We study the effects of CP violation on the nature of the chiral transition within the linear sigma model with two flavors of quarks. The finite-temperature effective potential containing contributions from nontrivial values for the parameter $θ$ is computed to one loop order and their minima structure is analyzed. Motivated by the possibility of observing the formation of CP-odd domains in high-energy heavy ion collisions, we also investigate the behavior of the effective potential in the presence of a strong magnetic background. We find that the nature of the chiral transition is influenced by both $θ$ and the magnetic field.
We study the chiral phase transition in the linear sigma model with 2 quark flavors and $N_c$ colors. One-loop calculations predict a first-order phase transition at both $μ=0$ and $μ\neq 0$. We also discuss the phase diagram and make a comparison with a thermal parametrization of existing heavy-ion experimental data.
The photoproduction rate of pentaquark $Θ^+$ is calculated in a hot and dense medium. At high temperature and density, due to the restoration of chiral symmetry, photoproduction energy threshold is increased. Above the thresold the production cross section is strongly enhanced.
The meson masses and mixing angles have been calculated for the scalar and pseudoscalar sector in the framework of the generalized 2+1 flavor Polyakov loop augmented quark meson linear sigma model. We have given the results for two different forms of the effective Polyakov loop potential. The comparison of results with the existing calculations in the bare 2+1 quark meson linear sigma model, shows that the restoration of chiral symmetry becomes sharper due to the influence of the Polyakov loop potential. We find that inclusion of the Polyakov loop in quark meson linear sigma model together wit…
A recently proposed approximate large-n ground state solution of the U_L(n)xU_R(n) symmetric linear sigma model is investigated at finite temperature. We study the coupled evaporation of two condensates corresponding to the symmetry breaking pattern U_L(3)xU_R(3) -> U_V(2), realized by the ground state in certain parts of the coupling space. The region of the fluctuation induced first order transitions and its second order boundary is mapped out. The existence of a tricritical point is conjectured.
The effective restoration of the chiral U(A)(1) symmetry in strong interactions is studied using the linear chiral SU(3)xSU(3) model at finite temperatures. We find that the disappearance of the chiral anomaly causes a considerable change in the meson mass spectrum. We propose several signals for detecting this chiral phase in ultrarelativistic heavy-ion collisions: The eta/pi0 ratio is enhanced by an order of magnitude, the a0 is suppressed in the K+K- mass spectrum, and the scalar kappa meson appears as a peak just below the K*(892) in the invariant piK mass spectrum.
It is by now well known that symmetries may be broken at high temperature. However,in renormalizable supersymmetric theories any internal symmetry gets always restored. In nonrenormalizable theories the situation is far less simple. We review here some recent work which seems to indicate that renormalizability is not essential for the restoration of internal symmetries in supersymmetry.
We analyze the $f_0(500)$ state generated as a pole of $ππ$ scattering within unitarized low-energy effective theories at finite temperature. First, we report on the $σ$ self-energy in the LSM, which is used as a benchmark in order to test the hypotheses carried out. The relation of that thermal pole with the scalar susceptibility is studied within a scalar saturation approach, which yields results complying with lattice data. The robustness and predictability of this method are studied in terms of the low-energy constants involved and the unitarization method. Our analysis highlights the impo…
The sigma-meson, which is at best a broad resonance in the vacuum, may suffer a substantial red-shift and appear as a soft and narrow collective mode at finite temperature and baryon densities. The physics behind this softening phenomena and its relation to the partial restoration of chiral symmetry are discussed. Possible experiments in laboratory to test the idea are also summarized.
Complex poles of the unitarized pi-pi scattering amplitude in nuclear matter are studied. Partial restoration of chiral symmetry is modeled by the decrease of in-medium pion decay constant f*_{pi}. For large chiral restoration (f*_{pi}/f_{pi} << 1), 2nd sheet poles in the scalar (sigma) and the vector (rho) mesons are both dictated by the Lambert W function and show universal softening as f*_{pi} decreases. In-medium pi-pi cross section receives substantial contribution from the soft mode and exhibits a large enhancement in low-energy region. Fate of this universality for small chiral restorat…
The entanglement extended Polyakov--Nambu--Jona-Lasinio model at zero chemical potential in the presence of an external magnetic field is studied. The effect of the entanglement parametrization is analyzed, in particular, on the pseudocritical transition temperatures and on the thermodynamical properties of the model. The model predicts that the coincidence or not of both chiral and deconfinement transition temperatures, in the presence of an external magnetic field, depends on the entanglement parametrization chosen.
