Sigma Meson Research Articles

The non-ordinary Regge behavior of the K^*_0(800) or kappa -meson versus the ordinary K^*_0(1430)

The Regge trajectory of an elastic resonance can be calculated from dispersion theory, instead of fitted phenomenologically, using only its pole parameters as input. This also provides a correct treatment of resonance widths in Regge trajectories, essential for very wide resonances. In this work we first calculate the K^*_0(1430) Regge trajectory, finding the ordinary almost real and linear behavior, typical of q bar{q} resonances. In contrast, for the K^*_0(800) meson, the resulting Regge trajectory is non-linear and has a much smaller slope than ordinary resonances, being remarkably similar to that of the f_0(500) or sigma meson. The slope of these unusual Regge trajectories seems to scale with the meson masses rather than with scales typical of quark degrees of freedom. We also calculate the range of the interaction responsible for the formation of these resonances. Our results strongly support a non-ordinary, predominantly meson–meson-like, interpretation for the lightest strange and non-strange resonances.

The sigma meson from QCD sum rules for large- $$N_c$$ N c Regge spectra

The QCD sum rules in the large-$N_c$ limit for the light non-strange vector, axial and scalar mesons are considered assuming a string-like linear spectrum for the radially excited states. We propose a improved method for combined analysis of these channels that gives a reasonable description of the observed spectrum. In the vector-axial case, fixing the pion decay constant and the gluon condensate we obtain more or less physical values for the masses of ground states and the quark condensate. Thus a typical need for this method to fix the mass of some ground state is overcome. Using in the scalar channel the values of presumably universal slope of radial trajectories and the quark condensate obtained in the vector-axial channel, we find that, in contrast to some strong claims in the literature, a prediction of light scalar state with a mass close to the mass of $f_0(500)$ seems to be natural in the considered approach and may follow in a natural way from the Regge phenomenology.

Properties of mesons in a strong magnetic field.

By extending the Phi -derivable approach in the Nambu–Jona-Lasinio model to a finite magnetic field we calculate the properties of pion, sigma , and rho mesons in a magnetic field at finite temperature not only in the quark–antiquark bound state scheme but also in the pion–pion scattering resonant state scenario. Our calculation as a result makes manifest that the masses of pi ^{0} and sigma meson can be nearly degenerate at the pseudo-critical temperature which increases with increasing magnetic field strength, and the pi ^{pm } mass ascends suddenly at almost the same critical temperature. Meanwhile the rho mesons’ masses decrease with the temperature but increase with the magnetic field strength. We also check the Gell-Mann–Oakes–Renner relation and find that the relation can be violated clearly with increasing temperature, and the effect of the magnetic field becomes pronounced around the critical temperature. With different criteria, we analyze the effect of the magnetic field on the chiral phase transition and find that the pseudo-critical temperature of the chiral phase cross, T_mathrm{c}^{chi }, is always enhanced by the magnetic field. Moreover, our calculations indicate that the rho mesons will get melted as the chiral symmetry has not yet been restored, but the sigma meson does not disassociate even at very high temperature. Particularly, it is the first to show that there does not exist a vector meson condensate in the QCD vacuum in the pion–pion scattering scheme.

Parameter fitting in three-flavor Nambu–Jona-Lasinio model with various regularizations

We study the three-flavor Nambu–Jona-Lasinio model with various regularization procedures. We perform parameter fitting in each regularization and apply the obtained parameter sets to evaluate various physical quantities, several light meson masses, decay constant and the topological susceptibility. The model parameters are adopted even at very high cutoff scale compare to the hadronic scale to study the asymptotic behavior of the model. It is found that all the regularization methods except for the dimensional one actually lead reliable physical predictions for the kaon decay constant, sigma meson mass and topological susceptibility without restricting the ultra-violet cutoff below the hadronic scale.

Nonequilibrium meson production in strong fields

We develop a kinetic equation approach to nonequilibrium pion and sigma meson production in a time-dependent, chiral symmetry breaking field (inertial mechanism). We investigate the question to what extent the low-momentum pion enhancement observed in heavy- ion collisions at CERN - LHC can be addressed within this formalism. In a first step, we consider the inertial mechanism for nonequilibrium production of a—mesons and their simultaneous decay into pion pairs for two cases of a mass evolution. The resulting pion distribution shows a strong low-momentum enhancement which can be approximated by a thermal Bose distribution with a chemical potential that appears as a trace of the nonequilibrium process of its production.

