The $\pi_0$ neutral meson pole mass is calculated in a strongly magnetized medium using the SU(2) Nambu-Jona-Lasinio model within the random phase approximation (RPA) at zero temperature and zero baryonic density. We employ a magnetic field dependent coupling, $G(eB)$, fitted to reproduce lattice QCD results for the quark condensates. Divergent quantities are handled with a magnetic field independent regularization scheme in order to avoid unphysical oscillations. A comparison between the running and the fixed couplings reveals that the former produces results much closer to the predictions from recent lattice calculations. In particular, we find that the $\pi_0$ meson mass systematically decreases when the magnetic field increases while the scalar mass remains almost constant. We also investigate how the magnetic background influences other mesonic properties such as $f_{{\pi}_0}$ and $g_{\pi_0 q q}$.Comment: 7 pages, 5 figures, v2 PLB versio

Within the covariant density functional theory of hypernuclear matter we build a series of equations of state for hypernuclear compact stars, by calibrating the coupling constants of the $\mathrm{\Xi }$-hyperon to the experimental binding energy of the single-$\mathrm{\Xi }$ hypernuclei ${}_{{\mathrm{\Xi }}^{-}}{}^{15}\mathrm{C}$ and ${}_{{\mathrm{\Xi }}^{-}}{}^{12}\mathrm{Be}$. Coupling constants of the $\mathrm{\Lambda }$-hyperon to nucleons have been calibrated on a vast collection of experimental data on single $\mathrm{\Lambda }$ hypernuclei and we employ those values. Uncertainties on the couplings of the $\mathrm{\Sigma }$-hyperon to nuclear matter, due to lack of experimental data, are accounted for by allowing for a wide variation of the well depth of $\mathrm{\Sigma }$ at rest in symmetric saturated nuclear matter. To account for uncertainties in the nucleonic sector at densities much larger than $n_0$, a rich collection of parametrizations is employed, some of them in agreement with existing constraints from nuclear physics and astrophysics. Neutron star properties are investigated with all these calibrated equations of state. The effects of the presence of hyperons on the radius, on the tidal deformability, on the moment of inertia, and on the nucleonic direct Urca process are discussed. The sensitivity of the hyperonic direct Urca processes to uncertainties in the nucleonic and hyperonic sectors is also addressed. It is shown that the relative variations of the radius, tidal deformability and moment of inertia from the values that characterize purely nucleonic stars are linearly correlated with the strangeness fraction. The maximum radius deviation, obtained for most massive neutron stars, is $\approx 10\%$. The reduction of the maximum mass, triggered by nucleation of strangeness, is estimated at $\approx 15\%–20\%$, out of which 5% comes from insufficient information on the $\mathrm{\Sigma }$-hyperon interactions. A total of 44 calibrated hyperonic equations of state are published as Supplemental Material.

A magnetic field independent regularization scheme (zMFIR) based on the Hurwitz-Riemann zeta function is introduced. The new technique is applied to the regularization of the mean-field thermodynamic potential and mass gap equation within the SU(2) Nambu-Jona-Lasinio model in a hot and magnetized medium. The equivalence of the new and the standard MFIR scheme is demonstrated. The neutral meson pole mass is calculated in a hot and magnetized medium and the advantages of using the new regularization scheme are shown.

We consider the two-flavor Nambu–Jona-Lasinio model within the random phase approximation (RPA) framework to evaluate the masses of the $\sigma$ and ${\pi }^0$ mesons and the ${\pi }^0$ decay constant in the presence of a magnetic field at vanishing temperatures and baryonic densities. The present work extends other RPA applications by fully considering the external momenta which enter the integrals representing the magnetized polarization tensor. We employ a a field-independent regularization scheme so that more accurate results can be obtained in the evaluation of physical quantities containing pionic contributions. As we show, this technical improvement generates results which agree well with those produced by lattice simulations and chiral perturbation theory. Our method may also prove to be useful in future evaluations of quantities, such as the shear viscosity and the equation of state of magnetized quark matter with mesonic contributions.

We study the regularization dependence of the Nambu-Jona–Lasinio model (NJL) predictions for some properties of magnetized quark matter at zero temperature (and baryonic density) in the mean field approximation. The model parameter dependence for each regularization procedure is also analyzed in detail. We calculate the average and difference of the quark condensates using different regularization methods and compare with recent lattice results. In this context, the reliability of the different regularization procedures is discussed.

A set of unified relativistic mean-field equations of state for hyperonic compact stars recently built in [M. Fortin, Ad. R. Raduta, S. Avancini, and C. Providência, Phys. Rev. D 101, 034017 (2020)] is used to study the thermal evolution of nonmagnetized and nonrotating spherically-symmetric isolated and accreting neutron stars under different hypothesis concerning proton $S$-wave superfluidity. These equations of state have been obtained in the following way: the slope of the symmetry energy is in agreement with experimental data; the coupling constants of $\mathrm{\Lambda }$ and $\mathrm{\Xi }$-hyperons are determined from experimental hypernuclear data; uncertainties in the nucleon-$\mathrm{\Sigma }$ interaction potential are accounted for; current constraints on the lower bound of the maximum neutron star mass are satisfied. Within the considered set of equations of state, the presence of hyperons is essential for the description of the cooling/heating curves. One of the conclusions we reach is that the criterion of best agreement with observational data leads to different equations of states and proton $S$-wave superfluidity gaps when applied separately for isolated neutron stars and accreting neutron stars in quiescence. This means that at least in one situation the traditional simulation framework that we employ is not complete and/or the equations of state are inappropriate. Another result is that, considering equations of state which do not allow for nucleonic dUrca or allow for it only in very massive NS, the low luminosity of SAX J1808 requires a repulsive $\mathrm{\Sigma }$-hyperon potential in symmetric nuclear matter in the range $U_{\mathrm{\Sigma }}^{(N)}\approx 10–30\mathrm{MeV}$. This range of values for $U_{\mathrm{\Sigma }}^{(N)}$ is also supported by the criterion of best agreement with all available data from INS and XRT.