Chiral symmetry restoration at nonzero temperature is studied in the framework of the O(4) linear sigma model and the U(N_f)_r x U(N_f)_l linear sigma model with N_f=2,3, and 4 quark flavors. We investigate the temperature dependence of the masses of the scalar and pseudoscalar mesons, and the non-strange, strange, and charm condensates within the Hartree approximation as derived from the Cornwall-Jackiw-Tomboulis formalism. We find that the masses of the non-strange and strange mesons at nonzero temperature depend sensitively on the particular symmetry of the model and the number of light qua…
We explore the effects of breaking and restoration of chiral and axial symmetries using an extended three-flavor Nambu-Jona-Lasinio model that incorporates explicitly the axial anomaly through the 't Hooft interaction. We implement a temperature (density) dependence of the anomaly coefficient motivated by lattice results for the topological susceptibility. The spectrum of scalar and pseudoscalar mesons is analyzed bearing in mind the identification of chiral partners and the study of its convergence. We also concentrate on the behavior of the mixing angles that give us relevant information on …
We study patterns of chiral symmetry breaking at zero temperature and its subsequent restoration at nonzero temperature within the $SU(3)_{r} \times SU(3)_{\ell}$ linear sigma model. Gap equations for the masses of the scalar and pseudoscalar mesons and the non-strange and strange quark condensates are systematically derived in the Hartree approximation via the Cornwall-Jackiw-Tomboulis formalism. In the chiral limit, the chiral symmetry restoring transition is found to be first order, as predicted by universality arguments. Taking the experimental values for the meson masses, however, the tra…
We study the restoration of chiral symmetry in linear sigma models with two quark flavors. The models taken into consideration have a U(2)_L x U(2)_R and an O(4) internal symmetry. The physical mesons of these models are sigma, pion, eta and a_0 where the latter two are not present in the O(4) model. Including two-loop contributions through sunset graphs we calculate the temperature behavior of the order parameter and the masses for explicit chiral symmetry breaking and in the chiral limit. Decay threshold effects introduced by the sunset graphs alter the temperature dependence of the condensa…
The effects of the Tsallis distribution which has two parameters, $q$ and $T$,on physical quantities are studied using the linear sigma model in chiral phase transitions. The Tsallis distribution approaches the Boltzmann-Gibbs distribution as $q$ approaches $1$. The parameter $T$ dependences of the condensate and mass for various $q$ are shown, where $T$ is called temperature. The critical temperature and energy density are described with digamma function, and the $q$ dependences of these quantities and the extension of Stefan-Boltzmann limit of the energy density are shown. The following fact…
Given Brown/Rho scaling we thought of the mesons which are observed in Nambu-Jona Lasinio theory as collective modes. The pi, sigma, rho and A_1, should go smoothly through T_c as the temperature rose, going massless as T comes to T_c.
