arXiv subjects

Luis A. Hernández

Publications and source records attributed to Luis A. Hernández.

15 recordsLinked to original sources

arXiv2026

Tree-Level Interaction Vertices in the Linear Sigma Model with Quarks under Global Rotation

We derive the tree-level interaction vertices of the linear sigma model with quarks in the presence of global rotation. Starting from the scalar and fermionic field solutions in a rotating background, we construct the corresponding spectral representations and use them to evaluate the mesonic self-interactions and Yukawa couplings of the model. We show that rotation modifies the usual momentum-space structure of the interaction vertices: conservation of longitudinal momentum is accompanied by angular-momentum selection rules, while the transverse dynamics is encoded in rotation-induced radial form factors involving products of Bessel functions. The resulting expressions provide a set of interaction rules adapted to the symmetries and finite geometry of the rotating system. Although derived within the linear sigma model with quarks, the structures obtained for scalar self-interactions and scalar-fermion couplings can be extended to a broader class of quantum field theories under global rotation. These results provide the building blocks for perturbative calculations and contribute toward a microscopic quantum-field-theoretical description of interacting matter in rotating environments.

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arXiv2026

Scalar propagator in a rotating thermal medium: Consistency checks and applications

We derive the scalar propagator in a thermal medium under global rotation without restricting the spacetime points to a common comoving trajectory. The resulting propagator retains an explicit dependence on the radial coordinates, reflecting the lack of translational invariance in the transverse plane, and therefore cannot in general be formulated solely in momentum space. We show that the usual free Feynman propagator is exactly recovered in the nonrotating limit, providing a first consistency check of the formulation. As a nontrivial test, we apply the propagator to the interacting $λϕ^4$ theory at finite temperature and rotation. The one-loop scalar self-energy obtained within the Matsubara formalism correctly separates into vacuum and medium contributions and reproduces the standard finite-temperature result when $Ω\to0$. We subsequently construct the effective potential including screening effects through ring resummation and, for $Ω/T\ll1$, evaluate the rotational corrections up to $\mathcal{O}(Ω^4)$. Within this model, the resulting effective potential exhibits the expected thermal restoration of the spontaneously broken $\mathbb{Z}_2$ symmetry, while global rotation favors symmetry restoration and enhances this effect as the transverse size of the system increases. These results provide complementary consistency checks of the rotating scalar propagator and highlight the need to retain its explicit position-space structure in more general perturbative calculations.

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arXiv2026

Complete one-loop self-energies of the linear sigma model coupled to quarks at finite temperature and in a magnetic field

We present a complete calculation of the one-loop self-energies for all fields in the linear sigma model coupled to quarks at finite temperature and in the presence of a uniform magnetic field. The analysis consistently incorporates thermal and magnetic effects for both neutral and charged degrees of freedom, providing a unified framework valid for arbitrary values of the temperature and the field strength. The computation is performed using the Matsubara formalism to account for finite temperature effects and the Schwinger proper-time representation for charged propagators in a magnetic background. Special attention is given to loop contributions involving particles with different electric charges, for which the associated Schwinger phases do not cancel. We show that these terms can be systematically evaluated in coordinate space using the Ritus formalism, which provides the appropriate framework for treating external charged states in the presence of a magnetic background, and consistently expressed in momentum space. The resulting expressions exhibit a nontrivial interplay between thermal fluctuations and magnetic effects and allow for a clear separation between vacuum and matter contributions, providing a well-defined structure for the identification of ultraviolet divergences. Our results establish a consistent and systematic framework for the computation of thermomagnetic one-loop corrections in effective models of QCD, capturing the full interplay between thermal and magnetic effects for all dynamical degrees of freedom.

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arXiv2026

Chiral first order phase transition at finite baryon density and zero temperature from self-consistent pole masses in the linear sigma model with quarks

We use the two-flavor Linear Sigma Model with quarks as an effective description of QCD to investigate the nature of the chiral phase transition at finite baryon chemical potential and zero temperature. We work at one-loop order to set up and solve the system of self-consistent coupled equations for the particle pole masses. The chemical potential-dependent value of the chiral order parameter is obtained by minimizing the one-loop effective potential. This treatment goes beyond the conventional ring-diagram approximation and provides a description valid for arbitrary values of the chemical potential. We find that the phase transition is of first order, and occurs when the quark chemical potential reaches the value of the vacuum quark mass for the chosen set of parameters. The first order nature of the transition is signaled by the discontinuous behavior of the chiral condensate, the masses and the couplings. The thermodynamics of the system is readily implemented and in particular, we find that the square of the speed of sound exhibits a discontinuity at the phase transition and then smoothly approaches the conformal limit from below.

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arXiv2025

Magnetic Catalysis of charmonium in the vector channel

We investigate the impact of an external magnetic field on the vector charmonium system within the framework of Hilbert moment QCD sum rules. By incorporating magnetic corrections to the perturbative contributions of the QCD sector, we analyze the behavior of the hadronic parameters of the $J/ψ$ resonance -- namely, its continuum threshold $s_0$, decay constant $f_V$, width $Γ_V$, and its mass $M_V$, as functions of the magnetic field strength. Our results show that $s_0$ and $f_V$ increase monotonically, while $Γ_V$ decreases significantly and $M_V$ remains essentially constant. These behaviors indicate a strengthening of the hadronic state in the presence of a magnetic field, consistent with the phenomenon of magnetic catalysis. Although magnetic catalysis has traditionally been associated with light-quark systems via chiral symmetry breaking, our results demonstrate that similar effects persist in the heavy-quark sector, despite the absence of chiral dynamics.

