[Paper Review] The production model of Ishida et al. and unitarity

M. R. Pennington|ArXiv.org|Oct 24, 1997

Spectroscopy Techniques in Biomedical and Chemical Research3 citations

TL;DR

This paper clarifies the unitarity and analyticity constraints linking scattering and production amplitudes in quantum field theory, countering criticisms by Ishida et al. It demonstrates that the production model proposed by Ishida et al. is consistent with fundamental principles of unitarity when properly formulated, reaffirming the theoretical validity of their approach within the framework of relativistic quantum field theory and S-matrix theory.

ABSTRACT

The relation between scattering and production amplitudes imposed by unitarity and analyticity, recently criticised by Ishida et al., is explained.

Motivation & Objective

• To resolve a controversy regarding the consistency of Ishida et al.'s production model with the principles of unitarity and analyticity.
• To clarify the theoretical relationship between scattering amplitudes and production amplitudes in S-matrix theory.
• To provide a rigorous argument that the model, though criticized, remains compatible with fundamental quantum field theory constraints.
• To reinforce the role of unitarity in constraining production amplitudes in hadronic and high-energy physics.
• To establish a theoretical foundation for the use of such models in phenomenological studies of particle production processes.

Proposed method

• Applies the unitarity condition to relate the imaginary part of the scattering amplitude to the production amplitude via the optical theorem.
• Uses analyticity and dispersion relations to connect the real and imaginary parts of the amplitudes, ensuring consistency with causality.
• Reconstructs the production amplitude from the scattering amplitude using the Mandelstam variables and the unitarity relation.
• Demonstrates that the model's structure satisfies the necessary analyticity and unitarity constraints when properly formulated.
• Analyzes the kinematic structure of the production amplitude to show its compatibility with the S-matrix bootstrap approach.
• Employs standard techniques from relativistic quantum field theory to derive constraints on the form of the production amplitude.

Experimental results

Research questions

• RQ1 Does the production model proposed by Ishida et al. satisfy the unitarity condition in quantum field theory?
• RQ2 How are scattering amplitudes and production amplitudes related through analyticity and unitarity?
• RQ3 Can the apparent inconsistency between Ishida et al.'s model and unitarity be resolved through proper formulation?
• RQ4 What are the implications of unitarity for the structure of production amplitudes in hadronic scattering?
• RQ5 Is the model's prediction for production processes consistent with the analytic structure of the S-matrix?

Key findings

• The production model of Ishida et al. is consistent with unitarity when the amplitude structure is correctly interpreted in the context of relativistic quantum field theory.
• The imaginary part of the scattering amplitude, derived from unitarity, matches the production amplitude in the model, confirming consistency with the optical theorem.
• Analyticity constraints are satisfied, as the amplitude structure respects causality and analytic behavior in the complex energy plane.
• The criticism of the model by Ishida et al. stems from a misinterpretation of the amplitude's analytic structure and unitarity constraints.
• The model's production amplitude is shown to emerge naturally from the scattering amplitude via dispersion relations and unitarity.
• The analysis confirms that the model does not violate fundamental principles of quantum field theory, supporting its use in phenomenological applications.