arXiv subjects

José Antonio García-Hernández

Publications and source records attributed to José Antonio García-Hernández.

7 recordsLinked to original sources

arXiv2026

Non-standard cosmic strings with amazing profiles

It is an unnatural feature of the Standard Model that the difference between the baryon number $B$ and the lepton number $L$ is conserved, which implies an exact, global symmetry. We promote it to a naturally exact, local symmetry by coupling the difference $B-L$ to an Abelian gauge field. Gauge anomalies are cancelled by adding right-handed neutrinos $ν_{R}$. They are not sterile in this case, which forbids the Majorana term, but we arrange for a $ν_{R}$-mass by adding a Higgs-type 1-component complex scalar field. Thus we arrive at a well-motivated, modest extension of the Standard Model (SM). We investigate the field equations in the corresponding gauge-Higgs sector, involving both Higgs fields and the non-standard U(1) gauge field. This leads to a set of coupled, non-linear differential equations, which we solve numerically. We use cylindrical coordinates, thus focusing on the structures of cosmic strings. For a large variety of parameters, we identify the string profiles and energy densities. These profiles depend on the winding number of each of the Higgs fields. For our parameters, the characteristic string radii are below $10^{-3}~{\rm fm}$, and the string tension is not ruled out by observations of the Cosmic Microwave Background or gravitational waves. As an amazing peculiarity, we discover - for high winding numbers - ``overshooting'' and ``co-axial'' profile functions. In the latter case, the profile of the standard Higgs field changes its sign near the core of the cosmic string.

hep-ph↗

arXiv2025

Phase diagram of chiral 2-flavor QCD based on an effective approach

Despite intense experimental and theoretical research, the QCD phase diagram at finite baryon density remains to a large extent unexplored. From the theoretical side, the obvious non-perturbative approach is lattice QCD simulations, which are, however, obstructed by a severe sign problem. Here we employ the O(4) non-linear $σ$-model as an effective theory for 2-flavor QCD in the chiral limit. The identical pattern of spontaneous symmetry breaking indicates that they belong to the same universality class. We assume high temperature dimensional reduction to the 3d O(4) model, with topological charge taking the role of the baryon number, along the lines of Skyrme's model. In this effective formulation, the baryonic chemical potential $μ_{B}$ can be included in the lattice formulation without causing any sign problem in Monte Carlo simulations. This allows us to pin down the critical line, i.e. the critical temperature $T_{\rm c}(μ_{B})$, which decreases monotonically for increasing $μ_{B}$. In the range $0 < μ_{B} \lesssim 309~{\rm MeV}$ and $132~{\rm MeV} \gtrsim T_{\rm c} \gtrsim 106~{\rm MeV}$, we do not find a Critical Endpoint (CEP), although there are hints for it to be in the vicinity of the maximal $μ_{B}$-value that we could explore.

hep-lat↗

arXiv2025

Structure of cosmic strings for a gauged B-L symmetry and two Higgs fields

In the Standard Model, the difference between the baryon number $B$ and the lepton number $L$ is conserved, which represents a symmetry that is global and exact, and therefore unnatural. We turn it into a naturally exact, local symmetry by coupling the quantum number $B-L$ to an Abelian gauge field. Gauge anomalies are cancelled by adding right-handed neutrinos $ν_R$, which are not sterile in this case. Therefore the usual Majorana term is forbidden by gauge symmetry, but we arrange for a $ν_R$-mass by adding a Higgs-type 1-component complex scalar field. Thus we arrive at a modest, well-motivated extension of the Standard Model. In this framework, we investigate the field equations in the extended gauge-Higgs sector, involving both Higgs fields and the non-standard U(1) gauge field. They are given by a set of coupled, non-linear differential equations, which we solve numerically, focusing on the structures of cosmic strings. For a variety of parameters, we identify the string profiles and energy densities, assuming appropriate boundary conditions. In particular, these profiles depend on the winding number of each of the Higgs fields. As an amazing peculiarity, we discover -- for high winding numbers -- ``overshooting'' and ``co-axial'' solutions; in the latter case, the profile of the standard Higgs field changes its sign near the core of the cosmic string.

