Narrow Results

We outline the extension of the globally chirally invariant N_f = 2 linear sigma model with vector and axial-vector degrees of freedom to N_f = 3. We present preliminary results concerning the scalar meson masses.

The effective chiral Lagrangian in both nonlocal form $L_{\mathrm{\text{ECCL}}}$ and standard local form $L_{\mathrm{\text{ECL}}}$, derived in the vacuum correlator formalism in QCD, is studied in the chiral perturbation theory. It is shown, that all coefficients of $L_{\mathrm{\text{ECL}}}$ can be computed via $q\bar{q}$ Green’s functions. In the $p^2$ order of $L_{\mathrm{\text{ECL}}}$ one obtains GOR relations and quark decay constants $f_a$ are calculated $a=1,\dots ,8$, while in the $p^4$ order the coefficients $L_1$, $L_2$, $L_3$, $L_4$, $L_5$, $L_6$ are obtained in good agreement with the values given by data. The chiral quark model is shown to be a simple consequence of $L_{\mathrm{\text{ECCL}}}$ with defined coefficients. It is demonstrated that $L_{\mathrm{\text{ECCL}}}$ gives an extension of the limiting low-energy Lagrangian $L_{\mathrm{\text{ECL}}}$ to arbitrary momenta.

In mean field approximation, the grand canonical potential of SU(3) Polyakov linear-$\sigma$ model (PLSM) is analyzed for chiral phase transition, ${\sigma }_l$ and ${\sigma }_s$ and for deconfinement order-parameters, $\varphi$ and ${\varphi }^{\ast }$ of light- and strange-quarks, respectively. Various PLSM parameters are determined from the assumption of global minimization of the real part of the potential. Then, we have calculated the subtracted condensates $({\mathrm{\Delta }}_{l,s})$. All these results are compared with recent lattice QCD simulations. Accordingly, essential PLSM parameters are determined. The modeling of the relaxation time is utilized in estimating the conductivity properties of the QCD matter in thermal medium, namely electric $[{\sigma }_{\mathrm{\text{el}}}(T)]$ and heat $[\kappa (T)]$ conductivities. We found that the PLSM results on the electric conductivity and on the specific heat agree well with the available lattice QCD calculations. Also, we have calculated bulk and shear viscosities normalized to the thermal entropy, $\xi /s$ and $\eta /s$, respectively, and compared them with recent lattice QCD. Predictions for $(\xi /s)/({\sigma }_{\mathrm{\text{el}}}/T)$ and $(\eta /s)/({\sigma }_{\mathrm{\text{el}}}/T)$ are introduced. We conclude that our results on various transport properties show some essential ingredients, that these properties likely come up with, in studying QCD matter in thermal and dense medium.

The SU(3) Polyakov linear-sigma model (PLSM) in mean-field approximation is utilized in analyzing the chiral condensates ${\sigma }_u$, ${\sigma }_d$, ${\sigma }_s$ and the deconfinement order parameters $\varphi$, $\bar{\varphi }$, at finite isospin asymmetry. The bulk thermodynamics including pressure density, interaction measure, susceptibility and second-order correlations with baryon, strange and electric charge quantum numbers are studied in thermal and dense medium. The PLSM results are confronted to the available lattice quantum chromodynamics (QCD) calculations. The excellent agreement obtained strengthens the reliability of fixing the PLSM parameters and therefore supports further predictions even beyond the scope of the lattice QCD numerical applicability. From the QCD phase structure at finite isospin chemical potential $({\mu }_I)$, we find that the pseudocritical temperatures decrease with the increase in ${\mu }_I$. We conclude that the QCD phase structure in $(T_{\chi }\text{–}{\mu }_I)$ plane seems to extend the one in $(T_{\chi }\text{–}{\mu }_B)$ plane.

The first order self-energy corrections of the kaon in the symmetric nuclear matter are calculated from kaon-nucleon scattering matrix elements using a chiral Lagrangian within the framework of relativistic mean field approximation. It shows that the effective mass and the potential of K⁺ meson are identical with those of K^- meson in the nuclear matter, respectively. The effective mass of the kaon in the nuclear matter decreases with the nuclear density increasing, and is not relevant to the kaon-nucleon Sigma term. The kaon-nucleus potential is positive and increases with the nuclear density. Moreover, the influence of the resonance Λ(1405) on the K^--nucleus potential due to the re-scattering term is discussed. Our results indicate the K^- meson could not be bound in the nuclei even if the contribution of Λ(1405) resonance is considered.

The effects of intermediate charmed mesons on charmonium transitions with the emission of one pion or eta meson are studied systematically. Based on a non-relativistic effective field theory we show that charmed meson loops are enhanced compared to the corresponding tree-level contributions for transitions between two S-wave charmonia as well as for transitions between two P-wave charmonia. On the contrary, for the transitions between one S-wave and one P-wave charmonium state, the loops need to be analyzed case by case and often appear to be suppressed. Extending these considerations to the b-quark sector, we propose a new method to extract the light quark mass ratio m_u/m_d using the ϒ(4S) → h_bπ⁰(η) bottomonia transitions.

The pseudoscalar meson-baryon octet interaction is studied within a nonlinear realized Lagrangian, and then the Bethe-Salpeter equation is solved in the unitary coupled-channel approximation. In sector of strangeness S = −1 and isospin I = 0, only one pole is generated dynamically in the 1400MeV region, which might correspond to the Λ(1405) particle. When the case of strangeness zero is studied, the s– and u– potentials are taken into account in the kernel, and a resonance state is produced in the 1500MeV region, which might be a counterpart of the N(1535) particle.

We investigate the Sivers distribution functions of sea quark in proton with chiral Lagrangian. The reasonable numerical results for the first momentum $x{\text{Δ}}^N{f}_{\overline{q}}^{\left(1\right)}\left(x\right)$ are obtained without any fine tuning of the parameters. Our results are also comparable with the recent phenomenological extractions.

We obtain the full U group chiral Lagrangian to the order p⁶ order, and check the existing results. We find one more linear relation in p⁴ order at U group, and some more linear relations in p⁶ order at SU group with tensor sources.