# Similar masses and lifetimes of the $\Delta$ baryons

Why do the four spin 3/2 $\Delta$ baryons have nearly identical masses and lifetimes despite their very different $u$ and $d$ quark compositions?

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– Qmechanic Jul 16 '14 at 22:29

## 1 Answer

Because of $u\leftrightarrow d$ isospin symmetry. For a more detailed explanation, see e.g. chapter 8 of 't Hooft's lecture notes. The pdf file is available here.

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What prereqs are there for understanding those notes? I really need to start formally learning QM,GR,QFT, &c, and this looks like a good place to start.. – Manishearth Feb 14 '12 at 15:55
't Hooft's notes are really about Lie groups. I would recommend as a prerequisite any QM course which studies at some length angular momentum operators and their commutation relations. – Qmechanic Feb 14 '12 at 16:14
...and/or a solid background in group theory. – dmckee Feb 14 '12 at 16:31
@Qmechanic I was talking about all of his lecture notes, sorry about that (staff.science.uu.nl/~hooft101/GtH_lectures.html). Is there any online resource to learn the prereqs? I don't understand this operator business, and I know what tensors are, but very little as to how they can be used (covariance, contravariance, etc). I have a similar situation with group theory: I know what it is, but not its details. And I can't find any place that explains the whole thing starting from the basics. – Manishearth Feb 15 '12 at 4:00