Singularities of Multiple Scattering Processes
The one-particle exchange graph (Fig. 1) is currently interpreted as representing the “exchange” of a “virtual” particle; it contributes a pole for an unphysical value t = m 2 of the momentum transfer squared: t ≡ (p x − p 3)2 (m is the mass of the exchanged particle).†
The N-particle threshold (or normal threshold) graph (Fig. 2) contributes a square root (N even) or logarithmic (N odd) branch point, at the value s = (m 1 + m 2 + m 3 + … + m N)2 of the total energy squared: s = (p 1 + p 2)2. Thus this singularity occurs for a physical value of the total energy, corresponding to the “opening of an N-particle channel” (m 1,m 2, …, m N, are the masses of these N-particles).
KeywordsMultiple Scattering Mass Shell Landau Equation Internal Line Effective Contact
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References and Comments
- 1.“Singularités des processus de diffusion multiple,” Ann. Inst. Henri Poincaré, Vol. VI, No. 2, p. 89–204, 1967. The presentation is made more accessible, and improved in some respects: For instance, in Section 2, the reasoning leading to Proposition 4 is made much simpler, thanks to the systematic study presented in Ref. 2.Google Scholar
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