The N/D Method and the Pion-Pion Scattering

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概要

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• In most of recent calculations based on the N/D formalism, the N function is replaced by the appropriate Born terms. Thus the resulting amplitude, N/D, includes a normalization point s_0. This s_0 dependence is not small. If the coupled integral equations for N and D are solved, then N/D should have no s_0 dependence. If the left hand singularities are approximated by a set of poles, the integral equation for N can be solved analytically. The amplitude N/D is expressed by an analytic function which does not involve s_0. The relations between a resonance position (m) and its reduced width (γ^2) are determined without any arbitrariness, in principle. This method is applied to the p-wave pion-pion resonance. It is shown that self-consistency can not be achieved for any reasonable values of m and γ^2, if we assume the Born term due to the ρ meson exchange as the left hand cut. In order to make a bootstrap mechanism operative, such effects as to make scattering amplitudes less singular at larger negative energies have to be taken into account. They may be substituted by introducing a phenomenological cutoff.

• 理論物理学刊行会の論文
• 1964-07-25

著者

• Kotani Tsuneyuki

  Department Of Physics Faculty Of Science Osaka University

• Adachi Toshimi

  The Tokyo Metropolitan Technical

• KAWAMURA Ryuji

  Department of Physics, Tokyo Metropolitan University

• Kawamura Ryuji

  Department Of Physics Tokyo Metropolitan University

関連論文

• Large-Angle and Forward Scatterings in the Relativistic Eikonal Approximation
• Observation of the (π,π) Resonance in the Pion Production Process
• On the β-decay of Λ and Σ^-Hyperons
• Production of Charged π-Meson by γ-Ray : Higher Order Corrections
• Dynamical Mechanism for Composite Particles : Report on Symposium on the Structure of S Matrix.
• An Impact Parameter Representation of the Scattering Problem
• Impact Parameter Formalism. IV : The Non-Zero Spin Case
• An Impact Parameter Formalism. III : Strong Absorption Model
• An Impact Parameter Representation of the Scattering Problem
• On the Extension of the Casimir Trick, I : On the Definition of Density Matrix and its Reduction
• The N/D Method and the Pion-Pion Scattering
• Analytic Property of Impact Parameter Amplitude
• On the Solution of the N/D Method
• The First Forbidden β-Decay
• An Impact Parameter Formalism
• The Eikonal Approximation in the Functional Integration Method
• Complex Angular Momentum and Impact Parameter Amplitude
• On the Mass Splitting under SU(3)^*
• A String Model Interpretation of ψ-Particles
• Unitarity Relation in an Impact Parameter Representation
• An Impact Parameter Formalism. II : High Energy Elastic Scattering
• The Impact Parameter Amplitude with a Direct-Channel Regge Pole

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