Meson Effective Masses Research Articles

Meson effective mass in the isospin medium in hard-wall AdS/QCD model

We study a mass splitting of light vector, axial-vector and pseudoscalar mesons in isospin medium in the framework of hard-wall model. We write an effective mass definition for the interacting gauge fields and scalar field introduced in gauge field theory in the bulk of AdS space-time. Relying on holographic duality we obtain a formula for the effective mass of a boundary meson in terms of derivative operator over the extra bulk coordinate. The effective mass found in this way coincides with the one obtained from finding of poles of the two-point correlation function. In order to avoid introducing distinguished infrared boundaries in the quantisation formula for the different mesons from the same isotriplet we introduce extra action terms at this boundary, which reduces distinguished values of this boundary to the same value. Profile function solutions and effective mass expressions were found for the in-medium $\rho$, $a_1$ and $\pi$ mesons.

Lifetime of Antibaryon Bound in Finite Nuclei

The study of finite nuclei containing antibaryon(s) in addition to nucleons is an interesting topic in nuclear physics. The calculation of the lifetime of an antibaryon embedded in a nucleus was performed in the framework of the standard quantum field theory. It was shown that the annihilation probability of the antibaryon in nuclei is strongly dependent on the effective masses of mesons involved in the annihilation channels. The contribution of the Dirac sea to the annihilation probability makes the lifetime of the antibaryon short. If the Dirac sea effect is neglected, the lifetime of the bound antibaryon tends to be longer with the nuclear density increasing. Particularly, when the nuclear density is larger than a critical value, the antibaryon may exist stably in a nucleus.

Criteria for nonlinear parameters of relativistic mean field models

Based on the properties of the critical and the actual effective masses of sigma and omega mesons, criteria to estimate the values of the isoscalar nonlinear terms of the standard relativistic mean field model that reproduce stable equations of state in respect to particle hole excitation at high densities are derived. The relation between nuclear matter stability and the symmetric nuclear matter properties are shown. The criteria are used to analyze in a more systematic way the high-density longitudinal and transverse instabilities of some parameter sets of relativistic mean field models. The critical role of the vector and vector-scalar nonlinear terms is also discussed quantitatively.

THE CJT CALCULATION IN STUDYING NUCLEAR MATTER BEYOND MEAN FIELD APPROXIMATION

We have introduced the Cornwall–Jackiw–Tomboulis (CJT) resummation scheme in studying nuclear matter. Based on the CJT formalism and using Walecka model, we have derived a set of coupled Dyson equations of nucleons and mesons. Neglecting the medium effects of the mesons, the usual mean field theory (MFT) results can be obtained. The beyond MFT calculations have been performed by thermodynamic consistently determining the meson effective masses and solving the coupled gap equations for nucleons and mesons together. The numerical results for the nucleon and meson effective masses at finite temperature and chemical potential in nuclear matter are discussed.

A diagrammatic derivation of the meson effective masses in the neutral color-flavor-locked phase of quantum chromodynamics

We offer a diagrammatic derivation of the effective masses of the axial flavor excitations in the electrical and color neutral CFL phase of QCD. In particular we concentrate on the excitations with the quantum numbers of the kaons: we show how their effective chemical potentials, responsible of their Bose-Einstein condensation and found previously on the basis of pure symmetry arguments, arise at the microscopic level by loop effects. We perform also the numerical evaluation of the relevant loops in the whole CFL regime Ms2/2μΔ ≤ 1, showing the existence of the enhancement of the kaon condensation with respect to the lowest order result. Finally we discuss the role of color neutrality in the microscopic calculation.

Properties of nuclear and neutron matter in a nonlinear σ– ω– ρ mean-field approximation with self- and mixed-interactions

Properties of nuclear and neutron matter are discussed in a nonlinear σ– ω– ρ mean-field approximation with self- and mixed-interactions of mesons and baryons. The nonlinear interactions of mesons are naturally renormalized as effective masses of mesons by thermodynamic consistency required by the theory of conserving approximations. The nonlinear mean-field approximation results in a thermodynamically consistent approximation that maintains Hugenholtz–Van Hove theorem and Landau's requirement of quasiparticles, and it is generally proved that the nonlinear approximation is equivalent to the Hartree approximation with effective masses of baryons and mesons. The approximation is applied to nuclear and neutron matter, which suggests that the lower bound of nuclear compressibility, K ∼ 150 MeV , be required to be consistent with the binding energy ( − 15.75 MeV at k F = 1.30 fm −1 ) and the maximum mass of neutron stars ( M max ⩾ 2.00 M ⊙ ). Since the contributions of nonlinear interactions are strictly confined as the effective masses of mesons and baryons, properties of nuclear and neutron matter will enable us to study the validity of nonlinear interactions of mesons. The implication of thermodynamic consistency to the hypothesis of naturalness is discussed. The density-dependence of the compressibility, symmetry energy together with effective masses of hadrons will be important constraints for nonlinear mean-field approximations, and the accumulating data together with accurate measurements of observables in high density and energy region will supply significant information in order to testify theoretical consistency of nuclear models.

