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Effect of singular operator products on a hard-pion calculation

Влияние сингулярных операторных проиэведений на вычисление с жесткими пионами

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Il Nuovo Cimento A (1965-1970)

Summary

A previous derivation of a hard-meson dynamical equation for the pion form factor is generalized to take into account the effect of singular operator products. The content of the relation in the limit of infinite momentum transfer is then investigated, yielding an expression for the asymptotic behaviour of an A1(1070) form factor with both external legs off shell.

Riassunto

Si generalizza una precedente deduzione di una equazione dinamica per mesoni duri del fattore di forma pionico per tener conto dell’effetto di prodotti singolari di operatori. Si esamina quindi il contenuto della relazione nel caso limite di impulso trasferito infinito, formando un’espressione per il comportamento asintotico di un fattore di forma di A1(1070) con entrambi i rami fuori stato.

Реэюме

Предыдуший вывод динамического уравнения для форм-фактора пиона обобшается, чтобы учесть влияние сингулярных операторных проиэведений. Затем исследуется содержание соотнощения в пределе бесконечного передаваемого импульса, при зтом получается выражение для асимптотического поведения форм-фактора А1(1070) с двумя внещними концами вне массовой поверхности.

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References

  1. J. J. Brehm, E. Golowich andS. C. Prasad:Phys. Rev. Lett.,23, 666 (1969).

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  6. A well-known reference pertaining to singular operator products isK. G. Wilson:Phys. Rev.,179, 1499 (1969).

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  8. Some overlap in formulae of our Sect.2 and ref. (5) is necessary not only for benefit of the reader, but also because of several algebraic errors in the latter.

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  10. In particular, had the calculation of ref. (1) employed the assumption (48) regarding the asymptotic form of ϱ(s), the spectral representation in (52) would require subtractions.

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Authors and Affiliations

  1. Department of Physics and Astronomy, University of Massachusetts, Amherst, Mass.

    E. Golowich

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  1. E. Golowich
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Golowich, E. Effect of singular operator products on a hard-pion calculation. Nuov Cim A 18, 747–759 (1973). https://doi.org/10.1007/BF02727590

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  • DOI: https://doi.org/10.1007/BF02727590

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