Properties of the sigma meson at finite temperature

We study the changes of the mass and width of the sigma meson in the framework of the Linear Sigma Model at finite temperature, in the one-loop approximation. We have found that as the temperature increases, the mass of sigma shifts down. We have also analyzed the [Formula: see text]-spectral function and we observe an enhancement at the threshold which is a signature of partial restoration of chiral symmetry, also interpreted as a tendency to chiral phase transition. Additionally, we studied the width of the sigma, when the threshold enhancement takes place, for different values of the sigma mass. We found that there is a brief enlargement followed by an abrupt fall in the width as the temperature increases, which is also related with the restoration of chiral symmetry and an indication that the sigma is a bound state of two pions.

Medium effects on the relaxation of dissipative flows in a hot pion gas

The relaxation times over which dissipative fluxes restore their steady state values have been evaluated for a pion gas using the 14-moment method. The effect of the medium has been implemented through a temperature dependent pi-pi cross-section in the collision integral which is obtained by including one-loop self-energies in the propagators of the exchanged rho and sigma mesons. To account for chemical freeze out in heavy ion collisions, a temperature dependent pion chemical potential has been introduced in the distribution function. The temperature dependence of the relaxation times for shear and bulk viscous flows as well as the heat flow is significantly affected.

Entropy in the quark–hadron transition

We study, in the PNJL model, how the entropy of interacting quarks reflects the change in the effective degrees of freedom as the temperature increases through the quark–hadron phase transition. With inclusion of mesonic correlations, the effective degrees of freedom change from those of pi and sigma mesons at low temperatures to those of free quarks at high temperatures, with a resultant second order phase deconfinement transition in the chiral limit.

Collective interaction of QCD strings and early stages of high-multiplicity pA collisions

We study the early stages of "central" pA and peripheral AA collisions. Several observables indicate that at a sufficiently large number of participant nucleons the system undergoes a transition into a new "explosive" regime. By defining a string-string interaction through the sigma meson exchange and performing molecular dynamics simulation, we argue that one should expect a strong collective implosion of the multi-string "spaghetti" state, creating significant compression of the system in the transverse plane. Another consequence is the collectivization of the "sigma clouds" of all strings into a chirally symmetric fireball. We find that these effects happen provided the number of strings $N_s > 30$ or so, as only such a number can compensate a small sigma-string coupling. These findings should help us to understand the subsequent explosive behavior, observed for the particle multiplicities roughly corresponding to this number of strings.

Nonequilibrium dynamics and transport near the chiral phase transition of a quark-meson model

Based on the 2PI quantum effective action of the linear sigma model with constituent quarks, we develop a transport approach to study systems out of equilibrium. In particular, we focus on the chiral phase transition as well as the critical point, where nonequilibrium effects near the phase transition give rise to critical behavior such as the fluctuation of the baryon number density. Predictions for long-range correlations and fluctuations of observables in our model could be used to study fundamental properties of the QCD phase transition. In the previous version of our transport model the chiral fields are implemented as mean fields, whereas quarks are treated as on-shell particles in the Vlasov equation with a dynamical force term. The current update includes also the distribution functions of sigma mesons and pions in a self-consistent way. On this basis a dissipation kernel between the mean fields and particle modes can be implemented.

Real-time correlation functions in the $$O(N)$$ O ( N ) model from the functional renormalization group

In the framework of the functional renormalization group (FRG) we present a simple truncation scheme for the computation of real-time mesonic n-point functions, consistent with the derivative expansion of the effective action. Via analytic continuation on the level of the flow equations we perform calculations of mesonic spectral functions in the scalar O(N) model, which we use as an exploratory example. By investigating the renormalization-scale dependence of the 2-point functions we shed light on the nature of the sigma meson, whose spectral properties are predominantly of dynamical origin.

