Summary
We studyK ℓ3 form factors assumingSU 3⊗SU 3 current commutation relations and pion-pole dominance of the axial-current divergence for small momentum transfer. We derive a correction to the Callan-Treiman relation which is small in the limit of nearSU 2⊗SU 2 invariance and large and negative in the limit of nearSU 3 invariance. In the latter limit, the corrected result conforms to the requirements of small «leakage» forSU 3 generators and predicts a negative value for the parameter ξ.
Riassunto
Si studiano i fattori di forma diK ℓ3 postulando le relazioni di commutazione della corrente diSU 3⊗SU 3 e il dominio del polo del pione sulla divergenza della corrente assiale per piccole quantità di moto trasferite. Si ricava una correzione alla relazione di Callan e Treiman, piccola nel limite della quasi invarianza diSU 2⊗SU 2 e grande e negativa nel limite della quasi invarianza diSU 3. In quest'ultimo limite, il risultato corretto è conforme alle richieste di piccolo «leakage» per i generatori diSU 3 e prevede un valore negativo per il parametro ξ.
Резюме
Мы изучаем форм-факторы Kℓ3, предполагаяSU 3⊗SU 3 коммутационные соотношения токов и преобладание пионного полюса в расходимости аксиального тока при малых передаваемых импульсах. Мы выводим поправку к соотношению Каллана-Треймана, которая является малой в пределеSU 2⊗SU 2 инвариантности, и большой и отрицательной в пределеSU 3 инвариантности. В последнем предельном случае, исправленный результат соответствует требованиям малой «утечки» дляSU 3 генераторов и предсказывает отрицательную величину для параметра ш.
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References
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Laboratoire Associé au C.N.R.S.
Traduzione a cura della Redazione.
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Gaillard, M.K. SU 3 orSU 2⊗SU 2: Kol3 form factors as a symmetry probe. Nuovo Cimento A (1965-1970) 61, 499–514 (1969). https://doi.org/10.1007/BF02756857
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DOI: https://doi.org/10.1007/BF02756857