Quarks effective masses and the pions

  • Thread starter jacopo23
  • Start date
11
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Hi everybody :)

A lagrangian of the u and d quarks where they don't have a mass, shares chiral SU(2) and U(1) symmetries.
In the vacuum, we write
[itex] <0| \bar{Q} Q | 0 > = \eta [/itex]
where Q is the douplet of u and d quarks. In such a way we break chiral symmetries.
The current associated with the three axial broken symmetries creates three goldstone bosons, the pions, and in the approximation where d and u are massless, the pions are massless too.

Now I just don't understand the following point: breaking the symmetry, we give a mass to u and d quarks, as Peskin says in pag. 669.
How can these quarks and their relative antiquarks form the pions, which we said to be massless?
 

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