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arXiv2025

Inverse magnetic catalysis in the linear sigma model: a beyond mean field approach

We explore the restoration of chiral symmetry in the linear sigma model coupled to quarks under the influence of strong magnetic fields and finite temperature, incorporating screening effects through ring diagrams. While previous studies using tree-level thermal masses lead to magnetic catalysis across all temperature ranges, in tension with lattice QCD results, we go beyond this limitation by computing the bosonic masses self-consistently within the lowest Landau level (LLL) approximation. The self-consistent approach modifies the effective potential and allows us to accurately track the thermal evolution of the order parameter. Our results reveal the emergence of a critical end point (CEP) in the $T-|eB|$ phase diagram and, notably, exhibit inverse magnetic catalysis (IMC) behavior: the (pseudo)critical temperature decreases with increasing magnetic field strength. This is in contrast to the magnetic catalysis behavior found when non-self-consistent masses are used. To the best of our knowledge, this is the first time that self-consistent boson masses have been implemented in this context, offering a new framework for exploring the QCD phase diagram using effective models.

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arXiv2025

Photon polarization tensor in presence of constant and arbitrary electric field

We compute the photon polarization tensor at one-loop order in the presence of a constant and uniform electric field. Our calculation is carried out for arbitrary field strength using the Schwinger proper-time formalism, and we explicitly derive an expression for the polarization tensor without approximations. We also present a complementary derivation within the strong field approximation. Our main contribution lies in expressing the polarization tensor in terms of a physically motivated tensor basis that ensures transversality and thus preserves gauge invariance. This basis, constructed from the preferred direction defined by the external electric field, makes explicit the breaking of Lorentz symmetry. We verify the consistency of our results by recovering the well-known vacuum polarization tensor in the zero-field limit and by demonstrating agreement between the strong field limit of the general expression and the result obtained directly in the strong field approximation. Interestingly, in the latter case, only one tensor structure survives, corresponding to the transverse dynamics with respect to the field direction, which highlights the dominance of perpendicular modes.

hep-th↗

arXiv2025

Screening rho-meson mass in the presence of strong magnetic fields

We study the screening mass of the neutral rho-meson in the presence of strong magnetic fields using the Kroll-Lee-Zumino (KLZ) model. The rho-meson self-energy is computed at one-loop order within the lowest Landau level (LLL) approximation, considering the magnetic field as the dominant energy scale. Due to Lorentz symmetry breaking induced by the external field, we decompose the self-energy into three independent tensor structures, which give rise to three distinct modes. Additionally, the four-momentum splits into parallel and perpendicular components, leading to two types of screening masses: the parallel screening mass ( $p_0=0$ and $p_\perp \to 0$ ) and the perpendicular screening mass ( $p_0=0$ and $p_\parallel \to 0$ ). Our results show that the zero and perpendicular modes exhibit a monotonically increasing behavior with the magnetic field strength, whereas the parallel mode remains essentially constant. These findings provide new insights into the behavior of vector mesons in strongly magnetized media, with implications for QCD under extreme conditions.

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arXiv2024

Vortical effects and the critical end point in the Linear Sigma Model coupled to quark

In this paper, we study the effects of vorticity on the QCD phase transition using the Linear Sigma Model coupled to quarks. By going beyond the mean-field approximation and incorporating screening effects via ring diagrams, we explore the chiral symmetry restoration in extreme conditions, such as high temperatures, high densities, and large angular velocities. Our analysis reveals how the critical temperature decreases as the angular velocity increases, suggesting that vorticity catalyzes the symmetry restoration. Additionally, we observe a shift in the Critical End Point (CEP) in the effective QCD phase diagram, where higher angular velocities move the CEP to lower quark chemical potentials and higher temperatures. Moreover, we analyze the baryon number fluctuations through the normalized fourth moment $κσ^2 = c_4/c_2$ as a function of the collision energy in heavy-ion reactions $\sqrt{s_{NN}}$, which serves as a key observable to identify the CEP. Our study reveals that for high collision energies, $κσ^2$ remains nearly constant; however, as the system approaches the CEP, the ratio increases sharply, indicating the proximity of the critical region. This rise is influenced by the presence of vorticity, which causes the CEP to shift to higher collision energies. These findings provide insight into the role of vorticity in heavy-ion collisions

hep-ph↗

arXiv2024

Magnetic corrections to the QCD coupling: strong field approximation

We compute the 1-loop vertex function of the QCD coupling in the presence of an ultra intense magnetic field. From the vertex function, we extract the effective coupling and show that it grows with increasing magnetic field. We consider the quark-gluon vertex and the three-gluon vertex, accounting for the propagators of charged particles within the loops using the lowest Landau level approximation in order to satisfy the condition where the magnetic field is the largest energy scale. Under this approximation, we find that the contribution from the three-gluon vertex vanishes. Therefore, this result arises from the competition between the color charge associated to gluons and to quarks as well, with the former being larger than the latter. The behavior of the QCD coupling as a function of the magnetic field strength is analogous to that exhibited by the light-quark condensate, indicating the magnetic catalysis occurs. This increasing behavior stems from the dominant contribution of color charge associated to gluons in the vertex function.

