Abstract:
Generalized vector form factors of the pion, related to the moments of the generalized parton distribution functions, are evaluated in the Nambu--Jona-Lasinio model with the Pauli-Villars regularization. The lowest moments (the electromagnetic and the gravitational form factors) are compared to recent lattice data, with fair agreement. Predictions for higher-order moments are also made. Relevant features of the generalized form factors in the chiral quark models are highlighted and the role of the QCD evolution for the higher-order GFFs is stressed.

Abstract:
The large-$N_c$ consistency conditions for axial vector and isovector magnetic couplings of pions to baryons are discussed from the point of view of low-energy current-algebra sum rules (Adler-Weisberger, Cabibbo-Radicati). In particular, we show how the result that ratios of axial vector and isovector magnetic coupling constants get corrections only at the order $1/N_c^2$ follows from the $N_c$-counting of appropriate cross sections. This counting is performed using various approaches at the quark and hadronic level. Other implications of our method are also presented.

Abstract:
We show that the Hagedorn temperature obtained from experimental spectra is larger for mesons than for baryons. Dual string models explain this behavior asymptotically.

Abstract:
Gauging of effective chiral quark models with non-local regulators is discussed in the context of solitons. In particular, we show that with the P-exponent method the current algebra is satisfied and the charges are properly quantized.

Abstract:
We analyze experimental particle spectra and show that the Hagedorn temperature is significantly larger for mesons than for baryons. The effect can be explained within dual string models: excitations of three strings in the baryon produce ``faster'' combinatorics than a single string in the meson, hence lead to a more rapid growth of baryons than mesons. Predictions of other approaches for the gross features of particle spectra are also discussed.

Abstract:
A mini-review of non-uniform phases in quark matter is presented, with particular attention to the pion condensation, also known as chiral density waves or chiral spirals. The phase diagram of strongly-interacting matter may involve such a phase, placed on the quarkyonic island between the baryonic phase and the chirally-restored quark-gluon plasma.

Abstract:
Vector meson correlators are studied in effective chiral quark models with both local and non-local regulators. A set of sum rules based on dispersion relations is derived, which allows for a comparison of model predictions to data. We show that the two Weinberg sum rules for vector correlators hold in the non-local model.

Abstract:
We analyze the proton-lead collisions at the LHC energy of 5.02TeV in the three-stage approach, previously used to successfully describe the relativistic A-A collisions. The approach consists of the early phase, modeled with the Glauber model, the event-by-event viscous 3+1 dimensional (3+1 D) relativistic hydrodynamics, and the statistical hadronization at freeze-out. We show that features typical of collective dynamics, such as the harmonic flow and the ridge structures in the two-particle correlations in relative azimuth and pseudorapidity, may be naturally explained in our framework. In the proton-nucleus system the harmonic flow is generated from an initially event-by-event deformed system and is entirely due to these initial fluctuations. Notably, fluctuations of strength of the initial Glauber sources which yield the observed distribution of hadron multiplicities and, at the same time, lead to correct values of the elliptic flow coefficients both from the two- and four-particle cumulant method, as measured by the ATLAS collaboration. The azimuthally asymmetric flow is not modified significantly when changing the viscosity coefficient, the initial time for the collective expansion, or the initial size of the fireball. The results present an estimate of the collective component in the two-particle correlations measured experimentally. We demonstrate that the harmonic flow coefficients can be experimentally measured with methods based on large rapidity gaps which reduce some of the other sources of correlations.

Abstract:
The interferometric radii in the system formed in ultra-relativistic proton-lead collisions are investigated in a framework based on event-by-event 3+1 dimensional viscous hydrodynamics. We argue that the most central p-Pb collisions undergoing collective expansion behave similarly to the peripheral nucleus-nucleus collisions. The interferometric observables can serve as signatures of the formation of an extended fireball.

Abstract:
We show that even moderate excess of neutrons over protons in nuclear matter, such as in ${}^{208} Pb$, can lead to large $\rho$-$\omega$ mixing at densities of the order of twice the nuclear saturation density and higher. The typical mixing angle is of the order of $10^o$. The mixing may result in noticeable shifts of the positions and widths of resonances. We also analyze temperature effects and find that temperatures up to 50 MeV have practically no effect on the mixing.