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.

The linear sigma model at a finite isospin chemical potential

The effect of a finite isospin chemical potential on the effective masses of mesons at finite temperature is investigated in the framework of the O(4) linear sigma model with explicit chiral symmetry breaking. We present a mechanism to include the isospin chemical potential in the model. By using the Cornwall–Jackiw–Tomboulis method of composite operators, we obtain a set of gap equations for the effective masses of the mesons and get the numerical results in the Hartree approximation. We find that the introduction of the chemical potential only affects the mass of the charged pions and sigma, while there is almost no effect on the mass of neutral pions.

η mesons in nuclear matter

The $\eta$-nucleon ($\eta$N) interactions are deduced from the heavy baryon chiral perturbation theory up to the next-to-leading-order terms. Combining the relativistic mean-field theory for nucleon system, we have studied the in-medium properties of $\eta$-meson. We find that all the elastic scattering $\eta$N interactions come from the next-to-leading-order terms. The $\eta $N sigma term is found to be about 280$\pm$130 MeV. The off-shell terms are also important to the in-medium properties of $\eta$-meson. On application of the latest determination of the $\eta$N scattering length, the ratio of $\eta$-meson effective mass to its vacuum value is near $0.84\pm0.015$, while the optical potential is about $-(83\pm5)$ MeV, at the normal nuclear density.

EFFECTIVE MESON MASSES, EFFECTIVE MESON–NUCLEON COUPLINGS AND NEUTRON STAR RADII

Using a generalized mean field theory, we have studied relations among effective meson masses, effective meson–nucleon couplings and equations of state (EOS) in asymmetric nuclear matter. If the effective ω-meson mass becomes smaller at high density, the EOS becomes stiffer. However, if we require that the ω-meson mean field is proportional to baryon density, the effective ω–nucleon coupling also becomes smaller at the same time as the effective ω-meson mass becomes smaller. Consequently, the EOS becomes softer. A similar relation is found for the effective ρ-meson mass and the effective ρ–nucleon coupling. We have also studied relations among effective meson masses, effective meson–nucleon couplings and a radius R of a neutron star. R depends somewhat on the value of the effective ω-meson mass and the effective ω–nucleon coupling.

Quasielastic electron scattering in relativistic mean-field theory

The density-dependent relativistic hadron (DDRH) field theory proposed recently is extended to investigate the longitudinal response function and the Coulomb sum rule in quasielastic electron scattering in the relativistic random phase approximation (RPA). The results in the DDRH model are compared with those in other models systematically. It is found that meson effective masses induced by the nonlinear terms in the nonlinear Walecka model should be used to obtain the meson Green’s functions when the longitudinal response function and the Coulomb sum rule are calculated. The effects of the δ and ρ mesons are clearly shown in quasielastic electron scattering, and the isospin-dependent attractive potential between nucleons due to the exchange of the δ-meson cancels the isospin-dependent repulsive contribution of the ρ-meson to a certain extent. The obtained results in the DDRH model are in good agreement with experimental data except for the Coulomb sum rule in 208Pb.

EFFECTIVE MESON MASS IN NUCLEAR MATTER BASED ON DISPERSION EQUATION INCLUDING ${\rm N} \bar{\rm N},\ \Delta \bar{\rm N},\ \bar\Delta {\rm N}$ EXCITATIONS

Effective meson masses of σ, ω, ρ and π in nuclear matter are calculated from the meson self-energy of the particle–antiparticle excitations. Instead of the traditional renormalization, the dispersion relation method is used to calculate the real part from the finite imaginary part, since the tensor coupling of the pion and ρ meson is not renormalized in the usual sense. In this paper, we show the effects from antidelta-nucleon and delta-antinucleon excitations in π meson mass beside nucleon–antinucleon excitation. It is also shown that agreement is obtained on the ω meson mass predicted by the subtraction method and ρ meson mass by the QCD sum rule method. It is concluded that the dispersion equation method leads to the fact that all the meson mass decreases as the baryon density increases, and it supports the chiral symmetry restoration.

Role of fluctuations in the linearσmodel with quarks

We study the thermodynamics of the linear sigma model with constituent quarks beyond the mean-field approximation. By integrating out the quark degrees of freedom we derive an effective action for the meson fields which is then linearized around the ground state including field fluctuations. We propose a new method for performing exact averaging of complicated functions over the meson field fluctuations. Both thermal and zero-point fluctuations are considered. The chiral condensate and the effective meson masses are determined self-consistently in a rigorous thermodynamic framework. At zero chemical potential the model predicts a chiral crossover transition which separates two distinct regimes: heavy quarks and light pions at low temperatures, but light quarks and heavy mesons at high temperatures. The crossover becomes a first order phase transition if the vacuum pion mass is reduced from its physical value.

