So why does baryon octet have the extra spin?

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SUMMARY

The baryon octet and decuplet both consist of three quarks, yet they exhibit different total spins of 1/2 and 3/2, respectively. The distinction arises from the ways in which three spin-1/2 particles can be combined, resulting in two possible total spins: 1/2 and 3/2. The concept of "extra spin" is misleading, as it implies an additional property rather than a different configuration of the same quark content.

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Xuekai Du
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baryon decuplet and octet have same quark content, but has spin 1/2 and 3/2. So what gives octet the extra spin?
 
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I don't think that is a meaningful question. You have two ways to combine three spin 1/2 particles to a total spin, 1/2 and 3/2. There is no "extra spin".
 

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