Vector Meson Fields Research Articles

The Method of Unitary Clothing Transformations in the Theory of Nucleon–Nucleon Scattering

The clothing procedure, put forward in quantum field theory (QFT) by Greenberg and Schweber, is applied for the description of nucleon–nucleon (N–N) scattering. We consider pseudoscalar (π and η), vector (ρ and ω) and scalar (δ and σ) meson fields interacting with 1/2 spin (N and $${\bar{N}}$$ ) fermion ones via the Yukawa-type couplings to introduce trial interactions between “bare” particles. The subsequent unitary clothing transformations are found to express the total Hamiltonian through new interaction operators that refer to particles with physical (observable) properties, the so-called clothed particles. In this work, we are focused upon the Hermitian and energy-independent operators for the clothed nucleons, being built up in the second order in the coupling constants. The corresponding analytic expressions in momentum space are compared with the separate meson contributions to the one-boson-exchange potentials in the meson theory of nuclear forces. In order to evaluate the T matrix of the N–N scattering we have used an equivalence theorem that enables us to operate in the clothed particle representation (CPR) instead of the bare particle representation with its large amount of virtual processes. We have derived the Lippmann–Schwinger type equation for the CPR elements of the T-matrix for a given collision energy in the two-nucleon sector of the Hilbert space $${\mathcal{H}}$$ of hadronic states.

The method of unitary clothing transformations in the theory of nucleon–nucleon scattering

The clothing procedure, put forward in quantum field theory by Greenberg and Schweber, is applied for the description of nucleon-nucleon (N-N) scattering. We consider pseudoscalar, vector and scalar meson fields interacting with 1/2 spin fermion ones via the Yukawa-type couplings to introduce trial interactions between "bare" particles. The subsequent unitary clothing transformations are found to express the total Hamiltonian through new interaction operators that refer to particles with physical (observable) properties, the so-called clothed particles. In this work, we are focused upon the Hermitian and energy-independent operators for the clothed nucleons, being built up in the second order in the coupling constants. The corresponding analytic expressions in momentum space are compared with the separate meson contributions to the one-boson-exchange potentials in the meson theory of nuclear forces. In order to evaluate the T-matrix of the N-N scattering we have used an equivalence theorem that enables us to operate in the clothed particle representation (CPR) instead of the bare particle representation with its huge amount of virtual processes. We have derived the Lippmann-Schwinger-type equation for the CPR elements of the T-matrix for a given collision energy in the two-nucleon sector of the Hilbert space of hadronic states and elaborated a code for its numerical solution in momentum space.

Non-Gaussian statistics and the relativistic nuclear equation of state

We investigate possible effects of quantum power-law statistical mechanics on the relativistic nuclear equation of state in the context of the Walecka quantum hadrodynamics theory. By considering the Kaniadakis non-Gaussian statistics, characterized by the index κ (Boltzmann–Gibbs entropy is recovered in the limit κ → 0 ), we show that the scalar and vector meson fields become more intense due to the non-Gaussian statistical effects ( κ ≠ 0 ). From a analytical treatment, an upper bound on κ ( κ < 1 / 4 ) is found. We also show that as the parameter κ increases the nucleon effective mass diminishes and the equation of state becomes stiffer. A possible connection between phase transitions in nuclear matter and the κ-parameter is largely discussed.

