Takeshi Kanki

Mechanism of High Energy Inelastic Collision and the Shrinkage of Diffraction Peak

Two mechanisms of high-energy inelastic collisions are given, each, of which causes an increase in the target radius and transparency. The mechanism of shrinkage in the diffraction peak of an elastic event or, in other words, the reason why the target radius can become infinity in the high energy limit, is clarified. (auth)

Use of the Generalized Jost Function in Quantum Field Theory An Extension of the Levinson Theorem

The structure of the S-matrix is investigated in terms of the so-called generalized Jost function. Starting from the partial wave dispersion relation, the analytic properties of this function can be derived in the single-channel scattering, and it is shown that there exists a close connection between the analyticity of this function and the generalized Levinson relation. In the case where the one-particle singularity in scattering amplitudes is caused by the elementary particle, the corresponding Jost function has a pole, while in the case where this singularity is caused by the composite bound) state, the Jost function does not have the pole. Singularities corresponding to the Castillejo- Dalitz-Dyson ambiguity are completely separated. Thus, by making the conjecture that the analyticity in the low-momentum region still remains in the multichannel case, the Levinson theorem can be extended to the multichannel case and to the S- matrix theory where the Hamiltonian is not used explicitly. A new representation of the S-matrix, and how the structure of the Smatrix changes according to each case mentioned above, is clarified.

SU 3 -symmetry breaking and slopes of baryon linear trajectories

The hypothesis that the dominant par t of the hadron Regge-trajectory function is linear in (mass) 2 has recently been used very popularly in many theoretical works. On lhe other hand, the Gell-Mann-Okubo (G~O) mass formula (~) is well satisfied for tile ground states of the octet and the decuplet trajectories. I t will be a natural expectation that the same symmetry breaking scheme, thus GMO mass formula, is valid for all higher excited states. But by the incompleteness of the experimental mass data, this hypothesis is not yet confirmed. For the mesons the above two hypotheses are trivially compatible and one of the solutions is a universali ty of the slopes. The compatibility, however, offers new problem for baryons, because the mass formlfla is now linear in mass but the t rajectory is quadratic. Experimental ly, the slopes of the baryon trajectories are different from each other. In this note we discuss the consequence of the compatibili ty of the two hypotheses for the baryon case together with the experimental situation. First of all we consider the very extreme case where the GMO formula is regorously satisfied for all physical points on the linear baryon trajectories; for the octet baryons (i)

On the Short Range Interaction between Pion and Nucleon

Asymptotic behaviors of the so-called force functions, dispersion integrals over left-hand cuts of partial-wave amplitudes, in pion-nucleon scattering are investigated. By virtue of the exponential decrease of fixed cos 8 amplitudes for s-?+oo with Ieos 81<1, the left-hand cut contributions to these amplitudes, from which we obtain the force function by doing the partial-wave projection, can be evaluated in terms of the right-hand cut integrals. The empirical formulae for high-energy scattering are used for evaluating these right-hand cut integrals. The two cases are considered, in which Krischs formula and Orears one a:re used for the large-angle scattering, respectively. For the case of Krischs formula, it is found that the asymptotic behavior of nN force function for any partial wave is dominated by the contribution from a diffraction-scattering term and this contribution gives rise to an attractive short-range force, and that for the P11 state, this attractive force seems to be somewhat weaker than that required in the previous N/D bootstrap calculation. For the case of Orears formula, no definite conclusion is obtained because of the possibility that large angle regions give rise to large contributions.

N/D Method and Inverse-Amplitude Method

It is shown that the conventional N/D method gives only such a special solution of the Chew-Mandelstam scattering equation as satisfies the Levinson theorem, while the inverse-amplitude method gives a general solution.

NOTE ON THE PION PROPAGATOR IN THE COMPOSITE THEORY

The pion is assumed to be a composite particle, composed of nucleons N and antinucleons. N-N interactions are considered to be fundamental, in the sense that the dissociated pion contribution probably dominates the as sociated pion contribution in the nucleon core region. The pion propagator may be expressed as a function of the N-N interaction higher-order terms. It is shown that the effect of the pion propagator on N-N interactions is appreciable, even at very small N-N separations; the n-p interaction is given as an example. (T.F.H.)

The Proton-Neutron Mass Difference and the Inner Structure of the Nucleon

A method is proposed which makes it possible to take into account the contribution from the pair state in the calculation of the proton-neutron mass difference without regard to the form of the matrix elements related to the pair state. It is shown that there exists a considerable difference between the result of our method and that of the Feynman-Speisman method in the internal region of the nucleon cloud. The model of form factors is considered in which the core exists only in the charge iso-scalar part. The result derived from this model is not satisfactory owing to the wrong sign of the mass difference. In order to get a good agreement with the empirical data it would be necessary to introduce a core at least into one of the form factors of the charge iso-vector type and of any kind of the magnetic moment type. The magnitude and the sign of the core is briefly estimated for each type of form factors.