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Quarks effective masses and the pions

  1. Oct 9, 2011 #1
    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?
  2. jcsd
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