Summary
A version of the one-particle-exchange approximation has been suggested by Chew in which the Regge-trajectory nature of the exchanged particle is taken into account. The prescription is explained in detail, and applied to the ππ,
and πω amplitudes. Comparison is made with earlier one-particle-exchange calculations in which the amplitude, even though analytic in the direct-channel angular momentum, comes from a force which represents the exchange of an elementary particle. We find the corrections to ππ and
scattering to be insignificant on the scale of accuracy of such models; but for πω scattering, the Regge-trajectory nature of the exchanged ρ-meson may be sufficient to change the sign of the force in the 1+ channel from a repulsion into an attraction, sufficient to create a resonance. Some kinematical properties of unequal-mass scattering amplitudes are discussed, especially the poles of the partial waves at the origin.
Riassunto
È stata suggerita da Chew una versione dell’approssimazione di scambio di una particella in cui si tiene conto della natura di traiettoria di Regge della particella scambiata. Si spiega dettagliatamente questa prescrizione e la si applica alle ampiezze ππ,
e πω. Si fa un confronto con precedenti calcoli dello scambio di una particella in cui l’ampiezza, anche se analitica nel momento angolare del canale diretto, proviene da una forza che rappresenta lo scambio di una particella elementare. Si trova che le correzioni allo scattering ππ e
sono insignificanti nel grado di precisione di tali modelli; salvo lo scattering πω. La natura di traiettoria di Regge del mesone ρ scambiato può essere sufficiente a cambiare il segno della forza nel canale 1+ da ripulsione in attrazione, sufficiente a creare una risonanza. Si discutono alcune proprietà cinematiche delle ampiezze di scattering di masse disuguali, specialmente i poli delle onde parziali all’origine.
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Literatur
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Except for numerical factors these are just particular cases of the formulae derived in ref. (8), Sect. II and Appendix A.
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Abers, E.S., Teplitz, V.L. Approximate one-trajectory exchange. Nuovo Cim 39, 739–757 (1965). https://doi.org/10.1007/BF02735841
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DOI: https://doi.org/10.1007/BF02735841