We use the linear sigma model with quarks to study the QCD phase diagram from the point of view of chiral symmetry restoration. We compute the leading order effective potential for high and low temperatures and finite quark chemical potential, up to the contribution of the ring diagrams to account for the plasma screening effects. We fix the values of the model couplings using physical values for the input parameters such as the vacuum pion and sigma masses, the critical temperature at vanishing quark chemical potential and the conjectured end point value of the baryon chemical potential of th…
An important role of the scalar isoscalar sigma-meson in the low-energy physics is discussed. The behavior of the sigma-meson in the hot and dense medium is studied. It is shown that in the vicinity of critical values of temperature(T) and chemical potential(m) the sigma-meson can become a sharp resonance. This effect can lead to a strong enhancement of the processes pi pi -> gamma gamma and pi pi-> pi pi near the two-pion threshold. Experimental observation of this phenomenon can be interpreted as a signal of approaching the domain where the chiral symmetry restoration and phase transition of…
The phase diagram of the three-flavor QCD is mapped out in the low mass corner of the m_pi-m_K--plane with help of the SU_L(3) x SU_R(3) linear sigma model (LSM). A novel zero temperature parametrization is proposed for the mass dependence of the couplings away from the physical point based on the the three-flavor chiral perturbation theory (U(3) ChPT). One-loop thermodynamics is constructed by applying optimized perturbation theory. The unknown dependence of the scalar spectra on the pseudoscalar masses limitates the accuracy of the predictions. Results are compared to lattice data and simila…
It is pointed out that the hadron spectroscopy should be a study of the structure of the QCD vacuum, low-energy elementary excitations on top of which are hadrons. Concentrating on the dynamical breaking of the chiral symmetry in the QCD vacuum, we emphasize the importance to clarify what is going on with mesons in the $I=J=0$-channel, i.e., the sigma meson channel, because it is connected to the quantum fluctuations of the chiral order parameter. After summarizing the significance of the sigma meson in QCD and low-energy hadron phenomenology, we give a review on some theoretical and experimen…
The chiral phase transition at a certain critical temperature is a restoration mechanism of the chiral symmetry, broken by the nonzero mass of quarks and mesons. The transition can be studied through several models, among which are the sigma models. An analysis is made on the linear and nonlinear sigma models with different approximations, and we show that the transition is of second order in both cases.
We study the structure of the sigma meson, the lowest-lying resonance of the pi pi scattering in the scalar-isoscalar channel, through the softening phenomena associated with the partial restoration of chiral symmetry. We build dynamical chiral models to describe the pi pi scattering amplitude, in which the sigma meson is described either as the chiral partner of the pion or as the dynamically generated resonance through the pi pi attraction. It is shown that the internal structure is reflected in the softening phenomena; the softening pattern of the dynamically generated sigma meson is qualit…
Chiral thermodynamics of charmed mesons is formulated at finite temperature within a $2+1+1$-flavored effective Lagrangian incorporating heavy quark symmetry. The charmed-meson mean fields act as an extra source which breaks the chiral symmetry explicitly. This leads to effective interactions between the light and heavy-light mesons, which intrinsically depend on temperature. Effective masses of the scalar and pseudoscalar charmed-mesons tend to approach each other as increasing temperature, so that the splitting between the chiral partners is reduced. These chiral splittings are shown to be l…
In this work, we review how the mass and the width of the $f_{0}(500)$ pole behave in a regime where temperature is below the critical chiral transition value. This is attained by considering a large-$N$ $O(N + 1)/O(N)$ invariant Non-Linear Sigma Model (NLSM) such that we can study the dynamical generation of a $f_{0}(500)$ resonance. Introducing thermal effects via the imaginary time formalism allows us to study the behavior of the pole and relate it to chiral restoration.
We investigate the generation of a gluon screening mass in Yang-Mills theory in the Landau gauge. We propose a gauge-fixing procedure where the Gribov ambiguity is overcome by summing over all Gribov copies with some weight function. This can be formulated in terms of a local field theory involving constrained, nonlinear sigma model fields. We show that a phenomenon of radiative symmetry restoration occurs in this theory, similar to what happens in the standard nonlinear sigma model in two dimensions. This results in a nonzero gluon screening mass, as seen in lattice simulations.
We analyze chiral restoration within the $O(N+1)/O(N)$ Non-Linear Sigma Model for large $N$ as an effective theory for low-energy QCD at finite temperature $T$. The free energy is constructed diagramatically to ${\cal O}(TM^3)$ in the pion mass expansion, which allows to derive the quark condensate and the scalar susceptibility in the chiral limit. At this order, we do not have to deal with renormalization, neither from divergences from mass tadpoles nor from those of higher order loop contributions. Our results for the critical behaviour are consistent with expectations from lattice analysis …
The pi pi scattering is studied in two-flavor chiral models with a finite pion mass to investigate the nature of the sigma meson which is observed as the lowest scalar-isoscalar resonance. We compare several models with different origins of the sigma meson, such as the chiral partner of the pion and the dynamically generated pi pi molecule. We find that the dynamically generated sigma meson exhibits a novel pattern of the threshold enhancement reflecting the s-wave nature of the resonance, which is qualitatively different from the softening of the chiral partner introduced as a bare field. Thi…
First we summarize the quark-level linear $σ$ model compositeness conditions and verify that indeed $m_σ= 2 m_q$ when $m_π= 0$ and $N_c=3$, rather than in the $N_c\to\infty$ limit, as is sometimes suggested. Later we show that this compositeness picture also predicts a chiral symmetry restoration temperature $T_c = 2f_π$, where $f_π$ is the pion decay constant. We contrast this self-consistent Z=0 compositeness analysis with prior studies of the compositeness problem.
