Gamma-5 vertex

  • Thread starter jdstokes
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Suppose I couple a fermion field to a scalar field using [itex]\mathrm{i} g \bar{\psi}\psi \varphi [/itex] and [itex]\mathrm{i} g \bar{\psi}\gamma_5\psi\varphi[/itex].

I'm trying to understand what would be the physical difference between these interactions. I know that [itex](1/2)(1\pm \gamma_5)[/itex] 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.
 
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  • #2
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Your first interaction lagrangian is a scalar coupling, while the second is a pseudoscalar coupling. Check how they both transform under parity.
 
  • #3
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What is the physical difference in the interactions apart from their transformation properties?
 
  • #4
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The symmetries of the interaction define what interactions they are used to model.
 
  • #5
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Suppose I couple a fermion field to a scalar field using [itex]\mathrm{i} g \bar{\psi}\psi \varphi [/itex] and [itex]\mathrm{i} g \bar{\psi}\gamma_5\psi\varphi[/itex].

I'm trying to understand what would be the physical difference between these interactions. I know that [itex](1/2)(1\pm \gamma_5)[/itex] 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...
 

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