We employ a continuum approach to the three valence-quark bound-state problem in relativistic quantum field theory to predict a range of properties of the proton's radial excitation and thereby unify them with those of numerous other hadrons. Our analysis indicates that the nucleon's first radial excitation is the Roper resonance. It consists of a core of three dressed-quarks, which expresses its valence-quark content and whose charge radius is 80% larger than the proton analogue. That core is complemented by a meson cloud, which reduces the observed Roper mass by roughly 20%. The meson cloud materially affects long-wavelength characteristics of the Roper electroproduction amplitudes but the quark core is revealed to probes with Q 2 3m 2 N .

We describe a calculation of the spectrum of flavour-SU (3) octet and decuplet baryons, their parity partners, and the radial excitations of these systems, made using a symmetry-preserving treatment of a vector × 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, flavour-antitriplet scalar, pseudoscalar and vector, and flavour-sextet axial-vector quark-quark correlations can all play an active role. 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.

Using a confining, symmetry-preserving regularisation of a vector×vector contact interaction, we compute the spectra of ground-state pseudoscalar and vector (fḡ) mesons, scalar and axial-vector (f g) diquarks, and J P = 1/2 + , 3/2 + (f gh) baryons, where f, g, h ∈ {u, d, s, c, b}. The diquark correlations are essentially dynamical and play a key role in formulating and solving the threevalence-quark baryon problems. The baryon spectrum obtained from this largely-algebraic approach reproduces the 22 known experimental masses with an accuracy of 2.9(2.4)%. It also possesses the richness of states typical of constituent-quark models, predicting many heavy-quark baryons not yet observed. This study indicates that diquark correlations are an important component of all baryons; and owing to the dynamical character of the diquarks, it is typically the lightest allowed diquark correlation which defines the most important component of a baryon's Faddeev amplitude. *

A symmetry-preserving approach to the two valence-body continuum bound-state problem is used to calculate the elastic electromagnetic form factors of the ρ-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 non-spherical, with magnetic and quadrupole moments that deviate ∼ 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 ρ and the proton, G p E , are used to argue that the character of emergent mass in the Standard Model can force a zero in G p E . Morover, 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. *

Within the framework of Dyson-Schwinger equations , we discuss the chiral phase transition of QCD with a chiral chemical potential μ 5 as an additional scale. We focus especially on the issues related to the widely accepted as well as interesting critical end point (CEP). With the help of a scalar susceptibility, we find that there might be no CEP 5 in the T − μ 5 plane, and the phase transition in the T − μ 5 plane might be totally crossover when μ < 50 MeV, which has apparent consistency with the lattice QCD calculation. Our study may also provide some useful hints to some other studies related to μ 5 .