Nucleon Loop Research Articles

ρ-MESON SPECTRAL FUNCTION IN HOT NUCLEAR MATTER

The ρ-meson spectral function in hot nuclear matter is studied by taking into account the pion and the nucleon loops within the quantum hadrodynamics (QHD) model as well as using an effective chiral SU(3) model. The effects of density and temperature on the spectral function of the ρ-meson are studied assuming the ρ-meson to be with a finite momentum. These investigations are performed using both the mean field approximation (MFA) and the relativistic Hartree (RHA) approximation. The inclusion of the nucleon loop is observed to considerably change the ρ-meson spectral function. Due to a larger mass drop of ρ-meson in the RHA, it is seen that the spectral function shifts towards the low invariant mass region, whereas in the MFA the spectral function is seen to be almost centered around the nominal ρ-pole, but develops a second peak due to the opening of the Nh-channel. Within both the Walecka and the chiral SU(3) models, it is observed that the ρ-meson spectral function has a strong dependence on the nucleon-ρ meson tensor coupling.

Effects of the Dirac sea on pion propagation in asymmetric nuclear matter

We study pion propagation in asymmetric nuclear matter (ANM). One of the interesting consequences of pion propagation in ANM is the mode splitting for the different charged states of pions. First we describe the pion-nucleon dynamics using the nonchiral model in which one starts with pseudoscalar $\ensuremath{\pi}N$ coupling, and the pseudovector representation is obtained via suitable nonlinear field transformations. For both of these cases, the effect of the Dirac sea is estimated. Subsequently, we present results using the chiral effective Lagrangian where the short-distance behavior (Dirac vacuum) is included by redefining the field parameters as done in the modern effective field theory approach developed recently. The results are compared with previous calculations for symmetric nuclear matter. Closed form analytical results are presented for the effective pion masses and dispersion relations by making a hard nucleon loop approximation and suitable density expansion.

Relativistic chiral mean field model for finite nuclei

We study the role of pion for the structure of finite nuclei. We take the chiral sigma model, where the pions are the Nambu–Goldstone bosons of the chiral symmetry breaking. We then take the finite pion mean field in the relativistic mean field approximation. We study first the nuclei in the range of A = 36 to A = 64 with equal number of neutrons and protons. We find that the magic number gap at N = Z = 28 appears due to the finite pion mean field effect. The pion provides a large spin–orbit splitting effect due to a mechanism totally different from the ordinary spin–orbit term of the relativistic origin. On the other hand, we are not able to shift the magic number appearing at A = 36 instead of A = 40 , which is now a motivation to work out the parity and charge projection. The standard projection technique provides an integro-differential equation for the Dirac equation. As an example, we work out 4He in the relativistic chiral mean field model. We find good properties for the ground state energy and the size and the pion energy contribution. The form factor also comes out to be quite satisfactory. We discuss further the renormalization procedure of the linear chiral model by treating both the nucleon loop and the boson loop in the Coleman–Weinberg renormalization scheme with the hope to calculate the negative energy contribution from the nucleon vacuum. We are able to obtain a stable chiral model Lagrangian with the nucleon vacuum polarization effect due to strong cancellation between the nucleon loop and the boson loop.

Kaon condensation and lambda–nucleon loop in the relativistic mean-field approach

The possibility of kaon condensation in high-density symmetric nuclear matter is investigated including both s- and p-wave kaon–baryon interactions within the relativistic mean-field (RMF) theory. Above a certain density, we have a collective K ¯ s state carrying the same quantum numbers as the antikaon. The appearance of the K ¯ s state is caused by the time component of the axial-vector interaction between kaons and baryons. It is shown that the system becomes unstable with respect to condensation of K– K ¯ s pairs. We consider how the effective baryon masses affect the kaon self-energy coming from the time component of the axial-vector interaction. Also, the role of the spatial component of the axial-vector interaction on the possible existence of the collective kaonic states is discussed in connection with Λ-mixing effects in the ground state of high-density matter. Implications of K K ¯ s condensation for high-energy heavy-ion collisions are briefly mentioned.

The Nambu–Jona–Lasinio model of light nuclei

The Nambu–Jona–Lasinio model of the deuteron suggested by Nambu and Jona–Lasinio (Phys. Rev. 124 (1961) 246) is formulated from the first principles of QCD. The deuteron appears as a neutron–proton collective excitation, i.e. a Cooper np–pair, induced by a phenomenological local four–nucleon interaction in the nuclear phase of QCD. The model describes the deuteron coupled to itself, nucleons and other particles through one–nucleon loop exchanges providing a minimal transfer of nucleon flavours from initial to final nuclear states and accounting for contributions of nucleon–loop anomalies which are completely determined by one–nucleon loop diagrams. The dominance of contributions of nucleon–loop anomalies to effective Lagrangians of low–energy nuclear interactions is justified in the large NC expansion, where NC is the number of quark colours.

Vacuum nucleon loops and naturalness

Phenomenological studies support the applicability of naturalness and naive dimensional analysis to hadronic effective lagrangians for nuclei. However, one-baryon-loop vacuum contributions in renormalizable models give rise to unnatural coefficients, which indicates that the quantum vacuum is not described adequately. The effective lagrangian framework accommodates a more general characterization of vacuum contributions without reference to a Dirac sea of nucleons.

The binding energy of nuclear matter in the chiral σ-ω model

The binding energy of nuclear matter is calculated in the chiral σ-ω model in an approximation to the Hartree-Fock scheme. Relativistic exchange energies and correlation energies including the effects of vacuum polarization are calculated. It is found that if one includes only the nucleon loop term in the meson self-energies, no satisfactory description of nuclear matter can be given. It is argued that by including the meson loop terms in the meson self-energies one can account for the saturation properties of nuclear matter.

