Goldstone boson-Gauge boson coupling in the Glashow-Weinberg-Salam (GWS) model

Question

In the GWS model it is expected to see terms like $sim gvpartial_mu phi W^mu$, where $g$ is a coupling constant, $v$ the VEV of the Higgs field, $phi$ a Goldstone boson, and $W$ a gauge boson. However in the expanded form of the standard model of particle physics where Goldstone bosons and Faddeev-Popov ghosts are explicitly shown, like here, they are absent. Did I missed something about those terms or is there a way to suppress them?

Jeanbaptiste Roux · Accepted Answer

These terms vanish by integration by parts due the $R_xi$ gauge choice $G^a=frac{1}{sqrt{xi}}(partial_mu A^{a,mu}-xi g F^a_{  i} chi_i)$ in the partition function :
begin{equation}
Zpropto int mathcal{D} A mathcal{D} chi exp left[ i int d^4 x left( mathcal{L}[A,chi] -frac{1}{2} G^a G^a right) right]det left( frac{delta G}{delta alpha} right)
end{equation}
Where one has expanded the scalar field about the expectation values: $phi_i=phi_{0i}+chi_i$

Y Tong · Answer

It's probably implicitly in the second section, as $phi^0-H=v$.

Goldstone boson-Gauge boson coupling in the Glashow-Weinberg-Salam (GWS) model

2 Answers

Add your own answers!

Ask a Question