Medium induced Lorentz symmetry breaking effects in nonlocal Polyakov–Nambu–Jona-Lasinio models

In this paper we detail the thermodynamics of two flavor nonlocal Polyakov-Nambu-Jona-Lasinio models for different parametrizations of the quark interaction regulators. The structure of the model is upgraded in order to allow for terms in the quark selfenergy which violate Lorentz invariance due to the presence of the medium. We examine the critical properties, the phase diagram as well as the equation of state. Furthermore, some aspects of the Mott effect for pions and sigma mesons are discussed explicitly within a nonlocal Polyakov-Nambu-Jona-Lasinio model. In particular, we continued the meson polarization function in the complex energy plane and under certain approximations, we were able to extract the imaginary part as a function of the meson energy. We were not able to calculate the dynamical meson mass, and therefore resorted to a technical study of the temperature dependence of the meson width by replacing the meson energy with the temperature dependent spatial meson mass. Our results show that while the temperature behavior of the meson widths is qualitatively the same for a wide class of covariant regulators, the special case where the nonlocal interactions are introduced via the instanton liquid model singles out with a drastically different behavior.

Pion and Sigma Meson Dissociation in a Modified NJL Model at Finite Temperature

We investigate pion and sigma meson correlations in hot quark matter within a modified NJL model. Special emphasis is on the transformation of mesonic bound states to resonances (Mott dissociation) when due to the partial chiral symmetry restoration with increasing temperature the threshold of quark-antiquark continuum states drops below the meson mass at the corresponding Mott temperature. The description is based on evaluating the polarization functions for quark-antiquark (meson) correlations as a function of the temperature and the results can be represented by introducing modulus and phase of the complex propagator functions for the mesonic states. We study the effect of modelling confinement by introducing a low-momentum cutoff in loop integrals. We make the ansatz that this cutoff is identified with the dynamically generated quark mass gap and find an increase of the continuum threshold which makes the otherwise unbound sigma meson a bound state in the vacuum. We discuss the in-medium behavior of the mesonic phase shifts including the Mott effect and find accordance with the Levinson theorem.

Unconstrained Hamiltonian formulation of low energy QCD

Using a generalized polar decomposition of the gauge fields into gaugerotation and gauge-invariant parts, which Abelianises the Non-Abelian Gauss-law constraints to be implemented, a Hamiltonian formulation of QCD in terms of gauge invariant dynamical variables can be achieved. The exact implementation of the Gauss laws reduces the colored spin-1 gluons and spin-1/2 quarks to unconstrained colorless spin-0, spin-1, spin-2 and spin-3 glueball fields and colorless Rarita-Schwinger fields respectively. The obtained physical Hamiltonian naturally admits a systematic strongcoupling expansion in powers of λ = g−2/3, equivalent to an expansion in the number of spatial derivatives. The leading-order term corresponds to non-interacting hybridglueballs, whose low-lying spectrum can be calculated with high accuracy by solving the Schrödinger-equation of the Dirac-Yang-Mills quantum mechanics of spatially constant fields (at the moment only for the 2-color case). The discrete glueball excitation spectrum shows a universal string-like behaviour with practically all excitation energy going in to the increase of the strengths of merely two fields, the “constant Abelian fields” corresponding to the zero-energy valleys of the chromomagnetic potential. Inclusion of the fermionic degrees of freedom significantly lowers the spectrum and allows for the study of the sigma meson. Higher-order terms in λ lead to interactions between the hybridglueballs and can be taken into account systematically using perturbation theory in λ, allowing for the study of IR-renormalisation and Lorentz invarianz. The existence of the generalized polar decomposition used, the position of the zeros of the corresponding Jacobian (Gribov horizons), and the ranges of the physical variables can be investigated by solving a system of algebraic equations. Its exact solution for the case of one spatial dimension and first numerical solutions for two and three spatial dimensions indicate that there is a finite number of solutions separated by Gribov horizons.

Identification of non-ordinary mesons from the dispersive connection between their poles and their Regge trajectories: The [formula omitted] resonance

We show how the Regge trajectory of a resonance can be obtained from its pole in a scattering process and analytic constraints in the complex angular momentum plane. The method is suited for resonances that dominate an elastic scattering amplitude. In particular, from the ρ(770) resonance pole in ππ scattering, we obtain its linear Regge trajectory, characteristic of ordinary quark–antiquark states. In contrast, the f0(500) pole—the sigma meson—which dominates scalar isoscalar ππ scattering, yields a nonlinear trajectory with a much smaller slope at the f0(500) mass. Conversely, imposing a linear Regge trajectory for the f0(500), with a slope of typical size, yields an elastic amplitude at odds with the data. This provides strong support for the non-ordinary nature of the sigma meson.

