I have been studying the spontaneous symmetry braking from Zee (Quantum Field theory ) and found in the page 224, he wrote the lagrangian as
$$\mathcal{L}=
\frac{1}{2}\{
λ
(∂φ)^2 + μ^2φ^ 2\} − \frac{\lambda}{4}(φ^4)$$
But according to sclar field theory I got from Ryder $$\mathcal{L}=\frac{1}{2}\{ λ (∂φ)^2 + μ^2φ^ 2\} − \frac{\lambda}{4!}(φ^4)$$ Am I doing wrong?
My another question is, the potential we have inserted in the Lagrangian is look like Mexican hat. What conditions will change the shape of the potential? Symmetry breaking means ,changing the Lagrangian with kinetic energy terms?