In my book (Greiner's Quantum Mechanics, vol2, symmetries) says after calculation with Clebsch-Gordan coefficients,(adsbygoogle = window.adsbygoogle || []).push({});

[tex]|\pi^0\rangle = \frac 1 2 (u\uparrow \overline{u} \downarrow + d\uparrow \overline{d} \downarrow - u\downarrow \overline{u} \uparrow - d\downarrow \overline{d} \uparrow ),[/tex]

And I confirmed it.

Ignoring spin, It's [tex]|\pi^0\rangle = \frac 1 {\sqrt{2}} (u \overline{u} + d \overline{d})[/tex]

However, some sites denote, it's the same: the sum (ex, this one, but others denote it's different; minus sign (ex. this one).

I wonder which is correct. I konw Internet resource is sometimes incorrect. And the latter is wiki... Or they mean the same? because [tex]u \overline{u}[/tex] and [tex]d \overline{d}[/tex] are orthogonal.

But if I do [tex]\hat{T_-}|\pi^+}\rangle = \hat{T_-}u\overline{d} = \frac 1 {\sqrt{2}} (u\overline{u} + d\overline{d}),[/tex] only plus is correct. (phase is ignored and each hand is normalized.)

So will anyone give me any hint which is correct or both are correct? I think at least plus is correct.

Thanks in advance!

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# Which is pion(0) makeup?

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