Summary
We study the problem of two equal-mass scalar bosons scattering in a P-state under the influence of « marginally singular » forces. Such forces arise from the exchange of a vector boson. We show that the solutions of theN/D equations have a one-parameter ambiguity which we relate to the existence in the theory of quasi-elementary particles. We speculate that the observed vector bosons might belong to this category. We also discuss the possibility of a special form of lefthand cut which would have the property that all solutions of theN/D equations would contain a resonance. We point out that if this were.to occur in the bootstrap context, it could provide a new mechanism for the determination of the coupling constant by crossing symmetry.
Riassunto
Si studia il problema dello scattering dello statoP di due bosoni scalari di ugual massa sotto l’influenza di forze « marginalmente singolari ». Tali forze nascono dallo scambio di un bosone vettoriale. Si dimostra oho le soluzioni delle equazioniN/D hanno un’ambiguità a un parametro che mettiarno in relazione con l’esistenza nella teoria di particelle quasi elementari. Si argomenta che i bosoni vettoriali osservati potrebbero appartenere a questa categoria. Si discute anche la possibilità di una speciale forma di taglio a sinistra che avrebbe la proprietà di introdurre una risonanza in tutte le soluzioni delle equazioniN/D. Si fa, infine, notare che, se ciò accadesse nel contesto del bootstrap, potrebbe fornire un nuovo meccanismo per la determinazione della costante d’accoppiamento per mezzo della simmetria incrociata.
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On leave of absence from the Eutherford High-Energy Laboratory, Chilton, Berks.
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Morgan, D. Marginally singular forces and their role in producing pseudovector resonances. Nuovo Cim 36, 813–831 (1965). https://doi.org/10.1007/BF02749783
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DOI: https://doi.org/10.1007/BF02749783