In-medium valence-quark distributions of ${\pi }^{+}$ and $K^{+}$ mesons in symmetric nuclear matter are studied by combining the Nambu–Jona-Lasinio model and the quark-meson coupling model. The in-medium properties of the current quarks, which are used as inputs for studying the in-medium pion and kaon properties in the Nambu–Jona-Lasinio model, are calculated within the quark-meson coupling model. The light-quark condensates, light-quark dynamical masses, pion and kaon decay constants, and pion- and kaon-quark coupling constants are found to decrease as nuclear density increases. The obtained valence quark distributions in vacuum for both the ${\pi }^{+}$ and $K^{+}$ could reasonably describe the available experimental data over a wide range of Bjorken-$x$. The in-medium valence $u$-quark distribution in the ${\pi }^{+}$ at $Q^2=16{\mathrm{GeV}}^2$ is found to be almost unchanged compared to the in-vacuum case. However, the in-medium to in-vacuum ratios of both the valence $u$-quark and valence $s$-quark distributions of the $K^{+}$ meson at $Q^2=16{\mathrm{GeV}}^2$ increase with nuclear matter density but show different $x$-dependence. Namely, the ratio for the valence $u$-quark distribution increases with $x$, while that for the valence $s$ quark decreases with $x$. These features are enhanced at higher density regions.

The internal structure of all lowest-lying pseudoscalar mesons with heavy-light quark content is studied in detail using an algebraic model that has been applied recently, and successfully, to the same physical observables of pseudoscalar and vector mesons with hidden-flavor quark content, from light to heavy quark sectors. The algebraic model consists on constructing simple and evidence-based Ansätze of the meson’s Bethe-Salpeter amplitude (BSA) and quark’s propagator in such a way that the Bethe-Salpeter wave function (BSWF) can then be readily computed algebraically. Its subsequent projection onto the light front yields the light front wave function (LFWF) whose form allows us a simple access to the valence-quark parton distribution amplitude (PDA) by integrating over the transverse momentum squared. We exploit our current knowledge of the PDAs of lowest-lying pseudoscalar heavy-light mesons to compute their generalized parton distributions (GPDs) through the overlap representation of LFWFs. From these three dimensional knowledge, different limits/projections lead us to deduce the related parton distribution functions (PDFs), electromagnetic form factors (EFFs), and impact parameter space GPDs (IPS-GPDs). When possible, we make explicit comparisons with available experimental results and earlier theoretical predictions.

We study dynamical chiral symmetry breaking for quarks in the fundamental representation of SU ( N _c ) for the N _f number of light quark flavors. We also investigate the phase diagram of quantum chromodynamics at finite temperature T and/or in the presence of a constant external magnetic field eB . The unified formalism for this analysis is provided by a symmetry-preserving Schwinger–Dyson equation treatment of a vector × vector contact interaction model which encodes several well-established features of quantum chromodynamics to mimic the latter as closely as possible. Deconfinement and chiral symmetry restoration are triggered above a critical value of N _f at T = 0 = eB . On the other hand, increasing temperature itself screens strong interactions, thus ensuring that a smaller value of N _f is sufficient to restore chiral symmetry at higher temperatures. We also observe the well-known phenomenon of magnetic catalysis for a strong enough magnetic field. However, we note that if the effective coupling strength of the model decreases as a function of magnetic field, it can trigger inverse magnetic catalysis in a certain window of this functional dependence. Our model allows for the simultaneous onset of dynamical chiral symmetry breaking and confinement for each case. Qualitative as well as quantitative predictions of our simple but effective model are in reasonably satisfactory agreement with lattice results and other reliable and refined predictions based upon intricate continuum studies of quantum chromodynamics.

Inspired by the recent development of an algebraic model which provides an adequate and unified description of the internal structure of the lowest-lying pseudoscalar mesons, belonging both to the light quarks sector and to the one of heavy quarks, we perform its first extension to the vector-meson case. The algebraic model describes the meson’s structure in terms of the spectral density function that appears in a Nakanishi integral representation of the covariant quark-antiquark bound-state amplitude, i.e., the Bethe-Salpeter amplitude. We compute the leading-twist light-front wave functions of the $\rho (770)$, $\varphi (1020)$, $J/\psi$, and $\mathrm{\Upsilon }(1S)$ mesons through their connection with the parton distribution amplitudes. Among the results we present, the following are of particular interest: (i) transverse light-front wave functions can be obtained algebraically from the corresponding parton distribution amplitudes, whereas that is not the case for longitudinal light-front wave functions, which requires an intermediate step where a spectral density function must be derived from the particular parton distribution amplitude; (ii) the derived spectral density functions show marked differences between light and heavy vector mesons, the latter being narrower as compared to the former, and these are also nonpositive definite, although the integral over the entire curve is larger than zero as expected; and (iii) the longitudinal and transverse light-front wave functions of vector mesons with light quark content exhibit steep $x$ and $p_{\perp }^2$ dependence, while those of the $J/\psi$ and $\mathrm{\Upsilon }(1S)$ mesons are characterized by narrow distributions in the $x$ range but, comparatively, much more gradual falloffs with respect to the $p_{\perp }^2$ range depicted.

$\mathrm{{\rm Y}}$ and ${\eta }_b$ nuclear bound-state energies are calculated for various nuclei, neglecting any possible effects of the widths. Essential input for the calculations, namely, the medium-modified $B$ and $B^{*}$ meson masses, as well as the density distributions in nuclei, are calculated within the quark-meson coupling (QMC) model. The attractive potentials for the $\mathrm{{\rm Y}}$ and ${\eta }_b$ mesons in nuclei are calculated from the mass shifts of these mesons in nuclear matter in the local density approximation. These potentials originate from the in-medium enhanced $BB$ and $B{B}^{*}$ loops in their respective self-energy. After an extensive analysis we conclude that our results suggest that the $\mathrm{{\rm Y}}$ and ${\eta }_b$ mesons should form bound states with all the nuclei considered.

We present updated and extended results for the $\eta$- and ${\eta }^{\prime }$-nucleus bound state energies, obtained by solving the Schrödinger and Klein-Gordon equations with complex optical potentials, for a wide range of nuclei. The $\eta$ and ${\eta }^{\prime }$ nuclear potentials are obtained in the local density approximation from the mass shift of these mesons in nuclear matter, which is calculated within the quark-meson coupling model. Our results show that the $\eta$ and ${\eta }^{\prime }$ mesons are expected to form mesic nuclei with all the nuclei considered. However, the signal for the formation of the $\eta$- and ${\eta }^{\prime }$-mesic nuclei may be difficult to identify experimentally due to possible large widths.