Can chiral symmetry help to explain the origin of hadron mass?
http://conservancy.umn.edu/bitstream/handle/11299/120289/glozman.pdf?sequence=1
Chiral symmetry is the invariance of the massless Dirac action under chiral rotations. It implies that Dirac fermions are massless. If it were an exact, global symmetry of the strong interactions, then the quarks would be massless. If it were spontaneously broken, then there would be massless (psuedo)scalar particles, the Goldstone bosons of this symmetry. These can be identified with the pions and the fact that the pions have a very small mass, indicates that the hypothesis isn't that bad, though not exact. The fact that the quarks could be massless doesn't imply that their bound states must be massless, however. The origin of hadron mass is the strong interactions of the quarks with the gluons and, to a lesser extent, the electroweak interactions of the quarks with the Higgs. This is tested by lattice simulations of QCD.
chiral symmetry is a possible symmetry of the Lagrangian under which the left-handed and right-handed parts of Dirac fields transform independently.
The electron, for instance-the charged leptons more generally and the quarks.
You said : "It implies that Dirac fermions are massless"
all the entities you mentioned posess a non zero rest mass.
Read the whole text-not just one sentence-and try to understand its meaning. IF chiral transformations are symmetries THEN Dirac fermions are massless. Leptons obtain their mass by spontaneous breaking of the electroweak symmetry, which is a *gauged* chiral symmetry, through interaction with the Higgs field-it's the fact that the symmetry is spontaneously broken, that implies that certain of its consequences are relevant for the massive phase; when taking into account the strong interactions, there's a whole theory behind the global chiral symmetry of the strong interactions. It's not possible to give a whole course on particle physics here, only the conclusions that are relevant for answering the original question.
Dirac type mass term can be written as
M (psi_R)^bar psi_L + h.c. where M is a complex number in general.
If psi_R and psi_L has different quantum numbers under certain global or local symmetry group then this term is forbidden. On the contrary, existence of this mass term implies that such a (chiral) symmetry is broken. For example SU(2)_L x U(1)Y model of Glashow, Weinberg and Salam, is a chiral theory where fermions are massless before the symmetry is broken; eventhough they do interact with the Higgs scalar field, i.e. there exists gauge invariant interaction terms contained in the Lagrangian density. After the symmetry is broken in the Higgs potential, Yukawa coupling multiplied by the VEV of Higgs scalar generates a (renormalizable) mass term. This is a Dirac mass term.
Stam,
IF chiral transformations are symmetries THEN Dirac fermions are massless.
ok..it regards the dirac spinors and their relation with the HIGGS Field.
It's not possible to give a whole course on particle physics here, only the conclusions that are relevant for answering the original question.
sorry I misunderstood since the beginning
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