary to be regarded as direct postulates in the Lagrangian anymore. (iv) The unification theory of gauge fields that are represented by affine connection can avoid the problem that a proton decays into a lepton in theories such as S U 5 . (v) There exists a geometric interpretation to the color confinement of quarks. In the affine connection representation, we can get better interpretations to the above physical properties; therefore, to represent gauge fields by affine connection is probably a necessary step towards the ultimate theory of physics. [ABSTRACT FROM AUTHOR]

There are two ways to unify gravitational field and gauge field. One is to represent gravitational field as principal bundle connection, and the other is to represent gauge field as affine connection. Poincaré gauge theory and metric-affine gauge theory adopt the first approach. This paper adopts the second. In this approach, (i) gauge field and gravitational field can both be represented by affine connection; they can be described by a unified spatial frame. (ii) Time can be regarded as the total metric with respect to all dimensions of internal coordinate space and external coordinate space. On-shell can be regarded as gradient direction. Quantum theory can be regarded as a geometric theory of distribution of gradient directions. Hence, gauge theory, gravitational theory, and quantum theory all reflect intrinsic geometric properties of manifold. (iii) Coupling constants, chiral asymmetry, PMNS mixing, and CKM mixing arise spontaneously as geometric properties in affine connection representation, so they are not necessary to be regarded as direct postulates in the Lagrangian anymore. (iv) The unification theory of gauge fields that are represented by affine connection can avoid the problem that a proton decays into a lepton in theories such as S U 5 . (v) There exists a geometric interpretation to the color confinement of quarks. In the affine connection representation, we can get better interpretations to the above physical properties; therefore, to represent gauge fields by affine connection is probably a necessary step towards the ultimate theory of physics. [ABSTRACT FROM AUTHOR]

There are two ways to unify gravitational field and gauge field. One is to represent gravitational field as principal bundle connection, and the other is to represent gauge field as affine connection. Poincaré gauge theory and metric-affine gauge theory adopt the first approach. This paper adopts the second. In this approach, (i) gauge field and gravitational field can both be represented by affine connection; they can be described by a unified spatial frame. (ii) Time can be regarded as the total metric with respect to all dimensions of internal coordinate space and external coordinate space. On-shell can be regarded as gradient direction. Quantum theory can be regarded as a geometric theory of distribution of gradient directions. Hence, gauge theory, gravitational theory, and quantum theory all reflect intrinsic geometric properties of manifold. (iii) Coupling constants, chiral asymmetry, PMNS mixing, and CKM mixing arise spontaneously as geometric properties in affine connection representation, so they are not necessary to be regarded as direct postulates in the Lagrangian anymore. (iv) The unification theory of gauge fields that are represented by affine connection can avoid the problem that a proton decays into a lepton in theories such as S U 5 . (v) There exists a geometric interpretation to the color confinement of quarks. In the affine connection representation, we can get better interpretations to the above physical properties; therefore, to represent gauge fields by affine connection is probably a necessary step towards the ultimate theory of physics. [ABSTRACT FROM AUTHOR]

Inspired by Laughlin's theory of the fractional quantum Hall effect, we explore the topological nature of the quark–gluon plasma (QGP) and the nucleons in the context of the Clifford algebra. In our model, each quark is transformed into a composite particle via the simultaneous attachment of a spin monopole and an isospin monopole. This is induced by a novel kind of meson endowed with both spin and isospin degrees of freedom. The interactions in the strongly coupled quark–gluon system are governed by the topological winding number of the monopoles, which is an odd integer to ensure that the overall wave function is antisymmetric. The states of the QGP and the nucleons are thus uniquely determined by the combination of the monopole winding number m and the total quark number N. The radius squared of the QGP droplet is expected to be proportional to m N. We anticipate the observation of such proportionality in the heavy ion collision experiments. [ABSTRACT FROM AUTHOR]

We discuss our present knowledge of α s , the fundamental running coupling or effective charge of Quantum Chromodynamics (QCD). A precise understanding of the running of α s (Q 2) at high momentum transfer, Q , is necessary for any perturbative QCD calculation. Equally important, the behavior of α s at low Q 2 in the nonperturbative QCD domain is critical for understanding strong interaction phenomena, including the emergence of mass and quark confinement. The behavior of α s (Q 2) at all momentum transfers also provides a connection between perturbative and nonperturbative QCD phenomena, such as hadron spectroscopy and dynamics. We first sketch the origin of the QCD coupling, the reason why its magnitude depends on the scale at which hadronic phenomena are probed, and the resulting consequences for QCD phenomenology. We then summarize latest measurements in both the perturbative and nonperturbative domains. New theory developments include the derivation of the universal nonperturbative behavior of α s (Q 2) from both the Dyson–Schwinger equations and light-front holography. We also describe theory advances for the calculation of gluon and quark Schwinger functions in the nonperturbative domain and the relation of these quantities to α s. We conclude by highlighting how the nonperturbative knowledge of α s is now providing a parameter-free determination of hadron spectroscopy and structure, a central and long-sought goal of QCD studies. [ABSTRACT FROM AUTHOR]

