arXiv subjects

J. M. Morgado

Publications and source records attributed to J. M. Morgado.

7 recordsLinked to original sources

arXiv2026

Real poles with opposite-sign residues in the non-perturbative quark propagator

We investigate the analytic structure of the quark propagator in the Landau gauge by dynamically coupling the standard gap equation to the non-perturbative quark-gluon vertex. Employing the full vertex basis, we demonstrate that for sub-GeV time-like momenta, the proper inclusion of the underlying dynamics leads to a pair of real poles with opposite-sign residues. In particular, in stark contradistinction to the results obtained in widely used approximations, we see no sign of complex conjugate poles. This distinctive analytic structure evades conceptual shortcomings frequently associated with complex conjugate poles while remaining fully compatible with the aspects of color confinement related to positivity violation. Crucially, this novel behavior is governed by a dominant triplet of vertex form factors: the tree-level component, the anomalous chromomagnetic moment, and a component we label as "spin-momentum curvature". By gradually tuning the individual strengths of these components, we demonstrate that while they contribute in distinct ways to the quark propagator, their joint action is vital for stabilizing the system. Together, they place the low-lying poles onto the real axis while producing a robust constituent quark mass of $350$ MeV.

hep-ph↗

arXiv2026

Quark-gluon vertex in the complex plane

In the present work we explore for the first time the general structure and properties of the nonperturbative quark-gluon vertex in the complex plane. Specifically, we focus on the transversely-projected quark-gluon vertex that emerges from a recently developed symmetry-preserving approach for the study of meson properties beyond the rainbow-ladder approximation. The analysis focuses on the so-called "soft-gluon" limit, which reduces the momentum-dependence of the corresponding vertex form factors to a single momentum variable. The complexification of this variable inside the defining integrals furnishes unambiguously all eight vertex form factors within a concrete domain of the complex variable, delimited by a characteristic parabola. The extent of this reliable domain is determined by the appearance of the first singularity in the integrands of the vertex integrals, where the standard Wick rotation must be duly supplemented by additional crucial contributions. This primary analytic region may be extended considerably by resorting to standard extrapolation methods, which remain valid up until the appearance of complex structures associated with the onset of physical processes. The generalization of the method to arbitrary gluon momenta, and its relevance for the determination of the quark propagator in the complex plane, are briefly discussed.

hep-ph↗

arXiv2026

Light mesons in the symmetric-vertex approximation

We compute the spectrum of light mesons, composed by up, down, and strange quarks, using a symmetry-preserving approximation that permits the inclusion of fully-dressed quark-gluon vertices in the key dynamical equations. This method is characterized by the use of the standard symmetric kinematic configuration as a seed in the corresponding Schwinger-Dyson equation, yielding finally the full kinematic dependence of all eight form factors composing the transversely-projected quark-gluon vertex. The extension of this approach to the case of distinct nonvanishing current quark masses is discussed, and the compatibility with the fundamental Ward-Takahashi identities demonstrated. The corresponding Bethe-Salpeter kernel is composed by three different diagrammatic structures, which may be deduced from the attendant quark gap equation by applying the standard "cutting" rules. The masses of the light mesons are computed by first determining the eigenvalue of the Bethe-Salpeter equation as a function of Euclidean momenta, and then using the Schlessinger extrapolation method to determine the Minkowski momentum for which this eigenvalue becomes unity. The resulting meson masses are in good agreement with experimental values, and substantially improve upon predictions from the rainbow-ladder approximation.

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arXiv2026

Pions reloaded

We present a novel version of the pion Bethe-Salpeter equation in the chiral limit, solved using as ingredients state-of-the-art QCD correlation functions. The constraints imposed by the axial Ward-Takahashi identities are exactly fulfilled, both formally and numerically.

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arXiv2026

Baryonic form factors of light pseudoscalar mesons

Employing the Bethe-Salpeter formalism, we present a computation of the space-like baryonic form factor for the pion and kaon. In the exact isospin-symmetric limit this observable is forbidden by $G$-parity, so that any nonzero signal constitutes a direct probe of the quark mass difference $m_d - m_u$. The form factors are evaluated in the impulse approximation using fully dressed quark propagators, meson Bethe-Salpeter amplitudes, and a dressed baryon-current vertex constrained by the vector Ward-Takahashi identity. The baryonic radius computed with this method for the pion is given by $\langle r_{\! B}^2\rangle_{π^+}^{1/2} = 0.043(2)$ fm, and is consistent with the available dispersive benchmarks. Our predictions for the kaons, namely $\langle r_{\!B}^2\rangle_{K^+}^{1/2} = 0.265(7)$ fm and $\langle r_{\!B}^2\rangle_{K^0}^{1/2} = 0.262(7)$ fm, indicate a larger spatial extent than in the pion case; these results have no dispersive counterparts, and are compatible with chiral QCD models.

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arXiv2022

Emergence of pion parton distributions

Supposing only that there is an effective charge which defines an evolution scheme for parton distribution functions (DFs) that is all-orders exact, strict lower and upper bounds on all Mellin moments of the valence-quark DFs of pion-like systems are derived. Exploiting contemporary results from numerical simulations of lattice-regularised quantum chromodynamics (QCD) that are consistent with these bounds, parameter-free predictions for pion valence, glue, and sea DFs are obtained. The form of the valence-quark DF at large values of the light-front momentum fraction is consistent with predictions derived using the QCD-prescribed behaviour of the pion wave function.

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arXiv2021

Concerning pion parton distributions

Analyses of the pion valence-quark distribution function (DF), ${u}^π(x;ζ)$, which explicitly incorporate the behaviour of the pion wave function prescribed by quantum chromodynamics (QCD), predict ${u}^π(x\simeq 1;ζ) \sim (1-x)^{β(ζ)}$, $β(ζ\gtrsim m_p)>2$, where $m_p$ is the proton mass. Nevertheless, more than forty years after the first experiment to collect data suitable for extracting the $x\simeq 1$ behaviour of ${u}^π$, the empirical status remains uncertain because some methods used to fit existing data return a result for ${u}^π$ that violates this constraint. Such disagreement entails one of the following conclusions: the analysis concerned is incomplete; not all data being considered are a true expression of qualities intrinsic to the pion; or QCD, as it is currently understood, is not the theory of strong interactions. New, precise data are necessary before a final conclusion is possible. In developing these positions, we exploit a single proposition, viz. there is an effective charge which defines an evolution scheme for parton DFs that is all-orders exact. This proposition has numerous corollaries, which can be used to test the character of any DF, whether fitted or calculated.

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