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Fabio L. Braghin

Publications and source records attributed to Fabio L. Braghin.

At least 19 recordsLinked to original sources
arXiv2026

Effects of flavor-mixings on charged kaon and pion parton distribution functions

We investigate the charged kaon and pion parton distribution functions (PDFs) in the U(3) Nambu--Jona-Lasinio model, considering a novel flavor-mixing interaction arising from vacuum polarization that differs from the instanton-induced 't~Hooft interaction. In this work, the proper-time regularization scheme is employed, and, effectively, it might take quark confinement into account. The gap equations, the meson masses, and the meson--quark coupling constants are calculated in the presence of flavor-mixing interactions. The valence-quark distributions of the charged kaon and pion are calculated and compared with existing experimental data and Jefferson Lab Angular Momentum analysis results at scales $μ^{2} =$ 4 and 27 GeV$^{2}$. The strength of mixing effects on the PDFs is found to be proportional to the quark effective masses and their differences. We further find that the dominant flavor mixing effects in the pion valence up-quark distribution at scales $μ^{2} =$ 27 and 4 GeV$^2$ are around $x \simeq 0.3$ and $x \simeq 0.8$, while for the kaon, the effects are shown at around $x \simeq 0.2$ and $x \simeq 0.7$. We also find similar strength of mixing effects on the PDFs at both scales $μ^{2} =4$ and 27 GeV$^{2}$; however, it certainly improves the pion and kaon PDFs.

hep-ph↗
arXiv2026

Magnetic field induced anomalous pion couplings

Effective pion-constituent quark couplings induced by relatively weak magnetic fields are calculated in the framework based in Weinberg's large Nc Effective Field Theory. These couplings (form factors) vanish in the vacuum. In particular, single-pion couplings to a scalar and a vector constituent quark currents are investigated. These couplings might correspond to a fluctuation of the neutral pion into a scalar quark-antiquark state (meson) and to a vector meson, respectively. Some possible phenomenological implications are discussed.

hep-ph↗
arXiv2025

Symmetry breaking effects in pion couplings to constituent quark currents

Pseudoscalar and axial neutral and charged pion-constituent quark coupling constants are investigated with nondegenerate quark masses in different kinematical points, off shell and on shell pions and constituent quarks. By considering a large quark mass expansion of a quark determinant in the presence of local pion field and of constituent quark background currents, gluonic effects are considered by means of an effective gluon propagator that dresses quark currents. For the neutral pion, mixing effects are introduced by means of the pion mixing to states $P_0$ and $P_8$, that give rise to the $π^0-η-η'$ meson mixing, and mixing of quark currents via corresponding mixing interactions. The relative behavior of charged and neutral pion coupling constants to quarks may be nearly the same - in the framework of the constituent quark model - as the pion-nucleon coupling constants if mixings are introduced. A very small pion coupling to strange quark current is also obtained. The dependence of the positive and negative pion-constituent quark coupling constant on the non-degeneracy of quark masses, for emission and absorption processes, is identified.

hep-ph↗
arXiv2025

Large quark mass Euler-Heisenberg type action for QCD with quark sources and its Abelian limit

The quark determinant in the presence of a background gluon field is calculated in a large quark mass approach within a derivative expansion by considering quark sources. The resulting low-energy QCD Effective Field Theory (EFT) is valid for non-homogeneous fields and it presents, besides the usual Euler-Heisenberg type gluon self-interactions, different types of corrections to the minimal quark-gluon interaction among which there are several imaginary terms. The Abelian limit of this effective action, i.e. an expanded Euler-Heisenberg effective action with fermion sources, is also found and it is shown to contain, therefore, corrections to the fermion-photon interactions, including imaginary terms. Different resulting properties are calculated such as: their contributions to the energy-momentum tensor and its trace, the Poynting vector, the chromo-electric permittivity and chromo-magnetic permeability. Conditions for these quantities, as well as for the corresponding Abelian limits, to be real are exhibited.