In-medium meson properties and field transformations

Since the existing calculations of the effective meson mass in nuclear medium involve approximations, it is important to examine whether they satisfy the general requirement of the equivalence theorem that the physical observables should be independent of the choice of field variables. We study here consequences of nucleon field transformations. As an illustrative case we consider the in-medium effective pion mass calculated for the s-wave pion-nucleon interaction in the linear density approximation. We demonstrate that it is necessary to include the Born term explicitly in order that the effective pion mass should obey the equivalence theorem.

Nucleon and meson effective masses in the relativistic mean-fieldtheory

Nucleon and meson effective masses in the nonlinear relativisticmean-field theory introducing a nonlinear ω-ρand σ coupling motivated by the quark-meson coupling modelis explored. It is shown that, in contrast to the usual Walecka model, notonly the effective nucleon mass meff,N but also the effective σ,ρ meson masses (meff,σ,meff,ρ) and the effective ω meson massmeff,ω are nucleon density dependent.

Application of an effective gauge-invariant model to nuclear matter inthe relativistic Hartree-Fock approximation

An effective nuclear model describing ω-, ρ- and axial-mesonsas gauge fields is applied to nuclear matter in the relativisticHartree-Fock approximation. The isoscalar two-pion exchange issimulated by a scalar field s similar to that used in the conventionalrelativistic mean-field approach. Two more scalar fields are essentialingredients of the present treatment:the σ-field, the chiral partner of the pion, and the Σ-field,the Higgs field for the ω-meson. Two versions of the model areused depending on whether the σ-field is considered as adynamical variable or `frozen', by taking its mass as infinite. The modelcontains four free parameters in the first case and three in the second onewhich are fitted to the nuclear matter saturation conditions.The nucleon and meson effective masses, compressibility modulus andsymmetry energy are calculated. The results prove the reliability of theDirac-Hartree-Fock approach within the linear realization of the chiralsymmetry.

EFFECTIVE VECTOR MESON MASSES IN A CUTOFF FIELD THEORY

Based on quantum hadrodynamics with a finite cutoff, the effective masses of vector mesons (ω,ρ) in nuclear medium are calculated. We use a low-energy effective Lagrangian which is obtained by integrating high-energy quantum fluctuations. Although we use an artificial cutoff, the cutoff-dependence can be removed order by order. It is also found that the effective ρ-meson mass [Formula: see text] decreases as the density increases. The rate of the decrease becomes smaller at high density. As a result, at the normal density, [Formula: see text] is 0.85~0.92.

HADES, the new electron-pair spectrometer at GSI

The High Acceptance DiElectron Spectrometer HADES is presently set up at GSI, Darmstadt, for the systematic study of hadron properties inside nuclear matter. Resonance widths and effective masses of vector mesons as well as electromagnetic transition formfactors of neutral mesons and baryon resonances will be investigated in the low in variant mass region M inv ≤ 1 GeV/c 2 with a resolution Δ M inv /M inv ≅ 1% (σ).

Studying in-medium hadron properties with HADES

The High Acceptance DiElectron Spectrometer HADES is presently set up at GSI, Darmstadt, for the systematic study of hadron properties inside nuclear matter at normal and medium temperatures and baryon densities. Electron pair spectroscopy will be used to measure resonance widths and effective masses of vector mesons as well as electromagnetic formfactors of neutral mesons and baryon resonances in the low mass region M < 1 GeV/c 2 . The spectrometer is designed for an invariant mass resolutionΔ M inv/M inv ≅ 1% (σ), a large signal to background ratio, and a high granularity.

Effective meson masses in nuclear matter based on a cutoff field theory

Effective masses of {sigma}, {omega}, {pi}, and {rho} mesons in nuclear matter are calculated based on a cutoff field theory. Instead of the traditional density-Feynman representation, we adopt the particle-hole-antiparticle representation for nuclear propagators so that unphysical components are not included in the meson self-energies. For an estimation of the contribution from the divergent particle-antiparticle excitations, i.e., vacuum polarization in nuclear matter, the idea of the renormalization group method is adopted. In this cutoff field theory, all the counterterms are finite and calculated numerically. It is shown that the predicted meson masses converge even if the cutoff {Lambda} is changed as long as {Lambda} is sufficiently large and that the prescription works well also for so-called nonrenormalized mesons such as {pi} and {rho}. According to this method, it is concluded that meson masses in nuclear matter have a weak dependence on the baryon density. {copyright} {ital 1997} {ital The American Physical Society}