We use the worldline formalism to derive integral representations for three classes of amplitudes in scalar field theory: (i) the scalar propagator exchanging N momenta with a scalar background field (ii) the “half-ladder” with N rungs in x-space (iii) the four-point ladder with N rungs in x-space as well as in (off-shell) momentum space. In each case we give a compact expression combining the N! Feynman diagrams contributing to the amplitude. As our main application, we reconsider the well-known case of two massive scalars interacting through the exchange of a massless scalar. Applying asymptotic estimates and a saddle-point approximation to the N-rung ladder plus crossed ladder diagrams, we derive a semi-analytic approximation formula for the lowest bound state mass in this model.

An interesting class of background field configurations in quantum electrodynamics (QED) is the $O(2)\times O(3)$ symmetric fields, originally introduced by S. L. Adler in 1972. Those backgrounds have some instantonlike properties and yield a one-loop effective action that is highly nontrivial but amenable to numerical calculation. Here, we use the recently developed “partial-wave-cutoff method” for a full mass range numerical analysis of the effective action for the “standard” $O(2)\times O(3)$ symmetric field, modified by a radial suppression factor. At large mass, we are able to match the asymptotics of the physically renormalized effective action against the leading two mass levels of the inverse mass expansion. For small masses, with a suitable choice of the renormalization scheme, we obtain stable numerical results even in the massless limit. We analyze the $N$-point functions in this background and show that, even in the absence of the radial suppression factor, the two-point contribution to the effective action is the only obstacle to taking its massless limit. The standard $O(2)\times O(3)$ background leads to a chiral anomaly term in the effective action, and both our perturbative and nonperturbative results strongly suggest that the small-mass asymptotic behavior of the effective action is, after the subtraction of the two-point contribution, dominated by this anomaly term as the only source of a logarithmic mass dependence. This confirms a conjecture by M. Fry.

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.

We explore a phenomenological extension of the Polyakov–Nambu–Jona-Lasinio (PNJL) model by introducing a curvature-sensitive effective contribution to the Polyakov-loop potential, motivated by the hypothesis that the non-perturbative QCD vacuum in the confined phase may retain a residual sensitivity to cosmic expansion. In a spatially flat FLRW background, this modification reduces to a term proportional to $\alpha {(H/H_0)}^{d}f(\Phi ,{\Phi }^{*})$, which naturally vanishes in the deconfined regime and behaves as an effective dynamical vacuum component at late times, without invoking a fundamental cosmological constant. The construction provides an effective thermodynamic description of the QCD sector within an adiabatic framework and introduces a minimal phenomenological extension characterized by the exponent d and the amplitude parameter $\alpha$. We analyze the cosmological implications at the background level and compare the model with low-redshift observations, including cosmic chronometers, Type Ia supernovae, HII galaxies, and quasars. Using Bayesian Monte Carlo techniques, we constrain the model parameters and compare its performance with the ΛCDM. Our results indicate that the modified PNJL cosmology provides a statistically competitive fit to current data while allowing small departures from the ΛCDM within observational uncertainties. We also investigate the impact of the coupling on the QCD phase diagram and the critical end point. The framework offers a tractable effective approach to connect confinement physics with late-time cosmology and suggests directions for further theoretical development in QCD under curved backgrounds.

An interesting class of background field configurations in quantum electrodynamics (QED) are the O(2)xO(3) symmetric fields, originally introduced by S.L. Adler in 1972. Those backgrounds have some instanton-like properties and yield a one-loop effective action that is highly nontrivial, but amenable to numerical calculation. Here, we use the recently developed "partial-wave-cutoff method" for a full mass range numerical analysis of the effective action for the "standard" O(2)xO(3) symmetric field, modified by a radial suppression factor. At large mass, we are able to match the asymptotics of the physically renormalized effective action against the leading two mass levels of the inverse mass expansion. For small masses, with a suitable choice of the renormalization scheme we obtain stable numerical results even in the massless limit. We analyze the N - point functions in this background and show that, even in the absence of the radial suppression factor, the two-point contribution to the effective action is the only obstacle to taking its massless limit. The standard O(2)xO(3) background leads to a chiral anomaly term in the effective action, and both our perturbative and nonperturbative results strongly suggest that the small-mass asymptotic behavior of the effective action is, after the subtraction of the two-point contribution, dominated by this anomaly term as the only source of a logarithmic mass dependence. This confirms a conjecture by M. Fry.