Meson-nucleon System Research Articles

Meson–nucleon coupling from AdS/QCD

In this manuscript, a unified approach to hadron physics from the holographic point of view is described. After the introduction of a general setup for the meson–nucleon system based on the bottom-up approach of QCD (AdS/QCD), as an illustration, we specifically examine meson–nucleon couplings. This is an example of the notion we call “holographic unification” in hadron physics.

Clothed generators of the Poincaré group in a meson-nucleon system with nonlocal interaction

The nonlocal extension of trilinear Yukawa-type interaction in a meson-nucleon system is carried out in the momentum space by introducing cut-off functions (form factors) into each interaction vertex. The possibility of constructing a relativistic invariant field theory with nonlocal interaction in the clothed particle representation is shown within an algebraic approach.

Clothing of particles in a meson-nucleon system: Operators of relativistic interactions. Diagram technique

A diagram technique is represented, which makes it possible to construct operators of relativistic interactions in the method of unitary clothing transformations. With the use of this technique, operators of physical processes in the second and third orders with respect to the coupling constant have been obtained.

Clothing of particles in the meson-nucleon system: Mass and charge renormalization

Generators of the Poincare group have been constructed in the instant form of relativistic dynamics in the second and third orders in the coupling constant, using the method of unitary clothing transformations. It is shown that the algebra of group generators is satisfied in the corresponding orders. The relativistic invariance of the calculated corrections to the particle masses and coupling constant is substantiated.

Clothing of particles in the meson-nucleon system: Mass and charge renormalization

Clothing of particles in the meson-nucleon system: Mass and charge renormalization

Relativistic Thomas-Fermi description of collective modes in droplets of nuclear matter.

Isoscalar collective modes in a relativistic meson-nucleon system are investigated in the framework of the time-dependent Thomas-Fermi method. The energies of the collective modes are determined by solving consistently the dispersion relations and the boundary conditions. The energy weighted sum rule satisfied by the models considered allows the identification of the giant resonances. The percentage of the energy weighted sum rule exhausted by the collective modes is in agreement with experimental data, but the agreement with the energy of the modes depends on the model considered. \textcopyright{} 1996 The American Physical Society.

Collective modes in a relativistic meson-nucleon system

Abstract Collective modes in a relativistic meson-nucleon system are investigated. The baryon ground state is treated in a mean-field approximation while the meson propagators are described with a relativistic random-phase approximation. Three types of collective modes are found: zero-sound, meson-branch modes, and modes which indicate an instability of the mean-field theory ground state. The mixing of scalar and vector mesons prevents the propagation of zero-sound at saturation density. This is in sharp contrast to nonrelativistic models which often have zero-sound. There is also important mixing between meson and nucleon-antinucleon excitations which greatly effect meson branch modes.

Effective operators in the relativistic meson-nucleon system

Taking the meson-nucleon system below threshold as an example, it is shown that it can formally be described by nucleonic degrees of freedom alone. In the Fock space of nucleons one has eigenvalue equations with different optional versions of effective interactions. The Hermitian version explicitly exhibits full relativistic invariance. The non-Hermitian form can be decomposed into one, two, three,..., particle operators. The latter requires the solution of the vacuum, one, two,..., nucleon problems. The techniques proposed are known from coupled cluster many body theory and do not invoke perturbation theory.

A Phase-Shift Analysis of Proton-Proton Scattering at PL=6 GeV/c

An energy-independent phase-shift analysis of proton-proton scattering data at PL =6 Ge V /c is performed under the peripheral (J~19) one-pion exchange assumption. Two solutions A and B are obtained which have the chi-square values 231 and 224, respectively, for the 279 experimental data points and the 94 floating parameters. These two solutions exhibit some similarities to the Berger-Irving-Sorensen (A) and the Kroll-Leader-von Schlippe (B) Regge­ pole amplitudes at small -t. In hadron physics the method of the partial wave analysis has been used to obtain the information of scattering amplitudes in low and intermediate energy region. Especially this method has contributed greatly to the clarification of the resona1ice scheme of meson-baryon systems. The association of the phase-shift an­ alysis with the baryon resonance started from its very beginning with Ll (1232). The history of phase-shift analysis of nucleon-nucleon system is as old as that of meson-nucleon system and this method has constantly supplied useful information, though the resonance problem has not occurred until recently_*) The practical utility of the method, as a model-independent way of deter­ mining the scattering amplitude, is confined to not-too-high-energy region. At high energy the phase-shift analysis suffers the difficulty due to a large number of free parameters and, as the energy goes higher, this approach will lose its ef­ fectiveness ultimately. However, the not-too-high-energy region has been pushed up fairly higher by the progress in computing machines and techniques. For proton-proton scattering this method has been applied up to 4 Ge VI c 2J and for pion-nucleon scattering up to 10 Ge VI c. sl

Mesonic degrees of freedom in nuclei and the definition of meson-exchange currents

We describe the nucleus by a meson-nucleon system. Starting from a covariant field theoretical Hamiltonian we derive an effective Schrodinger equation for the nucleonic components. The meson-exchange currents are then defined unarbitrarily by an effective operator (current) in the space of the nucleonic components. The advantage over theS-matrix method [1] is discussed. In the nonrelativistic limit the meson-current as well as the seagull (pair) current agrees with theS-matrix result. Recoil and wavefunction orthogonalization cancels completely in this limit.