Brane-induced Skyrmion onS3: Baryonic matter in holographic QCD

We study baryonic matter in holographic QCD with $\mathrm{D}4/\mathrm{D}8/\overline{\mathrm{D}8}$ multi-D brane system in type IIA superstring theory. The baryon is described as the ``brane-induced Skyrmion,'' which is a topologically nontrivial chiral soliton in the four-dimensional meson effective action induced by holographic QCD. We employ the ``truncated-resonance model'' approach for the baryon analysis, including pion and $\ensuremath{\rho}$ meson fields below the ultraviolet cutoff scale ${M}_{\mathrm{KK}}\ensuremath{\sim}1\text{ }\text{ }\mathrm{GeV}$, to keep the holographic duality with QCD. We describe the baryonic matter in large ${N}_{c}$ as single brane-induced Skyrmion on the three-dimensional closed manifold ${S}^{3}$ with finite radius $R$. The interactions between baryons are simulated by the curvature of the closed manifold ${S}^{3}$, and the decrease of the size of ${S}^{3}$ represents the increase of the total baryon-number density in the medium in this modeling. We investigate the energy density, the field configuration, the mass and the root-mean-square radius of single baryon on ${S}^{3}$ as the function of its radius $R$. We find a new picture of ``pion dominance'' near the critical density in the baryonic matter, where all the (axial) vector meson fields disappear and only the pion fields survive. We also find the swelling phenomena of the baryons as the precursor of the deconfinement, and propose the mechanism of the swelling in the general context of QCD. The properties of the deconfinement and the chiral symmetry restoration in the baryonic matter are examined by taking the proper order parameters. We also compare our truncated-resonance model with another instanton description of the baryon in holographic QCD, considering the role of cutoff scale ${M}_{\mathrm{KK}}$.

Warm protoneutron stars with strange mesons

In order to reproduce the observed strongly attractive ΛΛ interaction within relativistic models in a mean-field approximation, strange meson fields, namely the scalar meson field σ*(975) and the vector meson field ϕ(1020) have to be considered. In the present work we study the inclusion of these mesons in the equation of state (EOS) obtained with the nonlinear Walecka model with nucleons and hyperons at finite temperature and also fixed entropy per baryon after the deleptonization stage of the star. The calculations are done in a mean-field approximation and the consequences in the stellar properties are verified.

Relativistic stars with a linear equation of state: analogy with classical isothermal spheres and black holes

We complete our previous investigations concerning the structure and the stability of “isothermal” spheres in general relativity. This concerns objects that are described by a linear equation of state, P = q� , so that the pressure is proportional to the energy density. In the Newtonian limit q → 0, this returns the classical isothermal equation of state. We specifically consider a self-gravitating radiation (q = 1/3), the core of neutron stars (q = 1/3), and a gas of baryons interacting through a vector meson field (q = 1). Inspired by recent works, we study how the thermodynamical parameters (entropy, temperature, baryon number, mass-energy, etc.) scale with the size of the object and find unusual behaviours due to the non-extensivity of the system. We compare these scaling laws with the area scaling of the black hole entropy. We also determine the domain of validity of these scaling laws by calculating the critical radius (for a given central density) above which relativistic stars described by a linear equation of state become dynamically unstable. For photon stars (self-gravitating radiation), we show that the criteria of dynamical and thermodynamical stability coincide. Considering finite spheres, we find that the mass and entropy present damped oscillations as a function of the central density. We obtain an upper bound for the entropy S and the mass-energy M above which there is no equilibrium state. We give the critical value of the central density corresponding to the first mass peak, above which the series of equilibria becomes unstable. We also determine the deviation from the Stefan-Boltzmann law due to self-gravity and plot the corresponding caloric curve. It presents a striking spiraling behaviour like the caloric curve of isothermal spheres in Newtonian gravity. We extend our results to d-dimensional spheres and show that the oscillations of mass-versus-central density disappear above a critical dimension dcrit(q). For Newtonian isothermal stars (q → 0), we recover the critical dimension dcrit = 10. For the stiffest stars (q = 1), we find dcrit = 9 and for a self-gravitating radiation (q = 1/d )w e fi nddcrit = 9.96404372... very close to 10. Finally, we give simple analytical solutions of relativistic isothermal spheres in two-dimensional gravity. Interestingly, unbounded configurations exist for a unique mass Mc = c 2 /(8G).