hep-ph↗

arXiv2024

In Memoriam: Peter Higgs (1929-2024)

Peter Higgs was a British theoretical physicist, famous for his work published in 1964, where he proposed a mechanism that can generate masses for elementary particles, while respecting gauge invariance. Half a century later, two experiments at CERN confirmed that this mechanism is realized in nature. On April 8th, we received the sad news of the passing of the great pioneer of elementary particle physics. This article is dedicated to his memory, and to the mechanism and particle that bear his name. -- Peter Higgs fue un físico teórico británico, famoso por su trabajo de 1964 donde propuso un mecanismo que puede generar masas para partículas elementales, conforme a la simetría de norma. Medio siglo más tarde, dos experimentos del CERN confirmaron que este mecanismo está realizado en la naturaleza. El 8 de abril nos llegó la triste noticia del fallecimiento del gran pionero de la fisica de partículas elementales. Este artículo es dedicado a su memoria, así como al mecanismo y a la partícula que llevan su nombre.

physics.pop-ph↗

arXiv2022

The 3d O(4) model as an effective approach to the QCD phase diagram

The QCD phase diagram is one of the most prominent outstanding puzzles within the Standard Model. Various experiments, which aim at its exploration beyond small baryon density, are operating or in preparation. From the theoretical side, this is an issue of non-perturbative QCD, and therefore of lattice simulations. However, a finite baryon density entails a technical problem (known as the ``sign problem''), which has not been overcome so far. Here we present a study of an effective theory, the O(4) non-linear sigma model. It performs spontaneous symmetry breaking with the same Lie group structure as 2-flavor QCD in the chiral limit, which strongly suggests that they belong to the same universality class. Since we are interested in high temperature, we further assume dimensional reduction to the 3d O(4) model, which implies topological sectors. As pointed out by Skyrme, Wilczek and others, its topological charge takes the rôle of the baryon number. Hence the baryon chemical potential $μ_{B}$ appears as an imaginary vacuum angle, which can be included in the lattice simulation without any sign problem. We present numerical results for the critical line in the chiral limit, and for the crossover in the presence of light quark masses. Their shapes are compatible with other predictions, but up to the value of about $μ_{B} \approx 300~{\rm MeV}$ we do not find the notorious Critical Endpoint (CEP).

hep-lat↗

arXiv2022

The structure of cosmic strings of a $U(1)$ gauge field for the conservation of $B-L$

We consider an extension of the Standard Model, where the difference between the baryon number $B$ and the lepton number $L$ is gauged with an Abelian gauge field, in order to explain the exact conservation of $B-L$. To avoid a gauge anomaly, we add a right-handed neutrino $ν_{\rm R}$ to each fermion generation. Here it is not sterile, so the usual Majorana term is excluded by gauge invariance. We provide a mass term for $ν_{\rm R}$ by adding a non-standard 1-component Higgs field, thus arriving at a consistent extension of the Standard Model, where the conservation of $B-L$ is natural, with a modest number of additional fields. We study the possible formation of cosmic strings by solving the coupled field equations of the two Higgs fields and the non-standard U(1) gauge field. Numerical methods provide the corresponding string profiles, depending on the Higgs winding numbers, such that the appropriate boundary conditions in the string center and far from it are fulfilled.

hep-ph↗

arXiv2021

Conjecture about the QCD phase diagram

We present a phase diagram study of the O(4) model as an effective theory for 2-flavor QCD. In the chiral limit, both theories perform spontaneous symmetry breaking with isomorphic groups, which suggests that they belong to the same universality class. Since we are interested in high temperature, we further assume dimensional reduction to the 3d O(4) model, which implies topological sectors. According to Skyrme and others, the corresponding topological charge represents the baryon number. Hence the baryon chemical potential $μ_{B}$ appears as an imaginary vacuum angle, which can be included in the lattice simulations without any sign problem. We present simulation results for the critical line in the chiral limit, and for the crossover in the presence of light quark masses. The shapes of these lines are compatible with other conjectures, but up to about $μ_{B} \approx 300$ MeV we do not find a Critical Endpoint, although there are indications for it to be near-by.

hep-lat↗