We study thermal properties of a large-N massless pion gas using a low-energy QCD approach given by an $O(N +1)/O(N)$ Nonlinear Sigma Model. We build diagrammatically the associated finite free energy to $O(TM^{3})$ in the pion mass expansion through an effective vertex that considers all the contributions coming from closed diagrams. Subsequently, we calculate finite order parameters such as the quark condensate and its respective derivative, i.e., the scalar susceptibility, in the chiral limit, along with their associated critical exponents. These results are compared with our previous unita…
We investigate the chiral phase transition of the strongly interacting matter at nonzero temperature and baryon chemical potential $μ_B$ within an extended (2+1) flavor Polyakov constituent quark-meson model which incorporates the effect of the vector and axial vector mesons. The parameters of the model are determined by comparing masses and tree-level decay widths with experimental values. We examine the restoration of the chiral symmetry by monitoring the temperature evolution of condensates. We study the $T-ρ_B$ phase diagram of the model and find that a critical end point exists, although …
The phase diagram at finite temperature and density is investigated in the framework of the Polyakov linear sigma model (PLSM) with three light quark flavors in the mean field approximation. It is found that in the PLSM, the three phase transitions, i.e, the chiral restoration of $u,d$ quarks, the chiral restoration of $s$ quark, and the deconfinement phase transition are independent. There exists two-flavor quarkyonic phase at low density and three-flavor quarkyonic phase at high density. The critical end point (CEP) which separating the crossover from the first-order line in the PLSM model i…
It should be a typical subject in this workshop to explore possible change of hadron properties in association with that of QCD vacuum due to an environmental change. In this report, we first summarize what hadrons are expected to show such a change and how they do. Then we propose several experiments including the ones utilizing electron and photon beams for examining possible restoration of chiral symmetry in nuclei and the possible existence of the sigma meson. The experiments are based on the observation that the sigma meson may decrease the mass and the width along with the partial restor…
We explore the phase diagram and the modification of mesonic observables in a hot and dense medium using the (2+1) Polyakov-Nambu-Jona-Lasinio model. We present the phase diagram in the ($T,\,μ_B$)-plane, with its isentropic trajectories, paying special attention to the chiral critical end point (CEP). Chiral and deconfinement transitions are examined. The modifications of mesonic observables in the medium are explored as a tool to analyze the effective restoration of chiral symmetry for different regions of the phase diagram. It is shown that the meson masses, namely that of the kaons, change…
The modification of mesonic observables in a hot medium is analyzed as a tool to investigate the restoration of chiral and axial symmetries in the context of the Polyakov-loop extended Nambu--Jona-Lasinio model. The results of the extended model lead to the conclusion that the effects of the Polyakov loop are fundamental for reproducing lattice findings. In particular, the partial restoration of the chiral symmetry is faster in the PNJL model than in the NJL one, and it is responsible for several effects: the meson-quark coupling constants show a remarkable difference in both models, there is …
The effects of the axial anomaly are suppressed at high temperatures due to screening effects in the quark-gluon plasma. If the suppression is nearly complete close to the chiral transition temperature, this can have consequences for the nature of the phase transition. The use of a chiral action such as Domain Wall Fermions allows us to gain a deeper insight into the issue. Our lattice sizes were $16^3\times 8\times L_s$, with $L_s=32$ or 48, and our pion mass was approximately 200 MeV. We found that $U(1)_A$ stayed broken above the chiral transition. However the breaking was found to be due t…
We analize the role played by the thermal $f_0(500)$ state or $σ$ in chiral symmetry restoration. The temperature corrections to the spectral properties of that state are included in order to provide a better description of the scalar susceptibility $χ_S$ around the transition region. We use the Linear Sigma Model to establish the relation between $χ_S$ and the $σ$ propagator, which is used as a benchmark to test the approach where $χ_S$ is saturated by the $f_0(500)$ inverse self-energy. Within such saturation approach, a peak for $χ_S$ around the chiral transition is obtained when considerin…
We investigate the η'N two-body interaction in the context of the η' meson mass modification in the nuclear medium. It has been argued in several articles that the masses of η' and the other pseudoscalar mesons (π, K, η) should degenerate in the chiral-symmetric phase. It is expected that the reduction of the mass difference between eta and eta' would take place in the nuclear matter if one assumes that the decrease of the quark condensate at the normal nuclear density occurs with partial restoration of chiral symmetry. At low density, the in-medium self-energy giving the mass modification by …
We review recent theoretical progress in low-mass dilepton production at CERN-SpS energies. Various hadronic approaches to calculate the vector correlator in hot/dense hadronic matter are discussed and confronted with each other. Possible consequences for the nature of chiral restoration are indicated.