The octonion algebra is analyzed using a formalism that demonstrates its use in color quark confinement. In this study, we attempt to write a connection between octonion algebra and SU(3) c group generators, as well as color quarks representation. We demonstrated the glueballs construction in the extended octonionic color field and also proposed the prerequisite for octonion color confinement of hadrons. [ABSTRACT FROM AUTHOR]

Chiral dynamics is investigated using the chiral confining Lagrangian (CCL), previously derived from QCD with confinement interaction. Based on the calculations of the quark condensate, which is defined entirely by confinement in the zero quark mass limit, one can assert that chiral symmetry breaking is predetermined by confinement. It is shown that CCL retains all basic relations of the standard chiral theory but enables one to include quark degrees of freedom in the CCL. The expansion of the CCL provides the Gell–Mann–Oakes–Renner (GMOR) relations and the masses and decay constants of all chiral mesons, including η , η ′ . For the latter, one needs to define a nonchiral component due to confinement, while the orthogonality condition defines the wave functions and the eigenvalues. The resulting masses and decay constants of all chiral mesons are obtained in good agreement with the experimental and lattice data. [ABSTRACT FROM AUTHOR]

Quantum chromodynamics is the fundamental theory to describe strong interaction, where quarks and gluons have the color degrees of freedom. However, a single quark or gluon cannot be separated out and all observable particles are color singlet states. Color confinement or quark confinement conjecture can be proved by considering not only the strong interaction but also the electroweak interaction, which is the SU (3) c invariant. Any measurable state that has to be a color singlet is the direct consequence of the common symmetry of the standard model. Color non-singlet objects are created from the big bang when the interaction breaks SU (3) c symmetry based on the non-local Lagrangian. There is nearly no interaction between colored objects and the color singlet Universe when the momentum transfer is not large enough. Colored objects are reasonable candidates of dark matter and the missing anti-matter in the Universe can also be easily explained. Dark matter can be produced in a laboratory, which can be tested by measuring the energy loss and baryon number change in the extremely high energy collisions of particles and anti-particles. [ABSTRACT FROM AUTHOR]

We find a novel confinement mechanism in the two-flavor dense quark matter proposed recently, that consists of the 2SC condensates and the P-wave diquark condensates of d-quarks. This quark matter exhibiting color superconductivity as well as superfluidity is classified into two phases; confined and deconfined phases of vortices. We establish that the criterion of the confinement is color neutrality of Aharonov-Bohm (AB) phases: vortices exhibiting color non-singlet AB phases are confined by the so-called AB defects to form color-singlet bound states. In the deconfined phase, the most stable vortices are non-Abelian Alice strings, which are superfluid vortices with fractional circulation and non-Abelian color magnetic fluxes therein, exhibiting color non-singlet AB phases. On the other hand, in the confined phase, these non-Abelian vortices are confined to either a baryonic or mesonic bound state in which constituent vortices are connected by AB defects. The baryonic bound state consists of three non-Abelian Alice strings with different color magnetic fluxes with the total flux canceled out connected by a domain wall junction, while the mesonic bound state consists of two non-Abelian Alice strings with the same color magnetic fluxes connected by a single domain wall. Interestingly, the latter contains a color magnetic flux in its core, but this can exist because of color neutrality of its AB phase. [ABSTRACT FROM AUTHOR]

Quantum chromodynamics (QCD), the theory of the strong interactions, involves quarks interacting with non-Abelian gluon fields. This theory has many features that are difficult to impossible to see in conventional diagrammatic perturbation theory. This includes quark confinement, mass generation and chiral symmetry breaking. This paper is a colloquium level overview of the framework for understanding how these effects come about. [ABSTRACT FROM AUTHOR]

The confinement of quarks is one of the enduring mysteries of modern physics. There is a longstanding physics heuristic that confinement is a consequence of 'unbroken center symmetry'. This article gives mathematical confirmation of this heuristic, by rigorously defining of center symmetry in lattice gauge theories and proving that a theory is confining when center symmetry is unbroken. Furthermore, a sufficient condition for unbroken center symmetry is given: It is shown that if the center of the gauge group is nontrivial, and correlations decay exponentially under arbitrary boundary conditions, then center symmetry does not break. [ABSTRACT FROM AUTHOR]

