Search Results (7)

Using a Dyson–Schwinger approach, we perform an analysis of the non-trivial ground state of thermal $SU\left(N\right)$ Yang–Mills theory in the non-perturbative regime where chiral symmetry is dynamically broken by a mass gap. Basic thermodynamic observables such as energy density and pressure are derived analytically, using Jacobi elliptic functions. The results are compared with the lattice results. Good agreement is found at low temperatures, providing a viable scenario for a gas of massive glue states populating higher levels of the spectrum of the theory. At high temperatures, a scenario without glue states consistent with a massive scalar field is observed, showing an interesting agreement with lattice data. The possibility is discussed that the results derived in this analysis open up a novel pathway beyond lattice to precision studies of phase transitions with false vacuum and cosmological relics that depend on the equations of state in strong coupled gauge theories of the type of Quantum Chromodynamics (QCD). Full article

We suggest a new solution to the strong CP problem. The solution is based on the proper use of the boundary conditions for the QCD-generating functional integral. We expand the perturbative boundary conditions to both perturbative and nonperturbative fields integrated into the QCD-generating functional integral. It allows us to nullify the CP odd term in the QCD Lagrangian and, thus, to solve the strong CP problem. The presently popular solution to the strong CP problem of introducing axions violates the principle of renormalizability of the Quantum Field Theory, which is very successful phenomenologically. Our solution obeys the principle of renormalizability of the Quantum Field Theory and does not involve new exotic particles like axions. Full article

Understanding the strong interaction dynamics that govern the emergence of hadron mass (EHM) represents a challenging open problem in the Standard Model. In this paper we describe new opportunities for gaining insight into EHM from results on nucleon resonance ($N^{*}$) electroexcitation amplitudes (i.e., ${\gamma }_{v}p{N}^{*}$ electrocouplings) in the mass range up to 1.8 GeV for virtual photon four-momentum squared (i.e., photon virtualities $Q^2$) up to 7.5 GeV${}^2$ available from exclusive meson electroproduction data acquired during the 6-GeV era of experiments at Jefferson Laboratory (JLab). These results, combined with achievements in the use of continuum Schwinger function methods (CSMs), offer new opportunities for charting the momentum dependence of the dressed quark mass from results on the $Q^2$-evolution of the ${\gamma }_{v}p{N}^{*}$ electrocouplings. This mass function is one of the three pillars of EHM and its behavior expresses influences of the other two, viz. the running gluon mass and momentum-dependent effective charge. A successful description of the $\Delta \left(1232\right)3/2^{+}$ and $N\left(1440\right)1/2^{+}$ electrocouplings has been achieved using CSMs with, in both cases, common momentum-dependent mass functions for the dressed quarks, for the gluons, and the same momentum-dependent strong coupling. The properties of these functions have been inferred from nonperturbative studies of QCD and confirmed, e.g., in the description of nucleon and pion elastic electromagnetic form factors. Parameter-free CSM predictions for the electrocouplings of the $\Delta \left(1600\right)3/2^{+}$ became available in 2019. The experimental results obtained in the first half of 2022 have confirmed the CSM predictions. We also discuss prospects for these studies during the 12-GeV era at JLab using the CLAS12 detector, with experiments that are currently in progress, and canvass the physics motivation for continued studies in this area with a possible increase of the JLab electron beam energy up to 22 GeV. Such an upgrade would finally enable mapping of the dressed quark mass over the full range of distances (i.e., quark momenta) where the dominant part of hadron mass and $N^{*}$ structure emerge in the transition from the strongly coupled to perturbative QCD regimes. Full article

The interplay of chiral dynamics and gluodynamics plays an essential role in the nonperturbative QCD region, and the chiral phase transition and deconfinement phase transition are the main topics of QCD phase transitions under extreme conditions, e.g., finite temperature and/or baryon density, strong magnetic fields, and fast rotation. We briefly introduce our own recent progress from the theoretical side on QCD phase transitions and phase diagrams under extreme conditions related to the early universe, compact stars, and heavy-ion collisions. Full article

The QCD effective charge ${\alpha }_{g_1}\left(Q\right)$ is an observable that characterizes the magnitude of the strong interaction. At high momentum Q, it coincides with the QCD running coupling ${\alpha }_{\mathrm{s}}\left(Q\right)$. At low Q, it offers a nonperturbative definition of the running coupling. We have extracted ${\alpha }_{g_1}\left(Q\right)$ from measurements carried out at Jefferson Lab that span the very low to moderately high Q domain, $0.14\le Q\le 2.18$ GeV. The precision of the new results is much improved over the previous extractions and the reach in Q at the lower end is significantly expanded. The data show that ${\alpha }_{g_1}\left(Q\right)$ becomes Q-independent at very low Q. They compare well with two recent predictions of the QCD effective charge based on Dyson–Schwinger equations and on the AdS/CFT duality. Full article

Quantum chromodynamics (QCD) is the theory of strong interactions of quarks and gluons collectively called partons, the basic constituents of all nuclear matter. Its non-abelian character manifests in nature in the form of two remarkable properties: color confinement and asymptotic freedom. At high energies, perturbation theory can result in the growth and dominance of very gluon densities at small-x. If left uncontrolled, this growth can result in gluons eternally growing violating a number of mathematical bounds. The resolution to this problem lies by balancing gluon emissions by recombinating gluons at high energies: phenomena of gluon saturation. High energy nuclear and particle physics experiments have spent the past decades quantifying the structure of protons and nuclei in terms of their fundamental constituents confirming predicted extraordinary behavior of matter at extreme density and pressure conditions. In the process they have also measured seemingly unexpected phenomena. We will give a state of the art review of the underlying theoretical and experimental tools and measurements pertinent to gluon saturation physics. We will argue for the need of high energy electron-proton/ion colliders such as the proposed EIC (USA) and LHeC (Europe) to consolidate our knowledge of QCD knowledge in the small x kinematic domains. Full article

The Lagrangian that defines quantum chromodynamics (QCD), the strong interaction piece of the Standard Model, appears very simple. Nevertheless, it is responsible for an astonishing array of high-level phenomena with enormous apparent complexity, e.g., the existence, number and structure of atomic nuclei. The source of all these things can be traced to emergent mass, which might itself be QCD’s self-stabilising mechanism. A background to this perspective is provided, presenting, inter alia, a discussion of the gluon mass and QCD’s process-independent effective charge and highlighting an array of observable expressions of emergent mass, ranging from its manifestations in pion parton distributions to those in nucleon electromagnetic form factors. Full article