Hyperon coupling dependence of hadron matter properties in relativistic mean field model

The properties of hadronic matter at β equilibrium in a wide range of densities are described by appropriate equations of state in the framework of the relativistic mean field model. Strange meson fields, namely the scalar meson field σ* (975) and the vector meson field (1020), are included in the present work. We discuss and compare the results of the equation of state, nucleon effective mass, and strangeness fraction obtained by adopting the TM1, TMA, and GL parameter sets for nuclear sector and three different choices for the hyperon couplings. We find that the parameter set TM1 favours the onset of hyperons most, while at high densities the GL parameter set leads to the most hyperon-rich matter. For a certain parameter set (e.g. TM1), the most hyperon-rich matter is obtained for the hyperon potential model. The influence of the hyperon couplings on the effective mass of nucleon, is much weaker than that on the nucleon parameter set. The nonstrange mesons dominate essentially the global properties of dense hyperon matter. The hyperon potential model predicts the lowest value of the neutron star maximum mass of about 1.45 Msun to be 0.4-0.5 Msun lower than the prediction by using the other choices for hyperon couplings.

Massive mesons in Weyl–Dirac theory

In order to study the mass generation of the vector fields in the framework of a conformal invariant gravitational model, the Weyl–Dirac theory is considered. The mass of the Weyl’s meson fields plays a principal role in this theory, it connects basically the conformal and gauge symmetries. We estimate this mass by using the large-scale characteristics of the observed universe. To do this we firstly specify a preferred conformal frame as a cosmological frame, then in this frame, we introduce an exact possible solution of the theory. We also study the dynamical effect of the massive vector meson fields on the trajectories of an elementary particle. We show that a local change of the cosmological frame leads to a Hamilton–Jacobi equation describing a particle with an adjustable mass. The dynamical effect of the massive vector meson field presents itself in the form of a correction term for the mass of the particle.

Nonextensive effects on the relativistic nuclear equation of state

As widely known, the Walecka many-body field theory plays an important role in nuclear physics. This paper investigates such a theory in the context of quantum nonextensive statistical mechanics, characterized by a dimensionless parameter $q$. To this end, we consider nuclear matter described statistically by a power-law distribution which generalizes the standard Fermi-Dirac distribution ($q=1$). We show that the scalar and vector meson fields become more intense because of the nonextensive effects ($q\ensuremath{\ne}1$). From a numerical treatment, we also show that as the nonextensive parameter $q$ increases, the nucleon effective mass diminishes and the equation of state becomes stiffer. Finally, the usual Maxwell construction seems not to be necessary for isotherms with temperatures in the range $14l{k}_{B}Tl20$ MeV.

${\bar K}$-NUCLEAR DEEPLY BOUND STATES?

Following the prediction by Akaishi and Yamazaki of relatively narrow [Formula: see text]-nuclear states, deeply bound by over 100 MeV where the main decay channel [Formula: see text] is closed, several experimental signals in stopped K- reactions on light nuclei have been interpreted recently as due to such states. In this talk I review (i) the evidence from K--atom data for a deep[Formula: see text]-nucleus potential, as attractive as [Formula: see text] at nuclear matter density, that could support such states; and (ii) the theoretical arguments for a shallow potential, [Formula: see text]. I then review a recent work by Mareš, Friedman and Gal in which [Formula: see text]-nuclear bound states are generated dynamically across the periodic table, using a RMF Lagrangian that couples the [Formula: see text] to the scalar and vector meson fields mediating the nuclear interactions. The reduced phase space available for [Formula: see text] absorption from these bound states is taken into account by adding a density- and energy-dependent imaginary term, underlying the corresponding [Formula: see text]-nuclear level widths, with a strength constrained by K--atom fits. Substantial polarization of the core nucleus is found for light nuclei, with central nuclear densities enhanced by almost a factor of two. The binding energies and widths calculated in this dynamical model differ appreciably from those calculated for a static nucleus. These calculations provide a lower limit of [Formula: see text] on the width of nuclear bound states for [Formula: see text] binding energy in the range [Formula: see text].

