What Are the Key Differences Between Fermion and Scalar Field Interactions?

[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.

 

[Norman]

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

 

[jdstokes]

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

 

[Norman]

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

 

[HE_Matt]

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.

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...