A symmetry-preserving approach to the two valence-body continuum bound-state problem is used to calculate the elastic electromagnetic form factors of the $\rho$-meson and subsequently to study the evolution of vector-meson form factors with current-quark mass. To facilitate a range of additional comparisons, $K^{*}$ form factors are also computed. The analysis reveals that vector mesons are larger than pseudoscalar mesons; composite vector mesons are nonspherical, with magnetic and quadrupole moments that deviate $\sim 30\%$ from point-particle values; in many ways, vector-meson properties are as much influenced by emergent mass as those of pseudoscalars; and vector-meson electric form factors possess a zero at spacelike momentum transfer. Qualitative similarities between the electric form factors of the $\rho$ and the proton, $G_E^p$, are used to argue that the character of emergent mass in the Standard Model can force a zero in $G_E^p$. Moreover, the existence of a zero in vector-meson electric form factors entails that a single-pole vector-meson dominance model can only be of limited use in estimating properties of off-shell vector mesons, providing poor guidance for systems in which the Higgs mechanism of mass generation is dominant.

A class of Polyakov-loop-modified Nambu–Jona-Lasinio models has been used to support a conjecture that numerical simulations of lattice-regularized QCD defined with a chiral chemical potential can provide information about the existence and location of a critical end point in the QCD phase diagram drawn in the plane spanned by baryon chemical potential and temperature. That conjecture is challenged by conflicts between the model results and analyses of the same problem using simulations of lattice-regularized QCD (lQCD) and well-constrained Dyson-Schwinger equation (DSE) studies. We find the conflict is resolved in favor of the lQCD and DSE predictions when both a physically motivated regularization is employed to suppress the contribution of high-momentum quark modes in the definition of the effective potential connected with the Polyakov-loop-modified Nambu–Jona-Lasinio models and the four-fermion coupling in those models does not react strongly to changes in the mean field that is assumed to mock-up Polyakov-loop dynamics. With the lQCD and DSE predictions thus confirmed, it seems unlikely that simulations of lQCD with ${\mu }_5>0$ can shed any light on a critical end point in the regular QCD phase diagram.

We describe a calculation of the spectrum of flavor-$\text{SU}\left(3\right)$ octet and decuplet baryons, their parity partners, and the radial excitations of these systems, made using a symmetry-preserving treatment of a vector $\times$ vector contact interaction as the foundation for the relevant few-body equations. Dynamical chiral symmetry breaking generates nonpointlike diquarks within these baryons and hence, using the contact interaction, flavor-antitriplet scalar, pseudoscalar, vector, and flavor-sextet axial-vector quark-quark correlations can all play active roles. The model yields reasonable masses for all systems studied and Faddeev amplitudes for ground states and associated parity partners that sketch a realistic picture of their internal structure: ground-state, even-parity baryons are constituted, almost exclusively, from like-parity diquark correlations, but orbital angular momentum plays an important role in the rest-frame wave functions of odd-parity baryons, whose Faddeev amplitudes are dominated by odd-parity diquarks.

We study the chirally imbalanced hot and dense strongly interacting matter by means of the Dyson-Schwinger equations (DSEs). The chiral phase diagram is studied in the presence of chiral chemical potential μ ₅. The chiral quark condensate $$ \left\langle \overline{\psi}\psi \right\rangle $$ ψ ¯ ψ is obtained with the Cornwall-Jackiw-Tomboulis (CJT) effective action in concert with the Rainbow truncation. Catalysis effect of dynamical chiral symmetry breaking (DCSB) by μ ₅ is observed. We examine with two popular gluon models and consistency is found within the DSE approach, as well as in comparison with lattice QCD. The critical end point (CEP) location (μ _E , T _E ) shifts toward larger T _E but constant μ _E as μ ₅ increases. A technique is then introduced to compute the chiral charge density n ₅ from the fully dressed quark propagator. We find the n ₅ generally increases with temperature T , quark number chemical potential μ and μ ₅. Since the chiral magnetic effect (CME) is typically investigated with peripheral collisions, we also investigate the finite size effect on n ₅ and find an increase in n ₅ with smaller system size.

Within the framework of Dyson–Schwinger equations (DSEs), we discuss the equation of state (EOS) and quark number densities of 2+1 flavors, that is to say, $u$ , $d$ , and $s$ quarks. The chemical equilibrium and electric charge neutrality conditions are used to constrain the chemical potential of different quarks. The EOS in the cases of 2 flavors and 2+1 flavors are discussed, and the quark number densities, the pressure, and energy density per baryon are also studied. The results show that there is a critical chemical potential for each flavor of quark, at which the quark number density turns to nonzero from 0; and furthermore, the system with 2+1 flavors of quarks is more stable than that with 2 flavors in the system. These discussions may provide some useful information to some research fields, such as the studies related to the QCD phase transitions or compact stars.