# Gamma-5 vertex

1. Jun 2, 2008

### jdstokes

Suppose I couple a fermion field to a scalar field using $\mathrm{i} g \bar{\psi}\psi \varphi$ and $\mathrm{i} g \bar{\psi}\gamma_5\psi\varphi$.

I'm trying to understand what would be the physical difference between these interactions. I know that $(1/2)(1\pm \gamma_5)$ approximately projects out the left and right handed components of Dirac fields and that this is related to the fact that the weak interaction couples preferentially to left-handed particles and right-handed anti-particles, but other than that I'm pretty clueless.

Last edited: Jun 2, 2008
2. Jun 3, 2008

### Norman

Your first interaction lagrangian is a scalar coupling, while the second is a pseudoscalar coupling. Check how they both transform under parity.

3. Jun 3, 2008

### jdstokes

What is the physical difference in the interactions apart from their transformation properties?

4. Jun 4, 2008

### Norman

The symmetries of the interaction define what interactions they are used to model.

5. Jun 20, 2008

### HE_Matt

The weak force not only prefers left-handed; at tree level there is no weak coupling to right-handed fields.

The weak force is slightly more complicated than your model because vector bosons are vectors (duh). You can write the weak coupling as a sum of alpha*Vector + beta*Axial Vector couplings. Up to an internal minus sign (always mix it up), the weak coupling is pure V+A, so it couples solely to left-handed fields. The most obvious physical observable used to demonstrate this is the polarized e+/e- beam experiment of SLD...