Based on the Pomeranchuk theorem, one constructs the δ (s) parameter to measure the difference between experimental data for the particle–particle and particle–antiparticle total cross-section at same energy. The experimental data for the proton–proton and proton–antiproton total cross-section were used to show that, at the same energy, this parameter tends to zero as the collision energy grows. Furthermore, one assumes a classical description for the total cross-section, dividing it into a finite number of non-interacting disjoint cells, each one containing a quark–antiquark pair subject to the confinement potential. Near the minimum of the total cross-section, one associates δ (s) with the entropy generated by these cells, analogously to the X Y -model. Using both the Quigg–Rosner and Cornell confinement potentials and neglecting other energy contributions, one can calculate the internal energy of the hadron. One obtains that both the entropy and internal energy possess the same logarithmic dependence on the spatial separation between the pairs in the cell. The Helmholtz free energy is used to estimate the transition temperature, which is far from the temperature widely related to the Quark–Gluon Plasma. [ABSTRACT FROM AUTHOR]

The confinement problem is studied using the thick center vortex model. It is shown that the S U (3) Cartan subalgebra of the decomposed G (2) gauge theory can play an important role in the confinement. The Casimir eigenvalues and ratios of the G (2) representations are obtained using its decomposition to the S U (3) subgroups. This leads to the conjecture that the S U (3) subgroups also can explain the G (2) properties of the confinement. The thick center vortex model for the S U (3) subgroups of the G (2) gauge theory is applied without the domain modification. Instead, the presence of two S U (3) vortices with opposite fluxes due to the possibility of decomposition of the G (2) Cartan subalgebra to the S U (3) groups can explain the properties of the confinement of the G (2) group both at intermediate and asymptotic distances which is studied here. [ABSTRACT FROM AUTHOR]

Above the pseudocritical temperature T c of chiral symmetry restoration a chiral spin symmetry (a symmetry of the color charge and of electric confinement) emerges in QCD. This implies that QCD is in a confining mode and there are no free quarks. At the same time correlators of operators constrained by a conserved current behave as if quarks were free. This explains observed fluctuations of conserved charges and the absence of the rho-like structures seen via dileptons. An independent evidence that one is in a confining mode is very welcome. Here we suggest a new tool how to distinguish free quarks from a confining mode. If we put the system into a finite box, then if the quarks are free one necessarily obtains a remarkable diffractive pattern in the propagator of a conserved current. This pattern is clearly seen in a lattice calculation in a finite box and it vanishes in the infinite volume limit as well as in the continuum. In contrast, the full QCD calculations in a finite box show the absence of the diffractive pattern implying that the quarks are confined. [ABSTRACT FROM AUTHOR]

We extend earlier work by introducing an Einstein–Maxwell–Dilaton (EMD) action with two quark flavours. We solve the corresponding equations of motion in the quenched approximation (probe quark flavours) via the potential reconstruction method in presence of a background magnetic field in search for a self-consistent dual magnetic AdS/QCD model. As an application we discuss the deconfinement transition temperature confirming inverse magnetic catalysis, whilst for moderate values of the magnetic field also the entropy density compares relatively well with corresponding lattice data in the vicinity of the transition. [ABSTRACT FROM AUTHOR]

We investigate the contributions of the Cartan generators in the static potentials for various representations in the framework of the domain model of center vortices for SU(3) gauge theory. Using the center domains with the cores corresponding to only one Cartan generator H 8 , already given as a particular proposal, leads to some concavities in the potentials for higher representations. Furthermore, the string tension of the fundamental representation is the same at Casimir scaling and N -ality regimes. We add the contribution of the other Cartan generator H 3 to the potentials and therefore these shortcomings can be eliminated. However, we discuss that at intermediate range of distances the potentials induced by only H 8 agree with the Casimir scaling better than those corresponding to both Cartan generators. [ABSTRACT FROM AUTHOR]

We present new linear relations among the masses of S-wave tetraquarks with either one flavour (Q Q Q ¯ Q ¯) or two (Q Q q ¯ q ¯). Because the relations are sensitive to the hidden-colour, spin, and spatial degrees of freedom, comparison to experimental data can help to reveal the internal structure of tetraquarks, and discriminate among different theoretical models. Depending on the model, the relations are either exact, or valid in perturbation theory, and a thorough comparison with existing literature confirms their validity at the MeV level. Additionally, we explore the connections among tetraquark models, and show how those with effective (quark or diquark) masses are related to dynamical potential models. We also show how the spectrum of diquark models is effectively a limiting case of (more general) quark models, and in particular, that the diquark concept is most relevant in the particular combination Q Q q ¯ q ¯ , where Q is much heavier than q ¯. [ABSTRACT FROM AUTHOR]

