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Il Nuovo Cimento (1955-1965)

, Volume 37, Issue 2, pp 671–684 | Cite as

Minimal interactions at very high transfers

  • A. Martin
Article

Summary

It is shown that both large-transfer electron-proton scattering and large-angle proton-proton scattering may be consistent with, or close to, the lower limits obtained from dispersion theory. For form factors the fastest allowed decrease is exp[−⇏ |g2|], whereq is the fourmomentum transfer of the photon. For scattering amplitudes one gets exp [−C(θ)⇏s] or exp [−C(θ)√s log s] or exp [−C(θ)√s (log s)2] according to various detailed assumptions, where s is the square of the c.m. energy and θ the c.m. scattering angle. The conditions to impose on the growth of the form factors and the scattering amplitude outside the physical region to obtain these results are considerably weaker than the usual polynomial boundedness condition, and are likely to be satisfied by the actual form factors or scattering amplitudes.

Riassunto

Si dimostra che sia lo scattering elettrone-protone con grande trasferimento che lo scattering protone-protone a grande angolo possono essere in accordo con, o prossimi a, i limiti inferiori ottenuti dalla teoria della dispersione. Per i fattori di forma la piú rapida diminuzione permessa è exp [−√|q2|], in cuiq è il quadri-impulso trasferito del lotone. Per le ampiezze di scattering si ottiene exp [−C(=θ) √s] od exp [−C(θ)√s log s] od exp [−C(θ)√s(log s)2] secondo le varie speciflche ipotesi, dove s è il quadrato dell’energia nel centro di massa e θ l’angolo di scattering nel centro di massa. Le condizioni da imporre alla crescita dei fattori di forma e dell’ampiezza di scattering fuori della regione fisica per ottenere questi risultati sono considerevolmente più deboli delle usali condizioni al limite del polinomio, ed è verosimile che siano soddisfatte dai fattori di forma o dalle ampiezze di scattering effettivi.

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Copyright information

© Società Italiana di Fisica 1965

Authors and Affiliations

  • A. Martin
    • 1
  1. 1.CERNGeneva

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