We extend earlier studies of transverse Ward-Fradkin-Green-Takahashi identities in QED, their usefulness to constrain the transverse fermion-boson vertex and their importance for multiplicative renormalizability, to the equivalent gauge identities in QCD. To this end, we consider transverse Slavnov-Taylor identities that constrain the transverse quark-gluon vertex and derive its eight associated scalar form factors. The complete vertex can be expressed in terms of the quark’s mass and wave-renormalization functions, the ghost-dressing function, the quark-ghost scattering amplitude and a set of eight form factors. The latter parametrize the hitherto unknown nonlocal tensor structure in the transverse Slavnov-Taylor identity which arises from the Fourier transform of a four-point function involving a Wilson line in coordinate space. We determine the functional form of these eight form factors with the constraints provided by the Bashir-Bermudez vertex and study the effects of this novel vertex on the quark in the Dyson-Schwinger equation using lattice QCD input for the gluon and ghost propagators. We observe significant dynamical chiral symmetry breaking and a mass gap that leads to a constituent mass of the order of 500 MeV for the light quarks. The flavor dependence of the mass and wave-renormalization functions as well as their analytic behavior on the complex momentum plane is studied and as an application we calculate the quark condensate and the pion’s weak decay constant in the chiral limit. Both are in very good agreement with their reference values.

We study the effect of a refined electron-photon vertex on the dynamical breaking of chiral symmetry in reduced quantum electrodynamics. We construct an educated ansatz for this vertex that satisfies the required discrete symmetries under parity, time reversal, and charge conjugation operations. Furthermore, it reproduces its asymptotic perturbative limit in the weak coupling regime and ensures the massless electron propagator is multiplicatively renormalizable in its leading logarithmic expansion. Employing this vertex ansatz, we solve the gap equation to compute dynamically generated electron mass whose dependence on the electromagnetic coupling is found to satisfy Miransky scaling law. We also investigate the gauge dependence of this dynamical mass as well as that of the critical coupling above which chiral symmetry is dynamically broken. As a litmus test of our vertex construction, both these quantities are rendered virtually gauge independent within a certain interval of values considered for the covariant gauge parameter.

We compute masses of twenty positive parity first radial excitations of spin- 1 / 2 and spin- 3 / 2 baryons composed of u , d , s , c , and b quarks in a quark-diquark picture within a contact interaction model. These excitations comprise of two elements; one characterized by a zero in the Faddeev amplitude, representing a radial excitation of the quark-diquark system and the other marked by a zero in the diquark’s Bethe-Salpeter amplitude, corresponding to an intrinsic excitation of the diquark correlation. Wherever possible, we compare our results with other models and/or experiment. We verify that the masses obtained through our model conform to the spacing rules for all the baryons studied, whether light or heavy and whether of spin- 1 / 2 or spin- 3 / 2 . The computed masses do not just offer a guide to the future experimental searches but also compare well with the existing candidates for the possible radial excitations of some heavy baryons. Published by the American Physical Society 2024

We recently reported new results on the γ ( * ) + N ( 940 ) 1 2 + → Δ ( 1700 ) 3 2 − transition form factors using a symmetry-preserving treatment of a vector ⊗ vector contact interaction (SCI) within a coupled formalism based on the Dyson-Schwinger, Bethe-Salpeter, and Faddeev equations. In this work, we extend our investigation to the γ ( * ) + N ( 940 ) 1 2 + → N ( 1520 ) 3 2 − transition. Our computed transition form factors show reasonable agreement with experimental data at large photon virtualities. However, deviations emerge at low Q 2 , where experimental results exhibit a sharper variation than theoretical predictions. This discrepancy is expected, as these continuum QCD analyses account only for the quark-core of baryons, while low photon virtualities are dominated by meson cloud effects. We anticipate that these analytical predictions, based on the simplified SCI framework, will serve as a valuable benchmark for more refined studies and QCD-based truncations that incorporate quark angular momentum and the contributions of scalar and vector diquarks.

We report novel theoretical results for the γ ( * ) + N ( 940 ) 1 2 + → Δ ( 1700 ) 3 2 − transition, utilizing a symmetry-preserving treatment of a vector ⊗ vector contact interaction (SCI) within the Dyson-Schwinger equation formalism. In this approach, both nucleon N ( 940 ) 1 2 + and Δ ( 1232 ) ’s parity partner Δ ( 1700 ) 3 2 − are treated as quark-diquark composites, with their internal structures governed accordingly by a tractable truncation of the Poincaré-covariant Faddeev equation. Nonpointlike quark + quark (diquark) correlations within baryons, which are deeply tied to the processes driving hadron mass generation, are inherently dynamic in the sense that they continually break apart and recombine guided by the Faddeev kernel. For the nucleon, isoscalar-scalar and isovector-axial-vector diquarks dominate, while the Δ ( 1700 ) 3 2 − state includes contributions only from isovector-axial-vector diquarks, because the SCI excludes isovector-vector diquarks. Once the Faddeev wave function of the baryons involved in the electromagnetic transition is normalized, taking into account that its elastic electric form factor must be one at the on-shell photon point, we compute the transition form factors that describe the γ ( * ) + N ( 940 ) 1 2 + → Δ ( 1700 ) 3 2 − reaction and, using algebraic relations, derive the corresponding helicity amplitudes. When comparing with experiment, our findings highlight a strong sensitivity of these observables to the internal structure of baryons, offering valuable insights. Although the SCI framework has obvious limitations, its algebraic simplicity provides analytical predictions that serve as useful benchmarks for guiding more refined studies within QCD-based Dyson-Schwinger equation frameworks.

We employ a recently proposed form-invariant algebraic model for the quark propagator and the Bethe-Salpeter amplitude of pseudoscalar mesons to study the internal structure of η and η ′ mesons. This model facilitates the construction of the Bethe-Salpeter wave function, whose projection onto an appropriate flavor basis leads to the light-front wave function for convenient linear combinations of the s s ¯ and l l ¯ ∼ ( u u ¯ + d d ¯ ) states. Using an overlap representation, we compute the valence-quark generalized parton distributions (GPDs). The construction of the model ensures that this multidimensional quantity is determined entirely by the corresponding valence-quark distribution amplitudes. Once the GPDs are constructed, we carry out a straightforward derivation of other desired physical observables, such as the distribution functions and the electromagnetic form factors. We also provide explicit comparisons with available results, demonstrating that the present model offers a consistent physical picture for all ground-state pseudoscalar mesons.