Summary
We examine the Dyson-Schwinger equation for the quark propagator in quantum chromodynamics by employing the gauge technique with the object of investigating spontaneously broken flavor symmetry in the chiral limit of vanishing current quark masses. We show that dynamical breakdown of flavorSU V (N F ) symmetry does not occur, thus reiterating an assertion by Vafa and Witten. Our analysis is limited to three flavors but is generalizable to an arbitrary number of flavors,N F>3.
Riassunto
Si esamina l'equazione di Dyson-Schwinger per il propagatore di quark in cromodinamica quantistica impiegando la tecnica di gauge con l'obbiettivo di studiare la simmetria del sapore spontaneamente infranta nel limite chirale della masse dei quark di corrente tendenti a zero. Si mostra che la rottura dinamica della simmetria del saporeSU v (N F ) non avviene, rinforzando cosí un'asserzione di Vafa e Witten. La nostra analisi è limitata a tre sapori, ma è generalizzata a un numero zero arbitrario di saporiN F>3.
Резюме
Мы рассматриваем уравнение Дайсона-Швингера для кваркового пропагатора в квантовой хромодинамике, используя калибровочную технику, с целью исследования спонтанно нарушенной симметрии аромата в киральном пределе для исчезающе малых токовых кварковых масс. Мы показываем, что динамическое нарушениеSU V (N F ) симметрии аромата не возникает, т.е. подтверждается формулировка Вафа и Виттена. Наш анализ ограничен тремя ароматами, но может быть обобщен на произвольное число ароматов,N F>3.
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Acharya, R., Swamy, P.N. Constraints on dynamical flavor symmetry breaking in quantum chromodynamics: Vafa-Witten theorem. Nuov Cim A 98, 773–786 (1987). https://doi.org/10.1007/BF02786828
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DOI: https://doi.org/10.1007/BF02786828