# Quarks effective masses and the pions

1. Oct 9, 2011

### jacopo23

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
$<0| \bar{Q} Q | 0 > = \eta$
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?