= Solution
Assume $\lambda>0$ so that the <Higgs potential> is bounded below, and work at tree level in four spacetime dimensions with metric $(+---)$. For $\mu^2>0$, the minimum is $\Phi=0$. The quadratic terms describe \b[three massless gauge <bosons> and two complex scalars of <mass> $\sqrt{\mu^2}$], equivalently four real scalar degrees of freedom. These are the perturbative particle masses about this vacuum, without a claim about the nonperturbative asymptotic spectrum of an interacting non-Abelian theory.
Expanding the <gauge covariant derivative> with $T_j=\tau_j/2$ gives the interaction terms
$$
\mathcal L_{\rm int}=
\frac{ig}{2}W_j^\mu\big[(\partial_\mu\Phi^\dagger)\tau_j\Phi-\Phi^\dagger\tau_j\partial_\mu\Phi\big]
+\frac{g^2}{4}\Phi^\dagger\Phi\,W_j^\mu W_{j\mu}
-\lambda(\Phi^\dagger\Phi)^2.
$$
In the second term, the antisymmetric part of $\tau_j\tau_k$ vanishes against the symmetric gauge-field product. The corresponding <Feynman diagram> vertices have one vector and a scalar–antiscalar pair, two vectors and a scalar–antiscalar pair, or four scalar legs with two particles and two <antiparticles>. The first vertex carries a <momentum> difference from its <derivative>. The Pauli matrix in it determines which doublet components couple; the two-vector scalar vertex is proportional to $\delta_{jk}$. There is no cubic scalar interaction about the zero-field vacuum.
\Image[/past-exam-of-the-gauge-field-theory-course-of-the-university-of-cambridge/2012/paper-1-scalar-gauge-vertices.png]
{title=Scalar and gauge interaction vertices before and after the Higgs field acquires its vacuum value}
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