Clebsch–Gordan coefficients for : the first steps

I. Sánchez Lima and P.O. Hess

Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México, Apartado Postal 70–543, Circuito Exterior, C.U., 04510 México, D.F., México.

Recibido el 25 de enero de 2005
Aceptado el 15 de febrero de 2005

Abstract

The group chain U(8) O(8) SU(3) plays an important role in systems of many gluons and in a schematic model for QCD at low energy. In order to calculate decay probabilities one has to calculate the Clebsch–Gordan coefficients of this group chain. In this contribution we present the basic idea in the example of SU(3) SO(3). Afterwards, the polynomial states of the U(8) chain are constructed and the procedure to obtain the Clebsch–Gordan coefficients is outlined. Partial results are presented.

Keywords: Clebsch–Gordan coefficients; gluons; QCD.

Resumen

La cadena de grupos U(8) O(8) SU(3) juega un papel importante en sistemas de muchos gluones y en un modelo esquemático para QCD a bajas energías. Para poder calcular probabilidades de decaimiento se necesita calcular los coeficientes de Clebsch–Gordan para esa cadena de grupos. En esta contribución presentamos la idea básica en el ejemplo de SU(3) SO(3). Posteriormente, se contruye los estados polinomiales de la cadena U(8) y se indica cómo obtener los coeficientes de Clebsch–Gordan. Presentamos resultados parciales.

Descriptores: Coeficientes de Clebsch–Gordan; gluones; QCD.

PACS: 02.20.–a; 12.39.Mk

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Acknowledgment

Financial help from DGAPA, project No. IN119002, and CONA–CyT is acknowledged.

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