Chiral dynamics with confinement versus the standard chiral theory

Chiral dynamics is investigated using the chiral confining Lagrangian (CCL), previously derived from QCD with confinement interaction. Based on the calculations of the quark condensate, which is defined entirely by confinement in the zero quark mass limit, one can assert that chiral symmetry breaking is predetermined by confinement. It is shown that CCL retains all basic relations of the standard chiral theory but enables one to include quark degrees of freedom in the CCL. The expansion of the CCL provides the Gell–Mann–Oakes–Renner (GMOR) relations and the masses and decay constants of all chiral mesons, including [Formula: see text]. For the latter, one needs to define a nonchiral component due to confinement, while the orthogonality condition defines the wave functions and the eigenvalues. The resulting masses and decay constants of all chiral mesons are obtained in good agreement with the experimental and lattice data.

From noninteracting to interacting picture of quark–gluon plasma in the presence of a magnetic field and its fluid property

We have attempted to build a parametric-based simplified and analytical model to map the interaction of quarks and gluons in the presence of magnetic field, which has been constrained by quark condensate and thermodynamical quantities like pressure, energy density, etc., obtained from the calculation of lattice quantum chromodynamics (QCDs). To fulfill that mapping, we have assumed a parametric temperature and magnetic field-dependent degeneracy factor, average energy, momentum and velocity of quarks and gluons. Implementing this QCD interaction in calculation of transport coefficient at finite magnetic field, we have noticed that magnetic field and interaction both are two dominating sources, for which the values of transport coefficients can be reduced. Though the methodology is not so robust, but with the help of its simple parametric expressions, one can get a quick rough estimation of any phenomenological quantity, influenced by temperature and magnetic field-dependent QCD interaction.

The role of strangeness in chiral and $$U(1)_A$$ restoration

We use recently derived Ward identities and lattice data for the light- and strange-quark condensates to reconstruct the scalar and pseudoscalar susceptibilities ($$\chi _S^\kappa $$ χ S κ , $$\chi _P^K$$ χ P K ) in the isospin 1/2 channel. We show that $$\chi _S^\kappa $$ χ S κ develops a maximum above the QCD chiral transition, after which it degenerates with $$\chi _P^K$$ χ P K . We also obtain $$\chi _S^\kappa $$ χ S κ within Unitarized Chiral Perturbation Theory (UChPT) at finite temperature, when it is saturated with the $$K_0^*(700)$$ K 0 ∗ ( 700 ) (or $$\kappa $$ κ ) meson, the dominant lowest-energy state in the isospin 1/2 scalar channel of $$\pi K$$ π K scattering. Such UChPT result reproduces the expected peak structure, revealing the importance of thermal interactions, and makes it possible to examine the $$\chi _S^\kappa $$ χ S κ dependence on the light- and strange-quark masses. A consistent picture emerges controlled by the $$m_l/m_s$$ m l / m s ratio that allows one studying $$K-\kappa $$ K - κ degeneration in the chiral, two-flavor and SU(3) limits. These results provide an alternative sign for $$O(4)\times U(1)_A$$ O ( 4 ) × U ( 1 ) A restoration that can be explored in lattice simulations and highlight the role of strangeness, which regulated by the strange-quark condensate helps to reconcile the current tension among lattice results regarding $$U(1)_A$$ U ( 1 ) A restoration.

QCD phase diagram in a constant magnetic background

Magnetic catalysis is the enhancement of a condensate due to the presence of an external magnetic field. Magnetic catalysis at $$T=0$$ T = 0 is a robust phenomenon in low-energy theories and models of QCD as well as in lattice simulations. We review the underlying physics of magnetic catalysis from both perspectives. The quark-meson model is used as a specific example of a model that exhibits magnetic catalysis. Regularization and renormalization are discussed and we pay particular attention to a consistent and correct determination of the parameters of the Lagrangian using the on-shell renormalization scheme. A straightforward application of the quark-meson model and the NJL model leads to the prediction that the chiral transition temperature $$T_{\chi }$$ T χ is increasing as a function of the magnetic field B. This is in disagreement with lattice results, which show that $$T_{\chi }$$ T χ is a decreasing function of B, independent of the pion mass. The behavior can be understood in terms of the so-called valence and sea contributions to the quark condensate and the competition between them. We critically examine these ideas as well recent attempts to improve low-energy models using lattice input.

Quark, pion and axial condensates in three-flavor finite isospin chiral perturbation theory

We calculate the light-quark condensate, the strange-quark condensate, the pion condensate, and the axial condensate in three-flavor chiral perturbation theory ($$\chi $$ χ PT) in the presence of an isospin chemical potential at next-to-leading order at zero temperature. It is shown that the three-flavor $$\chi $$ χ PT effective potential and condensates can be mapped onto two-flavor $$\chi $$ χ PT ones by integrating out mesons with strange-quark content (kaons and eta), with renormalized couplings. We compare the results for the light-quark and pion condensates at finite pseudoscalar source with ($$2+1$$ 2 + 1 )-flavor lattice QCD, and we also compare the axial condensate at zero pseudoscalar and axial sources with lattice QCD data. We find that the light-quark, pion, and axial condensates are in very good agreement with lattice data. There is an overall improvement by including NLO effects.

Nonequilibrium Dynamics of the Chiral Quark Condensate under a Strong Magnetic Field

Strong magnetic fields impact quantum-chromodynamics (QCD) properties in several situations; examples include the early universe, magnetars, and heavy-ion collisions. These examples share a common trait—time evolution. A prominent QCD property impacted by a strong magnetic field is the quark condensate, an approximate order parameter of the QCD transition between a high-temperature quark-gluon phase and a low-temperature hadronic phase. We use the linear sigma model with quarks to address the quark condensate time evolution under a strong magnetic field. We use the closed time path formalism of nonequilibrium quantum field theory to integrate out the quarks and obtain a mean-field Langevin equation for the condensate. The Langevin equation features dissipation and noise kernels controlled by a damping coefficient. We compute the damping coefficient for magnetic field and temperature values achieved in peripheral relativistic heavy-ion collisions and solve the Langevin equation for a temperature quench scenario. The magnetic field changes the dissipation and noise pattern by increasing the damping coefficient compared to the zero-field case. An increased damping coefficient increases fluctuations and time scales controlling condensate’s short-time evolution, a feature that can impact hadron formation at the QCD transition. The formalism developed here can be extended to include other order parameters, hydrodynamic modes, and system’s expansion to address magnetic field effects in complex settings as heavy-ion collisions, the early universe, and magnetars.