Helicity violation in strong interaction?

[metter]

I have a proton and an antiproton scattering, via a pion exchange.

The matrix element has the form:
$$M=g*(\bar{u}_{1}\gamma ^{5}u_{2})\frac {1} {q^2-m^2}( \bar{v}_{1}\gamma ^{5}v_2)$$
Wher g is my coupling constant, and q the 4-momentum of the pion.

The problem is that when I compute the currents $$(\bar{u}_{1}\gamma ^{5}u_2)$$ and $$(\bar{v}_{1}\gamma ^{5}v_2)$$ in the helicity basis this terms are non zero only for a change of the helicity( my righthanded proton should change into a lefthanded proton and the same for my antiproton).

This would imply that the matrix element for a helicity 1 state going to a helicity -1 state is not zero, which implies helicity is not conserved.

Where am I getting it wrong?

 

[Meir Achuz]

Why do you think helicity conserved in strong interactions?

 

[blechman]

A scalar (or pseudoscalar) interaction is always L-R. This follows from Lorentz invariance, or from a more brute-force point of view, from the Dirac equation. The pion is a pseudoscalar, so you expect a helicity flip!

Chiral symmetry is broken in QCD, with pions being the goldstone bosons of the breaking. So this is totally consistent.

This leads to the infamous question that appears on graduate board exams for particle-physics PhD candidates: if there was no Higgs, what would be the mass of the Z boson? Answer: proton mass!

 

[metter]

Thnak you very much. You are right. I was confusing something, and your answers made me realize that.

Thanks again