hep-ph↗
arXiv2024

Strongly interacting matter in extreme magnetic fields

Magnetic fields are ubiquitous across different physical systems of current interest; from the early Universe, compact astrophysical objects and heavy-ion collisions to condensed matter systems. A proper treatment of the effects produced by magnetic fields during the dynamical evolution of these systems, can help to understand observables that otherwise show a puzzling behavior. Furthermore, when these fields are comparable to or stronger than Λ_QCD, they serve as excellent probes to help elucidate the physics of strongly interacting matter under extreme conditions of temperature and density. In this work we provide a comprehensive review of recent developments on the description of QED and QCD systems where magnetic field driven effects are important. These include the modification of meson static properties such as masses and form factors, the chiral magnetic effect, the description of anomalous transport coefficients, superconductivity in extreme magnetic fields, the properties of neutron stars, the evolution of heavy-ion collisions, as well as effects on the QCD phase diagram. We describe recent theory and phenomenological developments using effective models as well as LQCD methods. The work represents a state-of-the-art review of the field, motivated by presentations and discussions during the "Workshop on Strongly Interacting Matter in Strong Electromagnetic Fields" that took place in the European Centre for Theoretical Studies in Nuclear Physics and Related Areas (ECT*) in the city of Trento, Italy, September 25-29, 2023.

nucl-th↗
arXiv2024

Charged pions asymmetry from the decay of light neutral axial mesons due to interference

Effective three meson couplings, based in flavor U(3) quark-antiquark interactions, are considered to describe two light neutral axial meson Strong decays, $A \sim f_1(1285)$ and $f_{1S} (1420)$, and the charged rho meson decay in the following channels: $A \to ρ^\mp (770)+ π^\pm$, $A\to a_0^\mp (980) +π^\pm$ and $ρ^\pm \to π^\pm π^0$. By considering neutral meson mixings, such as $f_1(1285) - a_1^0(1260)$, $f_{1S}(1420) - a_1^0(1260)$ and $η-π^0$ for the channels investigated, the leading three-meson interactions may lead to decay amplitudes that undergo interference and a resulting ratio of decay rate into charged pions, $Γ_{π^+}/Γ_{π^-}$, slightly smaller than one. For that it will be assumed that the produced charged vector mesons or charged scalar mesons undergo absorption, decay into channels without charged pions, or any other inelastic process that may suppress their decays into charged pions.

hep-ph↗
arXiv2024

$U_A(1)$ symmetry breaking quark interactions from vacuum polarization

By considering the one loop background field method for a quark-antiquark interaction, mediated by one (non perturbative) gluon exchange, sixth order quark effective interactions are derived and investigated in the limit of zero momentum transfer for large quark and/or gluon effective masses. They extend fourth order quark interactions worked out in previous works of the author. These interactions break $U_A(1)$ symmetry and may be either momentum independent or dependent. Part of these interactions vanish in the limit of massless quarks, and several other -- involving vector and/or axial quark currents -- survive. In the local limit of the resulting interactions, some phenomenological implications are presented, which correspond to corrections to the Nambu-Jona-Lasinio model. By means of the auxiliary field method, the local interactions give rise to three meson interactions whose values are compared to phenomenological values found in the literature. Contributions for meson-mixing parameters are calculated and compared to available results.

hep-ph↗
arXiv2024

The Yukawa potential under weak magnetic field

Weak magnetic field induced corrections for the Yukawa potential due to one pion exchange between two constituent quarks (nucleons) are presented. For that, the constant magnetic field effect on the pion propagator and on the pion form factor are taken into account. An effective gluon propagator parameterized with an effective gluon mass ($M_g\sim 0.5$\,GeV) is considered. In the limit of magnetic field weak with respect to the constituent quark mass and pion mass, analytical and semi-analytical expressions can be obtained. Different types of contributions are found, isotropic or anisotropic, dependent on the pion mass and also on the constituent quark and effective gluon masses. Overall the corrections are of the order of $2\%$ to $5\%$ of the Yukawa potential at distances close to $2$fm, and they decrease slower than the Yukawa potential. The anistropic corrections are considerably smaller than the isotropic components. A sizable splitting between results due to magnetic field dependent neutral or charged pion mass is found.

hep-ph↗
arXiv2023

U(5) Nambu-Jona-Lasinio model with flavor dependent coupling constants: pseudoscalar and scalar mesons masses

