We estimate the $Upsilon$, $eta_b$ and $B^*$ meson mass shifts in symmetric nuclear matter. The interest is, whether the strengths of the bottomonium-(nuclear matter) and charmonium-(nuclear matter) interactions are similar or different. This is beca
use, each ($J/Psi,Upsilon$) and ($eta_c,eta_b$) meson group is usually assumed to have very similar properties based on the heavy charm and bottom quark masses. The estimate for the $Upsilon$ is made using an SU(5) effective Lagrangian and the anomalous coupling one, by studying the $BB$, $BB^*$, and $B^*B^*$ meson loop contributions for the self-energy. As for the $eta_b$, we include the $BB^*$ and $B^*B^*$ meson loop contributions in the self-energy. The in-medium masses of the $B$ and $B^*$ mesons appearing in the self-energy are calculated by the quark-meson coupling model. An analysis on the $BB$, $BB^*$, and $B^*B^*$ meson loops in the $Upsilon$ mass shift is made by comparing with the corresponding $DD, DD^*$, and $D^*D^*$ meson loops for the $J/Psi$ mass shift. Our prediction for the $eta_b$ mass shift is made including only the lowest order $BB^*$ meson loop. The $Upsilon$ mass shift, with including only the $BB$ loop, is predicted to be -16 to -22 MeV at the nuclear matter saturation density using the $Upsilon BB$ coupling constant determined by the vector meson dominance model with the experimental data, while the $eta_b$ mass shift is predicted to be -75 to -82 MeV with the SU(5) universal coupling constant determined by the $Upsilon BB$ coupling constant. Our results show an appreciable difference between the bottomonium-(nuclear matter) and charmonium-(nuclear matter) interaction strengths. We also study the $Upsilon$ and $eta_b$ mass shifts in a heavy quark (heavy meson) symmetry limit.
The ladder kernel of the Bethe-Salpeter equation is amended by introducing a different flavor dependence of the dressing functions in the heavy-quark sector. Compared with earlier work this allows for the simultaneous calculation of the mass spectrum
and leptonic decay constants of light pseudoscalar mesons, the $D_u$, $D_s$, $B_u$, $B_s$ and $B_c$ mesons and the heavy quarkonia $eta_c$ and $eta_b$ within the same framework at a physical pion mass. The corresponding Bethe-Salpeter amplitudes are projected onto the light front and we reconstruct the distribution amplitudes of the mesons in the full theory. A comparison with the first inverse moment of the heavy meson distribution amplitude in heavy quark effective theory is made.
$eta_c$-nucleus bound state energies are calculated for various nuclei. Essential input for the calculations, namely the medium-modified $D$ and $D^{*}$ meson masses, as well as the density distributions in nuclei, are calculated within the quark-mes
on coupling (QMC) model. The attractive potentials for the $eta_c$ meson in the nuclear medium originate from the in-medium enhanced $DD^{*}$ loops in the $eta_c$ self-energy. Our results suggest that the $eta_c$ meson should form bound states with all the nuclei considered.
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 $Q^2=16~mbox{GeV}^2$ 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 $Q^2=16~mbox{GeV}^2$ 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.
We present $Phi$- and $J/Psi$--nuclear bound state energies and absorption widths for some selected nuclei, using potentials in the local density approximation computed from an effective Lagrangian approach combined with the quark-meson coupling mode
l. Our results suggest that these mesons should form bound states with all the nuclei considered provided that these mesons are produced in nearly recoilless kinematics.
We derive the Landau-Khalatnikov-Frandkin transformation (LKFT) for the fermion propagator in quantum electrodynamics (QED) described within a brane-world inspired framework where photons are allowed to move in $d_gamma$ space-time (bulk) dimensions,
while electrons remain confined to a $d_e$-dimensional brane, with $d_e < d_gamma$, referred to in the literature as reduced quantum electrodynamics, RQED$_{d_gamma,d_e}$. Specializing to the case of graphene, namely, RQED$_{4,3}$ with massless fermions, we derive the nonperturbative form of the fermion propagator starting from its bare counterpart and then compare its weak coupling expansion to known one- and two-loop perturbative results. The agreement of the gauge-dependent terms of order $alpha$ and $alpha^{2}$ is reminiscent from the structure of LKFT in ordinary QED in arbitrary space-time dimensions and provides strong constraints for the multiplicative renormalizability of RQED$_{d_gamma,d_e}$.
We project onto the light-front the pions Poincare-covariant Bethe-Salpeter wave-function, obtained using two different approximations to the kernels of QCDs Dyson-Schwinger equations. At an hadronic scale both computed results are concave and signif
icantly broader than the asymptotic distribution amplitude, phi_pi^{asy}(x)=6 x(1-x); e.g., the integral of phi_pi(x)/phi_pi^{asy}(x) is 1.8 using the simplest kernel and 1.5 with the more sophisticated kernel. Independent of the kernels, the emergent phenomenon of dynamical chiral symmetry breaking is responsible for hardening the amplitude.