Formula omitted]–nuclear bound states in a dynamical model

A comprehensive data base of K − –atom level shifts and widths is re-analyzed in order to study the density dependence of the K ¯ –nuclear optical potential. Significant departure from a t eff ρ form is found only for ρ ( r ) / ρ 0 ≲ 0.2 and extrapolation to nuclear-matter density ρ 0 yields an attractive potential, about 170 MeV deep. Partial restoration of chiral symmetry compatible with pionic atoms and low-energy pion–nuclear data plays no role at the relevant low-density regime, but this effect is not ruled out at densities of order ρ 0 and beyond. K ¯ –nuclear bound states are generated across the periodic table self consistently, using a relativistic mean-field model Lagrangian which couples the K ¯ to the scalar and vector meson fields mediating the nuclear interactions. The reduced phase space available for K ¯ absorption from these bound states is taken into account by adding an energy-dependent imaginary term which underlies the corresponding K ¯ –nuclear level widths, with a strength required by fits to the atomic data. Substantial polarization of the core nucleus is found for light nuclei, and the binding energies and widths calculated in this dynamical model differ appreciably from those calculated for a static nucleus. A wide range of binding energies is spanned by varying the K ¯ couplings to the meson fields. Our calculations provide a lower limit of Γ K ¯ = 50 ± 10 MeV on the width of nuclear bound states for K ¯ -binding energy in the range B K ¯ ∼ 100 – 200 MeV . Comments are made on the interpretation of the FINUDA experiment at DAΦNE which claimed evidence for deeply bound K − p p states in light nuclei.

The importance of strange mesons in neutron star properties

In order to obtain the properties of compact stellar objects, appropriate equations of state have to be used. In the literature, strange meson fields, namely the scalar meson field sigma*(975) and the vector meson field phi(1020), had to be considered in order to reproduce the observed strongly attractive <FONT FACE=Symbol>LL</FONT> interaction. The introduction of these strange mesons makes the equations of state harder (EOS) due to the repulsive effect of the phi(1020) meson. In this work the inclusion of these mesons in the equation of state and their influence on the properties of the neutron stars are investigated.

ΔΔ Dibaryon Structure in Extended ChiralSU(3) Quark Model

The structure of ΔΔ dibaryon is studied in the extendedchiral SU(3) quark model in which vector meson exchanges are included.The effect of the vector meson fields is very similar to that of theone-gluon exchange (OGE) interaction. Both in the chiral SU(3) quarkmodel and in the extended chiral SU(3) quark model, the resultant massof the ΔΔ dibaryon is lower than the threshold of theΔΔ channel but higher than that of the ΔNπchannel.

Magnetic moments of baryons with a single heavy quark

We calculate the magnetic moments of heavy baryons with a single heavy quark in the bound-state approach. In this approach the heavy baryons is considered as a heavy meson bound in the field of a light baryon. The light baryon field is represented as a soliton excitation of the light pseudoscalar and vector meson fields. For these calculations we adopt a model that is both chirally invariant and consistent with the heavy quark spin symmetry. We gauge the model action with respect to photon field in order to extract the electromagnetic current operator and obtain the magnetic moments by computing pertinent matrix elements of this operator between the bound state wavefunctions. We compare our predictions for the magnetic moments with results of alternative approaches for the description of heavy baryon properties.

Structures of (ΩΩ)0+ and (ΞΩ)1+ in Extended Chiral SU(3) Quark Model**The project supported by National Natural Science Foundation of China

The structures of (ΩΩ)0+ and (ΞΩ)1+ are studied in the extended chiral SU(3) quark model in which vector meson exchanges are included. The effect from the vector meson fields is very similar to that from the one-gluon exchange (OGE) interaction. Both in the chiral SU(3) quark model and in the extended chiral SU(3) quark model, di-omega (ΩΩ)0+ is always deeply bound, with over one hundred MeV binding energy, and (ΞΩ)1+'s binding energy is around 20 MeV. An analysis shows that the quark exchange effect plays a very important role for making di-omega (ΩΩ)0+ deeply bound.

