Sigma Meson Mass Research Articles

Calculating composite-particle spectra in Hamiltonian formalism and demonstration in 2-flavor QED1+1d

We consider three distinct methods to compute the mass spectrum of gauge theories in the Hamiltonian formalism: (1) correlation-function scheme, (2) one-point-function scheme, and (3) dispersion-relation scheme. The first one examines spatial correlation functions as we do in the conventional Euclidean Monte Carlo simulations. The second one uses the boundary effect to efficiently compute the mass spectrum. The third one constructs the excited states and fits their energy using the dispersion relation with selecting quantum numbers. Each method has its pros and cons, and we clarify such properties in their applications to the mass spectrum for the 2-flavor massive Schwinger model at m/g = 0.1 and θ = 0 using the density-matrix renormalization group (DMRG). We note that the multi-flavor Schwinger model at small mass m is a strongly coupled field theory even after the bosonizations, and thus it deserves to perform the first-principles numerical calculations. All these methods mostly agree and identify the stable particles, pions πa (JPG = 1−+), sigma meson σ (JPG = 0++), and eta meson η (JPG = 0−−). In particular, we find that the mass of σ meson is lighter than twice the pion mass, and thus σ is stable against the decay process, σ → ππ. This is consistent with the analytic prediction using the WKB approximation, and, remarkably, our numerical results are so close to the WKB-based formula between the pion and sigma-meson masses, Mσ/Mπ = 3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{3} $$\\end{document}.

Neutron star properties with careful parametrization in the vector and axial-vector meson extended linear sigma model

The existence of quark matter inside the cores of heavy neutron stars is a possibility which can be probed with modern astrophysical observations. We use a vector and axial-vector meson extended quark-meson model to describe quark matter in the core of neutron stars. We discover that an additional parameter constraint is necessary in the quark model to ensure chiral restoration at high densities. By investigating hybrid star sequences with various parameter sets, we show that low sigma meson masses are needed to fulfill the upper radius constraints and that the maximum mass of stable hybrid stars is only slightly dependent on the parameters of the crossover-type phase transition. Using this observation and results from recent astrophysical measurements, a constraint of $2.5<{g}_{V}<4.3$ is set for the constituent quark--vector meson coupling. The effect of a nonzero bag constant is also investigated, and we observe that its effect is small for values adopted in previous works.

Implications of the fermion vacuum term in the extended SU(3) quark meson model on compact star properties

We study the impact of the fermion vacuum term in the SU(3) quark meson model on the equation of state and determine the vacuum parameters for various sigma meson masses. We examine its influence on the equation of state and on the resulting mass radius relations for compact stars. The tidal deformability $\Lambda$ of the stars is studied and compared to the results of the mean field approximation. Parameter sets which fulfill the tidal deformability bounds of GW170817 together with the observed two solar mass limit turn out to be restricted to a quite small parameter range in the mean field approximation. The extended version of the model does not yield solutions fulfilling both constraints. Furthermore, no first order chiral phase transition is found in the extended version of the model, not allowing for the twin star solutions found in the mean field approximation.

The Large-$N$ Limit with Vanishing Leading Order Condensate for Zero Pion Mass

It is conventionally assumed that the negative mass squared term in the linear sigma model version of the pion Lagrangian is $M^2 \sim \Lambda_{\rm QCD}^2$ in powers of $N_c$. We consider the case where $M^2 \sim \Lambda^2_{\rm QCD}/N_c$ so that to leading order in $N_c$ this symmetry breaking term vanishes. We present some arguments why this might be plausible. One might think that such a radical assumption would contradict lattice Monte Carlo data on QCD as function of $N_c$. We show that the linear sigma model gives a fair description of the data of DeGrand and Liu both for $N_c = 3$, and for variable $N_c$. The values of quark masses considered by DeGrand and Liu, and by Bali et. al. turn out to be too large to resolve the case we consider from that of the conventional large $N_c$ limit. We argue that for quark masses $m_{q} \ll \Lambda_{\rm QCD}/N_c^{3/2}$, both the baryon mass and nucleon size scale as $\sqrt{N_c}$. For $m_{q} \gg \Lambda_{\rm QCD}/N_c^{3/2}$ the conventional large-$N_c$ counting holds. The physical values of quark masses for QCD correspond to the small quark mass limit. We find pion-nucleon coupling strengths are reduced to order ${\cal O}(1)$ rather than ${\cal O}(N_c)$. Under the assumption that in the large $N_c$ limit the sigma meson mass is larger than that of the omega, and that the omega-nucleon coupling constant is larger than that of the sigma, we argue that the nucleon-nucleon large range potential is weakly attractive and admits an interaction energy of order $\Lambda_{\rm QCD}/N_c^{5/2} \sim 10$ MeV. With these assumptions on coupling and masses, there is no strong long range attractive channel for nucleon-nucleon interactions, so that nuclear matter at densities much smaller than that where nucleons strongly interact is a weakly interacting configuration of nucleons with strongly interacting localized cores.