By considering the background field method we calculate one-loop polarization corrections to the coupling constant of the flavor-U(5) Nambu-Jona-Lasinio (NJL) model with degenerate up and down quarks. They break flavor and chiral symmetries, and they can be written as $G_{ij}^Γ(\barψ λ_i Γψ) ( \barψ λ_j Γψ)$, for the scalar and pseudoscalar channels ($Γ=I , i γ_5$) and $i,j = 0,1,...,N_f^2-1$. Therefore, these coupling constants do not introduce further free parameters in the model which amount to five, six or seven in total. Their contributions to different observables are computed. The non-covariant three-dimensional regularization scheme is employed. Besides that, flavor dependence of cutoffs is implemented in an unambiguous way. It turns out that only two UV cutoffs ($Λ_f$) are best suitable. Nevertheless, the best results are obtained for nearly flavor-independent cutoffs. A quantum mixing due to the representations of the flavor group leads to different interactions for the quarks and for the meson states, respectively denoted by $G_{ff}$ and $G_{ij}$. This quantum mixing effect is responsible for a lowering of quark effective masses and a slight improvement of predictions of observables. A quite surprisingly good description of almost all the pseudoscalar meson masses (within nearly $5\%$) and most of the scalar meson masses -is obtained within nearly 10$\%$. Some problems to describe light scalar mesons masses still remain. The NJL-gap equations seems to overestimate the heavy quark condensates at the usual mean field level usually adopted for model. In spite of the good description of the meson masses, the pseudoscalar meson weak decay constant cannot be described by the NJL model with relativistic heavy quark propagators without further interactions or effects.

hep-ph↗
arXiv2023

Quark-antiquark states of the lightest scalar mesons within the Nambu-Jona-Lasinio model with flavor-dependent coupling constants

The quark antiquark components of the U(3) lightest scalar meson nonet are investigated by considering the Nambu-Jona-Lasinio model with flavor-dependent coupling constants that were derived by considering (non-perturbative) gluon exchange.The strange quark effective mass ($M_s^*$) is varied such that the strangeness content of these scalar mesons can be analyzed further. The neutral states $S_0$, $S_8$ and $S_3$, are adopted as the most relevant quark-antiquark components respectively of the $σ(500)$, $f_0(980)$ and $A_0^0(980)$ mesons. As a result, the mass hierarchy between states $S_0$ and $S_8$, and $K^*_0(700) - A_0(980)$ mesons, can be respectively inverted and corrected for quite low values of the strange quark constituent mass. Besides that, for some particular values of $M_s^*$, the masses of $σ(500)$ and $f_0(980)$ can also be obtained by considering the mixing coupling constant $G_{08}$. However, the masses of all the nine mesons are not described simultaneously in a self-consistent procedure and this goes along with the need of non-quark-antiquark states to completely describe their masses. A neutral-meson mixing matrix is defined and the leading mixing angle is found by fitting a correct value of the $σ(500)$-$f_0(980)$ mass difference. Two different estimates for the strengths of the mixings $A_0^0 \to f_0$ and $f_0 \to A_0^0$ are proposed, leading to somewhat different behaviors. Firstly, by assuming leading transitions to intermediary flavor eigenstates and secondly by considering a dynamical evolution. Results may be in good agreement with experimental values from BESS-III depending on the value of the strange quark effective mass.

hep-ph↗
arXiv2023

Pion constituent quarks couplings strong form factors: a dynamical approach

Form factors for pions interactions with constituent quarks are investigated as the leading effective couplings obtained from a one loop background field method applied to a global color model. Two pion field definitions are considered and the resulting eleven form factors are expressed in terms of components of the quark and gluon propagators that compose only two momentum dependent functions. A momentum dependent Goldberger Treiman relation is also obtained as one of the ratios between the form factors. The resulting form factors with pion momenta up to 1.5 GeV are exhibited for different quark effective masses and two different non-perturbative gluon propagators and they present similar behavior to fittings of experimental data from nucleons form factors. The corresponding pseudoscalar averaged quadratic radii (a.q.r.) and correction to the axial a.q.r. are presented as functions of the sea quark effective mass, being equal respectively to the scalar and vector ones at the present level of calculation.

hep-ph↗
arXiv2022

Magnetic field induced corrections to the NJL model coupling constant from vacuum polarization

Magnetic field dependent corrections for the coupling constant of the Nambu-Jona-Lasinio model are calculated by considering the one-loop background field method. These coupling constants turn out to break chiral and flavor symmetries and they lead to a slight improvement of the numerical values of the up and down quark condensates when compared to results from lattice QCD. The corresponding magnetic field dependencies of the neutral pion and kaon masses are also presented and compared with available lattice QCD calculations. The resulting magnetic field correction to the $η-η'$ mixing angle is also estimated.

hep-ph↗
arXiv2022

Classical Yang Mills equations with sources: consequences of specific scalar potentials