Contribution of higher meson resonances to the electromagnetic pion-mass difference

Some modifications of the formula for calculating the electromagnetic pion-mass difference are proposed on the basis of the chiral-symmetry-restoration phenomenon at high energies and the operator-product expansion of quark densities for vector (ρ) and axial-vector (a 1) meson fields. All calculations are performed through taking into account higher meson resonances in the vector and axial-vector channels. It is shown that the inclusion of only the first ρ 0 and a 1 radial excitations improves the results of the calculation for the electromagnetic pion-mass difference in relation to the known ones. The electromagnetic ρ-and a 1-meson decay constants and the constant L 10 of the effective chiral Lagrangian are estimated with the aid of the generalized Weinberg sum rules.

Baryon + Baryon → (ΩΩ)Jπ=0+ + X Cross Section Calculation**The project supported by National Natural Science Foundation of China

The cross sections of Ω + Ξ → (ΩΩ)Jπ=0+ + K(K*) and Ω + Ω → (ΩΩ)Jπ=0+ + η′(ϕ) are studied by using an effective Hamiltonian method. For the two pseudo-scalar meson production processes, the cross sections are still in the order of several μbs, but for the two vector meson production processes, the cross sections are about 10 times larger than those in pseudo-scalar meson production case when the coupling constants of vector meson fields are fixed according to gNNρ and fNNρ in NN scattering and the SU(3) relation.

The time-dependent relativistic mean-field theory and the random phase approximation

The Relativistic Random Phase Approximation (RRPA) is derived from the Time-Dependent Relativistic Mean-Field (TD RMF) theory in the limit of small amplitude oscillations. In the no-sea approximation of the RMF theory, the RRPA configuration space includes not only the usual particle–hole ph-states, but also αh-configurations, i.e. pairs formed from occupied states in the Fermi sea and empty negative-energy states in the Dirac sea. The contribution of the negative-energy states to the RRPA matrices is examined in a schematic model, and the large effect of Dirac-sea states on isoscalar strength distributions is illustrated for the giant monopole resonance in 116Sn. It is shown that, because the matrix elements of the time-like component of the vector-meson fields which couple the αh-configurations with the ph-configurations are strongly reduced with respect to the corresponding matrix elements of the isoscalar scalar meson field, the inclusion of states with unperturbed energies more than 1.2 GeV below the Fermi energy has a pronounced effect on giant resonances with excitation energies in the MeV region. The influence of nuclear magnetism, i.e. the effect of the spatial components of the vector fields is examined, and the difference between the nonrelativistic and relativistic RPA predictions for the nuclear matter compression modulus is explained.

Relativistic Mean-Field Study to Odd-A Nuclei Far from Stability**The project supported in part by a grant of a special researcher at RIKEN in Japan and by National Natural Science Foundation of China

Ground state properties of recently discovered odd-A nuclei near the particle-dripline have been investigated in the relativistic mean-field model. Special emphasis is placed on the effect of the spatial component of vector meson fields on ground state properties which is due to breaking of time reversal invariance for odd-A nuclei. Calculations show that its contribution to binding energies, radii and single particle energies is small but cannot be neglected completely for some drip-line nuclei because the last nucleon in them is very weakly bound. Calculated binding energies are in reasonably good agreement with present experimental data and estimated values in mass tables. The structure of newly discovered nuclei is also discussed.

Hyperfine splitting of low-lying heavy baryons

We calculate the next-to-leading order contribution to the masses of the heavy baryons in the bound-state approach for baryons containing a heavy quark. These 1 N C corrections arise when states of good spin and isospin are generated from the background solition of the light meson fields. Our study is motivated by the previously established result that light vector meson fields are required for this soliton in order to reasonably describe the spectrum of both the light and the heavy baryons. We note that the inclusion of light vector mesons significantly improves the agreement of the predicted hyperfine splitting with experiment. A number of aspects of this somewhat complicated calculation are discussed in detail.