Loop corrections and other many-body effects in relativistic field theories

Incorporation of effective masses into negative energy states (nucleon loop corrections) gives rise to repulsive many-body forces, as has been known for some time. Rather than renormalizing away the three- and four-body terms, we introduce medium corrections into the effective σ-exchange, which roughly cancel the nucleon loop terms for densities ϱ ∼ ϱnm, where ϱnm is nuclear matter density. Going to higher densities, the repulsive contributions tend to saturate whereas the attractive ones keep on growing in magnitude. The latter is achieved through use of a density-dependent effective mass for the σ-particle, mσ = mσ(ϱ), such that mσ(ϱ) decreases with increasing density. Such a behavior is seen e.g. in the Nambu-Jona-Lasinio model. It is argued that a smooth transition to chiral restoration implies a similar behavior. The resulting nuclear equation of state is, because of the self-consistency in the problem, immensely insensitive to changes in the mass or coupling constant of the σ-particle.

The quark triangle: Application to pion and eta decays

A general expression for the two-photon form factor of neutral pseudoscalar mesons is given in a quark triangle model. Various electromagnetic decay amplitudes are calculated, including Dalitz pair decays and the rare decay into a lepton pair, where an old calculation in a similar (nucleon loop) model is corrected. The results are in agreement with other calculations based on vector meson dominance, giving a new example of Q 2 duality. Some remarks concerning the soft limit in the processes are given

Relativistic Eikonal Formula for Production Processes

Eikonal formulae for the production process NN-7NN+mc are studied on the basis of a relativistic field-theoretical model in which the potential between nucleons, pion emission and absorption are all induced by a scalar field A. The functional integral method is used to derive formulae. Within the straight path approximation for the initial particles, it is shown that an exact impact parameter representation for production amplitude can be. obtained, including all internal interactions, in particular, nucleon loops. The amplitude is properly represented with the aid of three variables; i.e., transverse vector and two longitudinal coordinates. The latter two correspond to two moving intermediate nucleons respectively. These variables compose a vector in a four-dimensional space called frame, and a modified rapidity is introduced. Multiple scattering effects by the A field are investigated and a cluster expansion with respect to correlated A-lines is performed for eikonal phase of production amplitude.

Nucleon Loop as a Force in theππChannel

The $\ensuremath{\rho}$ meson is described as a $\ensuremath{\pi}\ensuremath{\pi}\ensuremath{-}N\overline{N}$ composite system, with $N$ exchange as a nondiagonal force between the two channels. The resulting nucleon loop, as a force in the $\ensuremath{\pi}\ensuremath{\pi}$ channel, gives far too strong attraction, if calculated with unmodified nucleon propagators. The necessary cutoff parameter in the nucleon propagators is compared with the same quantity obtained in the $\ensuremath{\Delta}(1236)$ channel. Pion self-energy effects are introduced to improve the resulting $\ensuremath{\rho}$ width, and crossing properties of the $\ensuremath{\pi}\ensuremath{\pi} p$ waves are discussed.

Axial-Current Divergences and the Reactionsγ+γ→Pions

A symmetry argument is presented that gives a relation between the small-momentum limits of the reactions $\ensuremath{\gamma}+\ensuremath{\gamma}\ensuremath{\rightarrow}$ odd number of pions, as calculated explicitly from a single nucleon (or quark) loop in a theory with a formally conserved axial-vector current. These limits are nonvanishing as a consequence of the Adler anomalies in the divergence of the axial-vector current. It is argued that the relationship derived should be true in any chiral model. The cross section for $\ensuremath{\gamma}+\ensuremath{\gamma}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}+{\ensuremath{\pi}}^{\ensuremath{-}}+{\ensuremath{\pi}}^{0}$ is calculated in terms of the measured ${\ensuremath{\pi}}^{0}\ensuremath{\rightarrow}2\ensuremath{\gamma}$ decay rate.

Mesic Effect in the Beta-Decay in a Nucleus

The mesic effect to the beta-decay in a nucleus is investigated. The Villars' type tribution which is compared with the ordinary axial vector coupling is estimated by the perturbation method. The comparable value with the fourth component of the ordinary · axial vector couplin'g is obtained. § I. Introduction The problem of the mesic effect in the beta-decay has been considered by many authors. For the renormalization of the vector coupling constant, con­ served vector current theory m) seems to be consistent with several experiments. For the axial vector coupling several attempts 2 l have been made but the problem is not well clarified. K. Kawarabayashi and the author examined the renormali­ zation of the axial vector coupling constant in the free nucleon beta-decal) by considering the virtual process, p->n + e + v, where the effective coupling constant was calculated by the nucleon loop. The result was in good accord with the experiments. The virtual process p-7-Jr + e + v, would also contribute to the mesic correction in the beta-decay in the nucleus. In this note we estimate the Villars' type contribution to compare it with the ordinary axial vector coupling constant by the perturbation method. First, we derive the two-body operator by taking p meson and pion as the intermediate state. Only the fourth com­ ponent is considered for simplicity. Then the Fermi gas model, closed shell plus a neutron, is chosen as the model of the nucleus which is a good approxi­ mation for heavy nuclei. The expectation value of the two-body operator is estimated in the above mentioned model and the result is compared with the· fourth component of the one-body axial vector operator. With a reasonable choice of the coupling constant of p meson with the nucleon, it is shown that the comparable value with the one-body operator is obtained.