|Aug2-11, 12:53 PM||#1|
SU(5) coupling question
I was reading a gauge field theory book and was told to refer to Quigg's Gauge Theories of the Strong, Weak, and Electromagnetic Interactions ch 9.2 The SU(5) Model, so I did not start from the first page of Quigg's book.
In page 277, he started from
Q = T3 + K To,
where T3 is a generator of SU(2) and To is a weak-isosinglet generator of SU(5).
Σ Q^2 = (1+K^2) Σ T3^2
working on 5* representation and get
K^2 = 5/3
So To differs by a factor of (3/5)^(1/2) from U(1) hypercharge operator Y, and
g' ^2 = (3/5) (g_SU(2))^2
My questions are,
1. Why is it that from K^2 = 5/3 we can get g' ^2 = (3/5) (g_SU(2))^2 ?
2. Since Q = I3 + (1/2)Y, why is it that To differs by a factor of (3/5)^(1/2) but not (1/2)*(3/5)^(1/2) from Y?
3. Is there any beginner friendly reference for the derivation of Σ Q^2 = (1+K^2) Σ T3^2 ?
|Aug3-11, 10:06 AM||#2|
2. - Solved.
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