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Il Nuovo Cimento A (1965-1970)

, Volume 55, Issue 4, pp 618–626 | Cite as

Superconvergence relations for\(\overline {\mathcal{N}} + {\mathcal{N}} \to \pi + \rho \) and\(\overline {\mathcal{N}} + {\mathcal{N}} \to \pi + \omega \)

  • A. Bartl
  • F. Widder
Article

Summary

Superconvergence relations for\(\overline {\mathcal{N}} + {\mathcal{N}} \to \pi + \rho \) and\(\overline {\mathcal{N}} + {\mathcal{N}} \to \pi + \omega \) are considered which follow from high-energy behaviour. Saturating these relations with a number of low-lying states we obtain\(g_\varphi {\mathcal{N}}/g_\omega {\mathcal{N}} = 0.06\), andmω=mρ andgρωπ=21 (GeV)−1 in good agreement with experiment. Assuming ρ-meson universality and vector-meson dominance we obtain\(g_\rho {\mathcal{N}} = 2.8,g_\omega {\mathcal{N}} = 6.4,f_\rho {\mathcal{N}} = 10.3\) in agreement, and\(f_\omega {\mathcal{N}} = 4.0\) in disagreement with the results of a least-squares fit of low-energy\({\mathcal{N}} - {\mathcal{N}}\) data.

Keywords

Helicity Amplitude Invariant Amplitude Kinematical Singularity Vector Dominance Model SUPERCONVERGENCE Relation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Сверхсходящиеся соотношения для\(\overline {\mathcal{N}} + {\mathcal{N}} \to \pi + \rho \) и\(\overline {\mathcal{N}} + {\mathcal{N}} \to \pi + \omega \)

Резюме

Рассматриваются сверхсходящиеся соотношения для\(\overline {\mathcal{N}} + {\mathcal{N}} \to \pi + \rho \) и\(\overline {\mathcal{N}} + {\mathcal{N}} \to \pi + \omega \), которые вытекают из поведения при высоких энергиях. При насыщении этох соттношений с помощью ряда низа низко-лежащих состояний, мы прлучаем\(g_\varphi {\mathcal{N}}/g_\omega {\mathcal{N}} = 0.06\),mω=mρ иgϱωπ (ΓэВ)−1, что находится в хорошем согласии с экспериментом. Предполагая универсальность ρ-мезона и преобладание векторного мезона, мы получаем\(g_\rho {\mathcal{N}} = 2.8,g_\omega {\mathcal{N}} = 6.4,f_\rho {\mathcal{N}} = 10.3\) в сгласии, и\(f_\omega {\mathcal{N}} = 4.0\), в противеречии с результатами подгонки наименьших квадратов для\({\mathcal{N}} - {\mathcal{N}}\) данаых при низких энергиях.

Riassunto

Si studiano le relazioni di superconvergenza per\(\overline {\mathcal{N}} + {\mathcal{N}} \to \pi + \rho \) e\(\overline {\mathcal{N}} + {\mathcal{N}} \to \pi + \omega \) che derivano dal comportamento di alta energia. Saturando queste relazioni con un numero di stati inferiori, si ottiene\(g_\varphi {\mathcal{N}}/g_\omega {\mathcal{N}} = 0.06\),mω=mρ egϱωπ (GeV)−1, in buon accordo con i dati sperimentali. Postulando l'universalità del mesone ρ e la dominanza del mesone vettoriale si ottiene\(g_\rho {\mathcal{N}} = 2.8,g_\omega {\mathcal{N}} = 6.4,f_\rho {\mathcal{N}} = 10.3\), in accordo con i risultati di un addattamento col metodo dei minimi quadrati dei dati di\({\mathcal{N}} - {\mathcal{N}}\) di bassa energia, e\(f_\omega {\mathcal{N}} = 4.0\) in disaccordo con questi dati.

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Copyright information

© Società Italiana di Fisica 1968

Authors and Affiliations

  • A. Bartl
    • 1
  • F. Widder
    • 2
  1. 1.Institut für Theoretische PhysikUniversität TübingenTübingen
  2. 2.Institut für Theoretische PhysikUniversität GrazGraz

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