Elementary derivation of intermediate-coupling and strong-coupling mass formulae for the nonrelativistic Lee model

It is pointed out that in both Tomonaga's intermediate-coupling approximation and North's strong-coupling approximation, the Hamiltonian can be written as the sum of two commuting operators,Q andK, each of which also commutes with the Hamiltonian. Furthermore, it is shown thatK2=−Q+ const, whereQ is the total-charge operator for the meson-nucleon system (and consequently its eigenvalues are known). Hence both the strong-coupling and intermediate-coupling approximations lead to the same type of «mass formula».

A soluble model of a coupled meson-nucleon system

An exactly soluble model, in which fermions in a many-body system interact through the exchange of a massive boson, is investigated. The model deals with the linear coupling of a neutral scalar meson field to fermion density fluctuations. These density fluctuations, or particle-hole excitations, are treated within the framework of the random phase approximation (RPA), while the meson degrees of freedom are treated exactly. Within the RPA, we obtain coupled oscillator equations of motion, which are subjected to a normal mode analysis. A dispersion relation for the normal mode energies is obtained, and the operators which create the properly “dressed” particle-hole and meson modes are constructed. The density-density correlation function and the meson Green's function are calculated exactly. The structure of the Green's functions is also explored from the point of view of their coupled equations of motion, which can be decoupled and solved in the RPA model. We also calculate the exact interaction energy, the scattering matrix for particle-hole pairs and the number of mesons produced by the interaction.

Field-Current Identities and Nucleon Radii

This paper presents the results of a calculation of the electromagnetic radii of nucleons predicated on the assumption of vector dominance for the hadronic electromagnetic current. Vector dominance is implemented through the use of field-current identities. A new feature of this work is an attempt, for the isovector radii, to take account of the structure of the $\ensuremath{\rho}$-nucleon vertex. While the numerical results are somewhat model-dependent, they do lend support to the view that the radii are determined by the low-energy dynamics of the meson-nucleon system.

Some Remarks on Feynman's Variational Method

Feynman's variational method is manipulated and applied to the one- particle Green function in the mesonnucleon system with ps coupling. (D.L.C.)

Associated production by non-local interaction

The observed associated production of the K mesons and 1 HNO/sub 3/. hyperons from meson-nucleon interactions in the T = 1/2 state may be obtained from two Feynman diagrams. In a recent paper, a composite model was introduced for K mesons. On the basis of the solution, all the observed phcnomena including that of associated production could be explained. Similar conclusions were also obtained in detailed calculations by MacCarthy on the meson-nucleon compound system for the hyperon. Thee nature of the wave function for the composite model suggests that one may also assume the particle as elementary, having a structural co-ordinate as suggested by Yukawa for other elementary particles. (A.C.)

Determinantal approach to meson-nucleon scattering

A treatment of scattering is presented where the construction of the scattering phase shifts is regarded as an energy value problem. Using the relation between the phase shift δ( E) and the energy shift ΔE, the phases can be obtained directly from the infinite determinant D(E)= det E−H E−H 0 = Π k E−E k E−E 0k Π k 1− ΔE k E−E 0k where E k are the energy eigenvalues of the interacting system and E ok are the corresponding eigenvalues for the noninteracting system. For the problem of potential scattering this procedure is directly applicable and leads to results equivalent to the Fredholm solution of the scattering integral equation. However, for the case of interest, the interacting meson-nucleon system D( E) does not exist, and in order to apply this method, D( E) must be factored into convergent subdeterminants D i ( E), each of which refer to a particular class of states. From D 1( E), the subdeterminant referring to a one-meson type state, the scattering phase shifts can be calculated. A procedure for constructing D 1( E) for the meson-nucleon system is developed by using the formal structure of D( E). This method is then applied to calculate meson-nucleon scattering in the static model. D 1( E) is expanded in a power series. The first two terms of the expansion yield a solution for the phase shift similar to results given by the Chew-Low one-meson approximation. Finally the result of a preliminary calculation with the fully relativistic interaction is discussed.

Ward's Identity in Neutral Scalar Meson-Nucleon System

Ward's Identity in Neutral Scalar Meson-Nucleon System

Self-Energy Effects on Meson-Nucleon Scattering According to the Tamm-Dancoff Method

The lowest-order Tamm-Dancoff equations for the meson-nucleon system are derived by the method of Cini, using the wave functions defined by Dyson. The contributions of the meson and nucleon self-energies to the kernel of the momentum-space integral equation are renormalized. Their effects are absorbed into the coupling ${G}^{2}$, making it momentum and energy dependent. The effective coupling turns out to exhibit an anomalous behavior, having a pole for a spacelike momentum, to which it is difficult to attach a sensible physical interpretation.

A Method for the Solution of Nuclear Bound-State Problems

It is shown that the Fredholm method for the solution of integral equations can be adapted to solve the covariant scattering equations for the proton-neutron system and the meson-nucleon system. A practical method is devised for obtaining the binding energies of the deuteron and hyperon in a fully covariant way. As a test of the method it has been applied to the corresponding non-covariant equation for the deuteron, and satisfactory numerical results are obtained.

VParticles and the Gamma Decay of a Neutral Pion

It is shown that the previous theoretical calculations of the lifetime for the gamma decay of the ${\ensuremath{\pi}}^{0}$ meson must be subject to an obvious modification because of the presence of new particles recently discovered experimentally. This may be regarded as an example of the fact that, in some cases, the meson-nucleon system cannot be treated as being isolated from the rest of the elementary particles. We cannot give an accurate numerical prediction for the lifetime until sufficient knowledge about the new particles is accumulated. Some features of Pais' theory of the $V$ particles are discussed in connection with this problem.