Some well known gauge scalar potential very often considered or used in the literature are investigated by means of the classical Yang Mills equations for the $SU(2)$ subgroups of $N_c=3$. By fixing a particular shape for the scalar potential, the resulting vector potentials and the corresponding color-charges sources are found. By adopting the spherical coordinate system, it is shown that spherically symmetric solutions, only dependent on the radial coordinate, are only possible for the Abelian limit, otherwise, there must have angle-dependent component(s). The following solutions for the scalar potential are investigated: the Coulomb potential and a non-spherically symmetric generalization, a linear potential $A_0 (\vec{r}) \sim (κr)$, a Yukawa-type potential $A_0 (\vec{r}) \sim (C e^{-r/r_0}/r)$ and finite spatial regions in which the scalar potential assumes constant values. The corresponding chromo-electric and chromo-magnetic fields, as well as the color-charge densities, are found to have strong deviations from the spherical symmetric configurations. We speculate these types of non-spherically symmetric configurations may contribute (or favor) for the (anisotropic) confinement mechanism since they should favor color charge-anti-charge (or three-color-charge) bound states that are intrinsically non spherically symmetric with (asymmetric) confinement of fluxes. Specific conditions and relations between the parameters of the solutions are also presented.

hep-ph↗
arXiv2021

Flavor-dependent U(3) Nambu Jona Lasinio coupling constant

A non-perturbative one gluon exchange quark-antiquark interaction is considered to compute flavor dependent U(3) Nambu-Jona-Lasinio (NJL)-type interaction of the form $G_{ij, Γ} (\barψ λ_i Γψ) ( \barψ λ_j Γψ)$ for $i,j=0...8$ and $Γ=I, i γ_5$ from one loop polarization process with non degenerate u-d-s quark effective masses. The resulting NJL-type coupling constants in all channels are resolved in the long-wavelength limit and numerical results are presented for different choices of an effective gluon propagator. Leading deviations with respect to a flavor symmetric coupling constant are found to be of the order of $(M_{f_2}^*-M_{f_1}^*)^n/(M_{f_2}^*+M_{f_1}^*)^n$, for $n=1,2$, where $M_{f_i}^*$ are the effective masses of quarks $f_1,f_2=u, d$ and $s$. The scalar channel coupling constants $G_{ij, s}$ can be considerably smaller than pseudoscalar ones. The effect of the flavor-dependence of coupling constants for the masses of pions and kaons may be nearly of the same order of magnitude as the effect of the u,d and s quark mass non-degeneracy. The effect of these coupling constants is also verified for some of the light scalar mesons masses, usually described by quark-antiquark states, and for some observables of the pseudoscalar mesons.

hep-ph↗
arXiv2018

Form factors for pions couplings to constituent quarks under weak magnetic field

By considering a one loop background field method for a nonperturbative one gluon exchange between quarks, leading electromagnetic form factors of pion couplings to constituent quarks are derived by means of from a large quark and gluon effective masses expansion. With this calculation the leading anisotropic corrections induced by a weak magnetic field for the pion-constituent quark form factors are obtained. Besides that, few effective couplings which emerge only due to the weak magnetic field that break chiral and isospin symmetry are also found. Numerical estimations for these magnetic field corrections are presented for two different nonperturbative gluon propagators. All of these corrections are ultraviolet finite and their relative values are found to be of order of $(eB_0/{M^*}^2)^n$ being $n=1$ for the vector and axial pion couplings and $n=2$ for the pseudoscalar and scalar ones. The corresponding anisotropic corrections to the Strong averaged quadratic radii in the plane perpendicular to the magnetic field are also calculated as functions of the quark effective mass.

hep-ph↗
arXiv2016

SU(2) low energy quark effective couplings in weak external magnetic field

In this work corrections to the usual flavor SU(2) Nambu-Jona-Lasinio coupling due to a weak external magnetic field are calculated by considering quark polarization in a (dressed) gluon exchange mechanism for quark interactions. The quark field is splitted into two components, one that condenses and another one that is a background field for interacting quarks, being the former integrated out. The resulting determinant is expanded for relatively large quark mass and small magnetic field, $(eB_0/{M^*}^2)<1$ by resolving magnetic field dependent low energy quark effective interactions. Besides the corrections for the NJL and vector NJL effective couplings, different $B_0-$dependent effective couplings that break isospin and chiral symmetry emerge.

hep-ph↗
arXiv2016

Lagrangian magnetic moment from polarization

An effective Lagrangian term for the electron magnetic moment, and more generally electromagnetic form factors, is calculated by considering the background field method. Two Fierz transformations are performed for a one-photon exchange interaction, and the ambiguity in doing such transformations is exploited. The resulting effective interaction may exhibit an approximated rotational chiral symmetry either for the scalar-pseudoscalar currents interaction or for the vector-axial currents interaction. The leading terms in the expansion of the fermion determinant yield the leading QED effective action with the complete one loop electromagnetic form factors. A model is proposed to produce the tree level magnetic moment term.

hep-ph↗