Consistent parameter fixing in the quark-meson model with vacuum fluctuations

We revisit the renormalization prescription for the quark-meson model in an extended mean-field approximation, where vacuum quark fluctuations are included. At a given cutoff scale the model parameters are fixed by fitting vacuum quantities, typically including the sigma-meson mass $m_\sigma$ and the pion decay constant $f_\pi$. In most publications the latter is identified with the expectation value of the sigma field, while for $m_\sigma$ the curvature mass is taken. When quark loops are included, this prescription is however inconsistent, and the correct identification involves the renormalized pion decay constant and the sigma pole mass. In the present article we investigate the influence of the parameter-fixing scheme on the phase structure of the model at finite temperature and chemical potential. Despite large differences between the model parameters in the two schemes, we find that in homogeneous matter the effect on the phase diagram is relatively small. For inhomogeneous phases, on the other hand, the choice of the proper renormalization prescription is crucial. In particular, we show that if renormalization effects on the pion decay constant are not considered, the model does not even present a well-defined renormalized limit when the cutoff is sent to infinity.

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.

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.

Effect of sigma meson on theD1(2430)→Dππdecay

We study the effect of sigma meson on the ${D}_{1}(2430)\ensuremath{\rightarrow}D\ensuremath{\pi}\ensuremath{\pi}$ decay by constructing an effective Lagrangian preserving the chiral symmetry and the heavy quark symmetry. The sigma meson is included through a linear sigma model, in which both the $q\overline{q}$ and $qq\overline{q}\overline{q}$ states are incorporated respecting their different $U(1{)}_{A}$ transformation properties. We first fit the sigma meson mass and $\ensuremath{\sigma}\mathrm{\text{\ensuremath{-}}}\ensuremath{\pi}\mathrm{\text{\ensuremath{-}}}\ensuremath{\pi}$ coupling constant to the $I=0$, $S$-wave $\ensuremath{\pi}\mathrm{\text{\ensuremath{-}}}\ensuremath{\pi}$ scattering data. Then, we show how the differential decay width $d\ensuremath{\Gamma}({D}_{1}\ensuremath{\rightarrow}D(\ensuremath{\pi}\ensuremath{\pi}{)}_{I=0,L=0})/d{m}_{\ensuremath{\pi}\ensuremath{\pi}}$ depends on the quark structure of the sigma meson. We find that our study, combing with the future data, can give a clue to understand the sigma meson structure.

Eight-quark interactions as a chiral thermometer

A NJL Lagrangian extended to six [1–3] and eight quark interactions [4] is applied to study temperature effects [5] (SU(3) flavor limit, massless case), and [6] (realistic massive case). The transition temperature can be considerably reduced as compared to the standard approach, in accordance with recent lattice calculations [7]. The mesonic spectra built on the spontaneously broken vacuum induced by the’ t Hooft interaction strength, as opposed to the commonly considered case driven by the four-quark coupling, undergoes a rapid crossover to the unbroken phase, with a slope and at a temperature which is regulated by the strength of the OZI violating eight-quark interactions. This strength can be adjusted in consonance with the four-quark coupling and leaves the spectra unchanged, except for the sigma meson mass, which decreases. A first order transition behavior is also a possible solution within the present approach.