We derive the low-energy limit of quantum chromodynamics (QCD) and provide evidence that in the 't Hooft limit, i.e. for a very large number of colors and increasing 't Hooft coupling, quark confinement is recovered. The low energy limit of the theory turns out to be a non-local Nambu–Jona-Lasinio (NJL) model. The effect of non-locality, arising from a gluon propagator that fits quite well to the profile of an instanton liquid, is to produce a phase transition from a chiral condensate to an instanton liquid, as the coupling increases with lower momentum. This phase transition suffices to move the poles of the quark propagator to the complex plane. As a consequence, free quarks are no longer physical states in the spectrum of the theory. [ABSTRACT FROM AUTHOR]

Several observations of high-mass neutron stars (NSs), as well as the first historic detection of the binary neutron star merger GW170817, have delivered stringent constraints on the equation of state (EoS) of cold and dense matter. Recent studies suggest that, in order to simultaneously accommodate a 2M⊙ NS and the upper limit on the compactness, the pressure has to swiftly increase with density and the corresponding speed of sound likely exceeds the conformal limit. In this work, we employ a unified description of hadron-quark matter, the hybrid quark-meson-nucleon (QMN) model, to investigate the EoS under NS conditions. We show that the dynamical confining mechanism of the model plays an important role in explaining the observed properties of NSs. [ABSTRACT FROM AUTHOR]

The topical workshop Strong QCD from Hadron Structure Experiments took place at Jefferson Lab from November 6–9, 2019. Impressive progress in relating hadron structure observables to the strong QCD mechanisms has been achieved from the ab initio QCD description of hadron structure in a diverse array of methods in order to expose emergent phenomena via quasi-particle formation. The wealth of experimental data and the advances in hadron structure theory make it possible to gain insight into strong interaction dynamics in the regime of large quark–gluon coupling (the strong QCD regime), which will address the most challenging problems of the Standard Model on the nature of the dominant part of hadron mass, quark–gluon confinement, and the emergence of the ground and excited state hadrons, as well as atomic nuclei, from QCD. This workshop aimed to develop plans and to facilitate the future synergistic efforts between experimentalists, phenomenologists, and theorists working on studies of hadron spectroscopy and structure with the goal to connect the properties of hadrons and atomic nuclei available from data to the strong QCD dynamics underlying their emergence from QCD. These results pave the way for a future breakthrough extension in the studies of QCD with an Electron–Ion Collider in the U.S. [ABSTRACT FROM AUTHOR]

We use functional methods to compute one-loop effects in Heavy Quark Effective Theory. The covariant derivative expansion technique facilitates the efficient extraction of matching coefficients and renormalization group evolution equations. This paper pro- vides the first demonstration that such calculations can be performed through the algebraic evaluation of the path integral for the class of effective field theories that are (i) constructed using a non-trivial one-to-many mode decomposition of the UV theory, and (ii) valid for non-relativistic kinematics. We discuss the interplay between operators that appear at intermediate steps and the constraints imposed by the residual Lorentz symmetry that is encoded as reparameterization invariance within the effective description. The tools presented here provide a systematic approach for computing corrections to higher order in the heavy mass expansion; precision applications include predictions for experimental data and connections to theoretical tests via lattice QCD. A set of pedagogical appendices comprehensively reviews modern approaches to performing functional calculations algebraically, and derives contributions from a term with open covariant derivatives for the first time. [ABSTRACT FROM AUTHOR]

We use top-down holography to study the thermodynamics of a one-parameter family of three-dimensional, strongly coupled Yang-Mills-Chern-Simons theories with M-theory duals. For generic values of the parameter, the theories exhibit a mass gap but no confinement, meaning no linear quark-antiquark potential. For two specific values of the parameter they flow to an infrared fixed point or to a confining vacuum, respectively. As in the Klebanov-Strassler solution, on the gravity side the mass gap is generated by the smooth collapse to zero size of a cycle in the internal geometry. We uncover a rich phase diagram with thermal phase transitions of first and second order, a triple point and a critical point. [ABSTRACT FROM AUTHOR]

Hydrodynamics of the non-relativistic compressible fluid in the curved spacetime is derived using the generalized framework of the stochastic variational method (SVM) for continuum medium. The fluid-stress tensor of the resultant equation becomes asymmetric for the exchange of the indices, different from the standard Euclidean one. Its incompressible limit suggests that the viscous term should be represented with the Bochner Laplacian. Moreover the modified Navier–Stokes–Fourier equation proposed by Brenner can be considered even in the curved spacetime. To confirm the compatibility with the symmetry principle, SVM is applied to the gauge-invariant Lagrangian of a charged compressible fluid and then the Lorentz force is reproduced as the interaction between the Abelian gauge fields and the viscous charged fluid. [ABSTRACT FROM AUTHOR]