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## Main Question or Discussion Point

Hello!

I hear an elementary particle course and I wonder about one question: There is the multiplett of [tex]\pi^+, \pi^0, \pi^-[/tex]. It is said that all have Isospin 1 and [tex]I_z = -1,0,1[/tex]. So far so good. So these particles are to form a two-dimensional irreducible representation of SU(2). They are composed of a quark and an antiquark in the form:

[tex]\pi^+ : u\bar d[/tex]

[tex]\pi^0 : u\bar u - d\bar d[/tex]

[tex]\pi^- : d\bar u[/tex]

So, this should be the I = 1 part of [tex]\frac{1}{2}\otimes\frac{1}{2} = 0\oplus 1[/tex]. But on p. 26 my Maggiore says that these states are given as above but with a plus sign! The one with the minus sign is said to be the scalar representation.

So where is the mistake if there is any? I also can't see why the state with a minus should be a scalar representation. Hope somebody can help me out of confusion.

Thanks!

Blue2script

PS: By the way, maybe someone can also explain me the deeper meaning and use of the hypercharge. Up to now for me its only a definition used in representing multipletts in Young diagrams...

I hear an elementary particle course and I wonder about one question: There is the multiplett of [tex]\pi^+, \pi^0, \pi^-[/tex]. It is said that all have Isospin 1 and [tex]I_z = -1,0,1[/tex]. So far so good. So these particles are to form a two-dimensional irreducible representation of SU(2). They are composed of a quark and an antiquark in the form:

[tex]\pi^+ : u\bar d[/tex]

[tex]\pi^0 : u\bar u - d\bar d[/tex]

[tex]\pi^- : d\bar u[/tex]

So, this should be the I = 1 part of [tex]\frac{1}{2}\otimes\frac{1}{2} = 0\oplus 1[/tex]. But on p. 26 my Maggiore says that these states are given as above but with a plus sign! The one with the minus sign is said to be the scalar representation.

So where is the mistake if there is any? I also can't see why the state with a minus should be a scalar representation. Hope somebody can help me out of confusion.

Thanks!

Blue2script

PS: By the way, maybe someone can also explain me the deeper meaning and use of the hypercharge. Up to now for me its only a definition used in representing multipletts in Young diagrams...