I review recent results obtained within chiral effective models, on the phase structure of hot quark matter in a strong magnetic background. After a brief introduction, I focus on the results obtained within two chiral models improved with the Polyakov loop. The models differ for the content of interactions, but both of them are tuned to reproduce Lattice QCD thermodynamics at zero and imaginary chemical potential. One of them takes into account an explicit Polyakov loop dependence of the coupling; the other one neglects this contribution, but takes into account multi-quark interactions. A com…
We review recent results on properties of the meson gas relevant for Heavy Ion Collision and Nuclear Matter experiments, within the framework of chiral lagrangians. In particular, we describe the temperature and density evolution of the $σ$ and $ρ$ poles and its connection with chiral symmetry restoration, as well as the chemical nonequilibrated phase and transport coefficients.
We investigate the screening masses of neutral pions and sigma mesons in hot and magnetized quark matter in the framework of a two-flavor lattice-improved Nambu-Jona-Lasinio (NJL) model with a magnetic field dependent coupling constant, which is determined by utilizing the results from lattice QCD simulations. Since such model can well reproduce inverse magnetic catalysis (IMC), by comparing with the standard NJL model, we systemically analyze the impacts of IMC on the temperature and magnetic field dependences of the longitudinal and transverse screening masses of the chiral partners, i.e. π^…
We present a study of the $ππ$ scattering amplitude in the $σ$ and $ρ$ channels at finite temperature and nuclear density within a chiral unitary framework. Meson resonances are dynamically generated in our approach, which allows us to analyze the behavior of their associated scattering poles when the system is driven towards chiral symmetry restoration. Medium effects are incorporated in three ways: (a) by thermal corrections of the unitarized scattering amplitudes, (b) by finite nuclear density effects associated to a renormalization of the pion decay constant, and complementarily (c) by ext…
In the mean-field approximation we study the chiral soliton within the linear sigma model in a thermal vacuum. The chiral soliton equations with different boundary conditions are solved at finite temperatures and densities. The solitons are discussed before and after the chiral restoration. We find that the system has soliton solutions even after the chiral restoration and they are very different from those before the chiral restoration, which indicates that the quarks are still bounded after the chiral restoration.
