I'm having a little trouble recreating some things from a paper and it is due to my lack of knowledge of working with Flavor-Spin wavefunctions.(adsbygoogle = window.adsbygoogle || []).push({});

I'm trying to show that :

[tex]

\left\langle \Lambda \left|b_s^{\dagger }b_b\right|\Lambda _b\right\rangle =\frac{1}{\sqrt{3}}

[/tex]

and

[tex]

\left\langle p \left|b_u^{\dagger }b_c\right|\Lambda _c^+\right\rangle =\frac{1}{\sqrt{2}}

[/tex]

These two papers both take their operation from the same text, but none of it explicitly shows how they get it or what wavefunctions they use. I assume this is because it is ELEMENTARY but while searching around, many books/articles give different wavefunctions using different approaches.

I'm wondering where I should start. I feel like this should be a simple multiplication but everytime I try it I don't get their answers.

From you guys, do any of you know offhand know the flavor-spin states for a lambda and p (both in s=1/2)? One paper gives both octet proton flavor wavefunctions as :

[tex]p'=\frac{1}{\sqrt{2}}(\text{udu}-\text{duu})[/tex]

[tex]p\text{''}=\frac{1}{\sqrt{6}}(2\text{uud}-\text{duu}-\text{udu})[/tex]

Which is right? Or is it that only in a linear combination with some spin states to make the total flavor-spin function symmetric :

[tex]\left.|56,S=\frac{1}{2},8\right\rangle =\frac{1}{\sqrt{2}}(p'\chi '+p\text{''}\chi \text{''})[/tex]

where the spinors are pretty much the same as the protons function but with spin arrows up and down instead of "u u d".

Am I on the right track?

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# Flavor Spin Wavefunctions

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