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as4 - interactions in this world Estimate the following...

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Physics 253b Assignment #4 updated Monday 1 st March, 2010, 09:35 I like problems involving imaginary worlds. Here is one. It should be very straightforward (probably too much so) once you understand what I am talking about. As always, please email with questions. 4-1 . Suppose that you are transported to a world with different quark mass. There are still three light quarks, u , d and s , so there is an approximate SU (3) flavor symmetry and the u is very light so you can assume m u = 0 . But m d = m s / 3 (this is a larger m d than we have in our world). Consider matrix elements between spin up baryon states at rest. Suppose that h Σ + | ¯ 0 s | Ξ 0 i = 1 . 09 Because this not equal to 1 (the SU (3) symmetry result), you conclude that this is an SU (3) symmetry effect of the quark mass matrix (assume that you can ignore the electromagnetic
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Unformatted text preview: interactions in this world). Estimate the following matrix elements (also between spin up baryon states at rest): h P | ¯ uγ d | N i h Σ + | ¯ sγ d | P i and explain your reasoning. The results should be close to what you expect from perfect SU (3) symmetry. Note that the signs matter here and I have tried to get the sign of the given matrix element right in the sense of being close to the conventional SU (3) value. But the signs are somewhat convention dependent, so you should explain how you are trying to get them right, but we won’t take anything off if you don’t. 1...
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