Effective multiquark interactions with explicit breaking of chiral symmetry

In a long distance Lagrangian approach to the low lying meson phenomenology we present and discuss the most general spin zero multi-quark interaction vertices of non-derivative type which include a set of effective interactions proportional to the current quark masses, breaking explicitely the chiral SU(3)_L X SU(3)_R and U_A(1) symmetries. These vertices are of the sameorder in Nc counting as the 't Hooft flavor determinant interaction and the 8 quark interactions which extend the original leading in Nc four quark interaction Lagrangian of Nambu and Jona-Lasinio. The Nc assignements match the counting rules based on arguments set by the scale of spontaneous chiral symmetry breaking. With path integral bosonization techniques which take appropriately into account the quark mass differences we derive the mesonic Lagrangian up to 3-point mesonic vertices. We demonstrate that explicit symmetry breaking effects in interactions are essential to obtain the correct empirical ordering and magnitude of the splitting of certain states such as m_K < m_eta for the pseudoscalars and m{kappa(800)} < m{a0(980)} m{f0(980)} in the scalar sector, and achieve total agreement with the empirical low lying meson mass spectra. With all parameters of the model fixed by the spectra we analyze further a bulk of two body decays at tree level of the bosonic Lagrangian: the strong decays of the scalars sigma->pi pi, f0->pi pi, kappa->pi K, a0(980)->pi eta, as well as the two photon decays of a0, f0 and sigma mesons and the anomalous decays of the pseudoscalars {pi,eta,eta'}-> 2 photons. Our results for the strong decays are within the current expectations and the pseudoscalar radiative decays are in very good agreement with data. The radiative decays of the scalars are smaller than the observed values for the f0 and the sigma, but reasonable for the a0. A detailed discussion accompanies all the results.

Improved Nucleon Properties in the Extended Quark Sigma Model

The quark sigma model describes the quarks interacting via exchange the pions and sigma meson fields. A new version of mesonic potential is suggested in the frame of some aspects of the quantum chromodynamics (QCD). The field equations have been solved in the mean-field approximation for the hedgehog baryon state. The obtained results are compared with previous works and other models. We conclude that the suggested mesonic potential successfully calculates nucleon properties.

Properties and Composition of the $f_0(500)$ Resonance

In this talk we review our recent developments on the understanding of the nature of the f_0(500) resonance---or sigma meson---coming from the N_c expansion, dispersion relations with Chiral Perturbation Theory, as well as finite energy sum rules and semi-local duality.

Sigma meson in vacuum and nuclear matter

We have obtained the value of the interaction constant g σππ that adjusts the values obtained in the E791 Collaboration at Fermilab and BES Collaboration at the Beijing Electron Positron Collider experiments. To get this we have used the concept of critical width to make compatible the parameters obtained from the Breit-Wigner formula and those obtained from the density function. Also, the total width and effective mass modification of the sigma meson in nuclear matter has been studied in the Walecka model, assuming that the sigma couples to a pair of nucleon-antinucleon states and to particle-hole states, including the in-medium effect of sigma-omega mixing. We have considered, for completeness, the coupling of sigma to two virtual pions. We have found that the sigma meson mass decreases with respect to its value in vacuum and that the contribution of the sigma-omega mixing effect on the mass shift is relevant.

Mechanism of pion production in αp scattering at 1 GeV/nucleon

The one-pion and two-pion production in the p(alpha, alpha prime)X reaction at an energy of E{alpha} = 4.2 GeV has been studied by simultaneous registration of the scattered alpha particles and the secondary pion or proton. The obtained results demonstrate that the inelastic alpha-particle scattering on the proton at the energy of the experiment proceeds either through excitation and decay of Delta resonance in the projectile or through excitation in the target proton of the Roper resonance, which decays mainly on a nucleon and a pion or a nucleon and a sigma meson - system of two pions in the isospin I = 0, S-wave.