Meson mass at real and imaginary chemical potentials

Chemical-potential dependence of pi and sigma meson masses is analyzed at both real and imaginary chemical potentials, ${\ensuremath{\mu}}_{\mathrm{R}}$ and ${\ensuremath{\mu}}_{\mathrm{I}}$, by using the Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model that possesses both the extended ${\mathbb{Z}}_{3}$ symmetry and chiral symmetry. In the ${\ensuremath{\mu}}_{\mathrm{I}}$ region, the meson masses have the Roberge-Weiss periodicity. The ${\ensuremath{\mu}}_{\mathrm{I}}$ dependence of the meson masses becomes stronger as temperature increases. We argue that meson masses and physical quantities in the ${\ensuremath{\mu}}_{\mathrm{R}}$ region will be determined from lattice QCD data on meson masses in the ${\ensuremath{\mu}}_{\mathrm{I}}$ region by using the PNJL model, if the data are measured in the future.

Nonlocal chiral quark models with wavefunction renormalization: Sigma properties andπ−πscattering parameters

We analyze the sigma meson mass and width together with the pion-pion scattering parameters in the context of nonlocal chiral quark models with wave function renormalization (WFR). We consider both nonlocal interactions based on the frequently used exponential form factor, and on fits to the quark mass and renormalization functions obtained in lattice calculations. In the case of the sigma properties, we obtain results which are less dependent on the parametrization than in the standard local Nambu-Jona-Lasinio model, and which are in reasonable agreement with the recently reported empirical values. We also show that the inclusion of the WFR tend to improve the description of the $\ensuremath{\pi}\mathrm{\text{\ensuremath{-}}}\ensuremath{\pi}$ scattering parameters, with the lattice inspired parametrization providing the best overall results. Finally, we analyze the connection of the nonlocal quark models discussed here with chiral perturbation theory, and present the model predictions for the low-energy constants relevant for $\ensuremath{\pi}\mathrm{\text{\ensuremath{-}}}\ensuremath{\pi}$ scattering to $O(4)$ in the chiral expansion.

Reconsideration of the 2-Flavor NJL Model with Dimensional Regularization at Finite Temperature and Density

We study the 2-flavor Nambu--Jona-Lasinio (NJL) model at finite temperature, $T$, and chemical potential, $\mu$, in the dimensional regularization. The pion and sigma meson masses are calculated at finite $T$ and $\mu$. The color superconductivity is also discussed in the extended NJL model. We obtain the phase structure of the chiral and color symmetry in the dimensional regularization and compare the results with ones obtained in the cut-off regularization.

A calculation of the physical mass of sigma meson

We calculate the physical mass and the width of the sigma meson by considering that it couples in vacuum to two virtual pions. The mass is calculated by using the spectral function, and we find that it is about 600MeV. In addition, we obtained the value of 250MeV for the width of its spectral function. The value obtained for the mass, is in an excellent agreement with that reported in the Particle data Book for the sigma meson, which is also named f0(600). This result also shows that the sigma meson can be considered as a two pion resonance.

Low density instability in relativistic mean field models

The effects of the symmetry energy softening of the relativistic mean field (RMF) models on the properties of matter with neutrino trapping are investigated. It is found that the effects are less significant than those in the case without neutrino trapping. The weak dependence of the equation of state on the symmetry energy is shown as the main reason of this finding. Using different RMF models the dynamical instabilities of uniform matters, with and without neutrino trapping, have been also studied. The interplay between the dominant contribution of the variation of matter composition and the role of effective masses of mesons and nucleons leads to higher critical densities for matter with neutrino trapping. Furthermore, the predicted critical density is insensitive to the number of trapped neutrinos as well as to the RMF model used in the investigation. It is also found that additional nonlinear terms in the Horowitz-Piekarewicz and Furnstahl-Serot-Tang models prevent another kind of instability, which occurs at relatively high densities. The reason is that the effective sigma meson mass in their models increases as a function of the matter density.

Effect of Coherent State of Quarks and Mesons on Hadron Properties

The effect of coherent state of quarks and mesons on hadron properties has been investigated in a chiral quark model. A new parameter set is derived. A comparison with previous work shows that the properties of the nucleon and delta are greatly improved by increasing the degree of coherent and the sigma-meson mass.