At large N_c, cold nuclear matter is expected to form a crystal and thus spontaneously break translational symmetry. The description of chiral symmetry breaking and translational symmetry breaking can become intertwined. Here, the focus is on aspects of chiral symmetry breaking and its possible restoration that are by construction independent of the nature of translational symmetry breaking---namely spatial averages of chiral order parameters. A system will be considered to be chirally restored provided all spatially-averaged chiral order parameters are zero. A critical question is whether chi…
It has been argued by Pisarski and Wilczek that finite temperature restoration of the chiral symmetry SU(Nf) x SU(Nf) is first-order for Nf >=3. This type of chiral symmetry with a large Nf may appear in the Higgs sector if one considers models such as walking technicolor theories. We examine the first-order restoration of the chiral symmetry from the point of view of the electroweak phase transition. The strength of the transition is estimated in SU(2) x U(1) gauged linear sigma model by means of the finite temperature effective potential at one-loop with the ring improvement. Even if the mas…
The fate of symmetries at high temperature determines the dynamics of the very early universe. It is conceivable that temperature effects favor symmetry breaking instead of restoration. Concerning global symmetries, the non-linear sigma model is analyzed in detail. For spontaneously broken gauge symmetries, we propose the gauge boson magnetic mass as a ``flag'' for symmetry (non)-restoration. We consider several cases: the standard model with one and two Higgs doublets in the perturbative regime, and the case of a strongly interacting Higgs sector. The latter is done in a model independent way…
We show that the $σ/f_0(500)$ state with finite-temperature $T$ corrections to its spectral properties included, plays an essential role for the description of the scalar susceptibility $χ_S$, signaling chiral symmetry restoration. First, we use the $O(4)$ Linear Sigma Model as a testbed to derive the connection between $χ_S$ and the $σ$ propagator and to check the validity and reliability of the approach where $χ_S$ is saturated by the $σ/f_0(500)$ inverse self-energy, which we calculate at finite $T$ to one loop. A more accurate phenomenological description is achieved by considering the sat…
We present our recent results for the rho and sigma mesons considered as resonances in pion-pion scattering in a thermal bath. We use chiral perturbation theory to fourth order in p for the low energy behaviour, then extend the analysis via the unitarization method of the Inverse Amplitude into the resonance region. The width of the rho broadens about twice the amount required by phase space considerations alone, its mass staying practically constant up to temperatures of order 150 MeV. The sigma meson behaves in accordance to chiral symmetry restoration expectations.
We discuss the recent status in the theoretical understanding of dilepton production in central heavy-ion reactions with the Pb-beam at the full CERN-SpS energy of 158 AGeV. In the low-mass region ($M\le$~1 GeV) a strong broadening of the vector meson resonances in hot and dense matter (especially for the $ρ$ meson) entails thermal dilepton rates very reminiscent to perturbative $q\bar q$ annihilation close to the expected phase boundary of the chiral symmetry restoring transition. A consistent description of the experimentally observed enhancement at both low and intermediate masses (1.5 GeV~…
We study the temperature evolution of the rho and sigma mass and width, using a unitary chiral approach. The one-loop pion-pion scattering amplitude in Chiral Perturbation Theory at finite temperature is unitarized via the Inverse Amplitude Method. Our results predict a clear increase with T of both the rho and sigma widths. The masses decrease slightly for high T, while the rho-pion-pion coupling increases. The rho behavior seems to be favored by experimental results. In the sigma case, it signals chiral symmetry restoration.
In the introduction, we will discuss the symmetries of QCD, its breaking in the physical vacuum and its restoration at finite temperature and/or density. Then we will discuss what exact relations can be made between chiral symmetry restoration and the imaginary part of the vector vector correlation function, which is directly related to the dilepton spectrum coming from a hot and/or dense medium. Finally, we will focus on the vector meson pole appearing in the imaginary part and discuss results on how the shape changes using QCD sum rules in medium. In particular, we will discuss three charact…
We consider the $O(N+1)/O(N)$ Non-Linear Sigma Model for large $N$ as an effective theory for low-energy QCD at finite temperature $T$, in the chiral limit. At $T=0$ this formulation provides a good description of scattering data in the scalar channel and generates dynamically the $f_0(500)$ pole, the pole position lying within experimental determinations. Previous $T=0$ results with this model are updated using newer analysis of pion scattering data. We calculate the pion scattering amplitude at finite $T$ and show that it satisfies exactly thermal unitarity, which had been assumed but not fo…
We consider the evolution of critical temperature both for the formation of a pion condensate as well as for the chiral transition, from the perspective of the linear sigma model, in the background of a magnetic field. We developed the discussion for the pion condensate in one loop approximation for the effective potential getting magnetic catalysis for high values of B, i.e. a raising of the critical temperature with the magnetic field. For the analysis of the chiral restoration, we go beyond this approximation, by taking one loop thermo-magnetic corrections to the couplings as well as plasma…
By using the symmetry improved CJT effective formalism developed by Pilaftsis and Teresi, the chiral phase transition is reconsidered in the framework of the $O(4)$ linear sigma model in chiral limit. Our results confirm the restorations of the second-order phase transition and the Goldstone theorem in the Hartree approximation. Finally, we explicitly calculate the effective potentials via the order parameter for various temperatures and address advantages of the present method in comparison with the $O(N)$ model in large-$N$ approximation.