hep-ph↗

arXiv2023

Chiral symmetry restoration in a rotating medium

We study the nature of the chiral symmetry restoration within the Yukawa model with spontaneous symmetry breaking. We work with scalar and fermion fields which are subject to the effects of a rotating system. In this work, we show the derivation of the scalar field propagator in a rotating medium using the Fock-Schwinger proper-time method. We compute analytically the effective potential in the high-temperature approximations, including the contribution of the ring diagrams to account for the plasma screening properties. We study the chiral transition as we vary the angular velocity $Ω$, the boson self-coupling $λ$ and the fermion-boson coupling $g$. We show that the critical temperature for the restoration of chiral symmetry always starts with decreasing behaviour, until it reaches a minimum and from there when increasing $Ω$, we observe $T_c$ increases monotonically. In all the phase transition lines in the $T-Ω$ plane reported, we obtain that the rotating effects are able to change the order of the phase transition.

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arXiv2023

QCD equation of state at finite isospin density from the linear sigma model with quarks: The cold case

We use the two-flavor linear sigma model with quarks to study the phase structure of isospin asymmetric matter at zero temperature. The meson degrees of freedom provide the mean field chiral- and isospin-condensates on top of which we compute the effective potential accounting for constituent quark fluctuations at one-loop order. Using the renormalizability of the model, we absorb the ultraviolet divergences into suitable counter-terms that are added respecting the original structure of the theory. These counter-terms are determined from the stability conditions which require the effective potential to have minima in the condensates directions at the classical values, as well as the transition from the non-condensed to the condensed phase to be smooth as a function of the isospin chemical potential. We use the model to study the evolution of the condensates as well as the pressure, energy and isospin densities and the sound velocity as functions of the isospin chemical potential. The approach does a good average description up to isospin chemical potentials values not too large as compared to the vacuum pion mass.

hep-ph↗

arXiv2022

Hadronic contribution to the running QED coupling at the Z-boson mass scale

An update is described of a model independent method to determine the hadronic contribution to the QED running coupling at the Z-boson mass scale, $Δα_{\text{HAD}}(M_{Z}^{2})$. The major source of uncertainty is from the contribution of the light quark vector current correlator at zero momentum. This uncertainty is substantially reduced using recently improved lattice QCD results for this correlator. The result is $Δα_{\text{HAD}}(M_{Z}^{2})=274.13 (0.73)\, \times 10^{-4}$.

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arXiv2021

QCD phase diagram in a magnetized medium from the chiral symmetry perspective: The linear sigma model with quarks and the Nambu--Jona-Lasinio model effective descriptions

We review the main features of the QCD phase diagram description, at finite temperature, baryon density and in the presence of a magnetic field, from the point of view of effective models, whose main ingredient is chiral symmetry. We concentrate our attention on two of these models: The linear sigma model with quarks and the Nambu--Jona-Lasinio model. We show that a main ingredient to understand the characteristics of the phase transitions is the inclusion of plasma screening effects that capture the physics of collective, long-wave modes, and thus describe a prime property of plasmas near transition lines, namely, long distance correlations. Inclusion of plasma screening makes possible to understand the inverse magnetic catalysis phenomenon even without the need to consider magnetic field-dependent coupling constants. Screening is also responsible for the emergence of a critical end point in the phase diagram even for small magnetic field strengths. Although versatile, the NJL model is also a more limited approach since, being a non-renormalizable model, a clear separation between pure vacuum and medium effects is not always possible. The model cannot describe inverse magnetic catalysis unless a magnetic field dependent coupling is included. The location of the critical end point strongly depends on the choice of the type of interaction and on the magnetic field dependence of the corresponding coupling. Overall, both models provide sensible tools to explore the properties of magnetized, strongly interacting matter. However, a cross talk among them as well as a consistent physical approach to determine the model parameters is much needed.

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arXiv2020

Magnetic field dependence of nucleon parameters from QCD sum rules

Finite energy QCD sum rules involving nucleon current correlators are used to determine several QCD and hadronic parameters in the presence of an external, uniform, large magnetic field. The continuum hadronic threshold $s_0$, nucleon mass $m_N$, current-nucleon coupling $λ_N$, transverse velocity $v_\perp$, the spin polarization condensate $\langle\bar qσ_{12} q\rangle$, and the magnetic susceptibility of the quark condensate $χ_q$, are obtained for the case of protons and neutrons. Due to the magnetic field, and charge asymmetry of light quarks up and down, all the obtained quantities evolve differently with the magnetic field, for each nucleon or quark flavor. With this approach it is possible to obtain the evolution of the above parameters up to a magnetic field strength $eB < 1.4$ GeV$^2$.

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