EFFICIENT DESCRIPTION FOR π AND σ MESONS BY RESONATING MEAN-FIELD APPROXIMATION TO TWO-FLAVOR NAMBU-JONA-LASINIO MODEL

We have applied the resonating (Res-) mean-field approximation (MFA) to fermion systems with large quantum fluctuations over the usual MFA to a naive Nambu-Jona-Lasinio (NJL) model involving no current quark mass term. In our approach, as part of the model the normalization volume is kept finite, which plays an important role. This attempt has been quite successful in explaining the pion and sigma-meson masses, but the values of the order parameter for quark condensate and the pion decay constant are too small. This fact suggests us that the Res-MFA including no isospin causes such a problem. To avoid the serious drawback, if we naturally extend the NJL model to include two-flavor degrees of freedom and make an SU(2)fresonating Hartree-Fock (Res-HF) approximation, it is expected that the magnitudes of the order parameter and the pion decay constant are much improved. Using this extended NJL model, they are calculated again and both the numerical values [Formula: see text] and fπreach good agreements with their experimental ones.

Vector meson dominance pion electromagnetic form factor with σ-model loop corrections

A model is developed for electromagnetic form factor of the pion. One-loop corrections are included in the linear sigma-model. The rho-meson contribution is added in an extended VMD model. The form factor, calculated without fitting parameters, is in a good agreement with experiment for space-like and time-like photon momenta. Loop corrections to the two-pion hadronic contribution a^{(had, \pi)}_\mu to the muon anomalous magnetic moment are calculated. The optimal value of the sigma-meson mass appears to be close to the rho-meson mass.

Dispersion Relation of σ Meson and Pion at Finite Nuclear Density in Chiral σ Model**The project supported by National Natural Science Foundation of China under Grant Nos. 10275099 and 10175096, and the Science Foundation of Guangdong Province of China under Grant No. 001182

The propagators of pion and sigma meson at a finite nuclear density and zero temperature are studied in chiral σ model. Their dispersion relations are calculated numerically in one-loop approximation. In order to avoid the so-called tachyon pole appearing in the one-loop propagators of pion and sigma meson, we regard the mass of sigma meson as a free parameter and adjust it to fit the nuclear saturation properties. For equal to 3075 MeV, the tachyon pole does not appear at the normal nuclear density. Thus the dispersion relation can be calculated in chiral σ model in one-loop level for the first time.

SU(2)×SU(2) chiral quark model with nonlocal interaction

Masses and interactions of light mesons are described in the framework of the model with the chiral invariant SU(2)×SU(2) four-quark interaction. The nonlocal kernel of the interaction is chosen in the form that ensures the absence of ultraviolet divergences in the Feynman diagrams and poles in the quark propagator. Within this model, we demonstrate that, in the chiral limit, the pion mass equals zero and the Goldberger-Treiman relation is fulfilled. The sigma-meson mass and the widths of strong decays σ → ππ, ρ → νν are estimated.

Pion and sigma meson properties in a relativistic quark model

A variety of strong and electroweak interaction properties of a pion and a light scalar $\ensuremath{\sigma}$ meson are computed in a relativistic quark model. Under the assumption that the resulting coupling of these mesons to the constituent quarks is identical, the $\ensuremath{\sigma}$ meson mass is determined as ${M}_{\ensuremath{\sigma}}=385.4\mathrm{MeV}.$ We discuss in detail the gauging of the nonlocal meson-quark interaction and calculate the electromagnetic form factor of the pion and the form factors of the ${\ensuremath{\pi}}^{0}\ensuremath{\rightarrow}\ensuremath{\gamma}\ensuremath{\gamma}$ and $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\sigma}}\ensuremath{\gamma}\ensuremath{\gamma}$ processes. We obtain explicit expressions for the relevant form factors and evaluate the leading and next-to-leading orders for large Euclidean photon virtualities. Turning to the decay properties of $\ensuremath{\sigma},$ we determine the width of the electromagnetic $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\sigma}}\ensuremath{\gamma}\ensuremath{\gamma}$ transition and discuss the strong decay $\stackrel{\ensuremath{\rightarrow}}{\ensuremath{\sigma}}\ensuremath{\pi}\ensuremath{\pi}.$ In a final step we compute the nonleptonic decays $\stackrel{\ensuremath{\rightarrow}}{D}\ensuremath{\sigma}\ensuremath{\pi}$ and $\stackrel{\ensuremath{\rightarrow}}{B}\ensuremath{\sigma}\ensuremath{\pi}$ relevant for the possible observation of the $\ensuremath{\sigma}$ meson. All our results are compared to available experimental data and to results of other theoretical studies.