rpp2010-rev-su3-isoscalar-factors

rpp2010-rev-su3-isoscalar-factors - 37. SU(3) isoscalar...

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37. SU(3) isoscalar factors and . .. 1 37. SU(3) ISOSCALAR FACTORS AND REPRESENTATION MATRICES Written by R.L. Kelly (LBNL). The most commonly used SU(3) isoscalar factors, corresponding to the singlet, octet, and decuplet content of 8 8and10 8, are shown at the right. The notation uses particle names to identify the coefficients, so that the pattern of relative couplings may be seen at a glance. We illustrate the use of the coefficients below. See J.J de Swart, Rev. Mod. Phys. 35 , 916 (1963) for detailed explanations and phase conventions. A is to be understood over every integer in the matrices; the exponent 1 / 2oneach matrix is a reminder of this. For example, the Ξ Ω K element of the 10 10 8 matrix is 6 / 24 = 1 / 2. Intramultiplet relative decay strengths may be read directly from the matrices. For example, in decuplet octet + octet decays, the ratio of Ω Ξ K and Δ partial widths is, from the 10 8 × 8matr ix , Γ(Ω Ξ K ) Γ(Δ ) = 12 6 × (phase space factors) . (37 . 1) Including isospin Clebsch-Gordan coefficients, we obtain, e.g. , Γ(Ω ∗− Ξ 0 K ) Γ(Δ
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rpp2010-rev-su3-isoscalar-factors - 37. SU(3) isoscalar...

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