I know the process it's possible. It's listed in the PDG:
https://pdglive.lbl.gov/BranchingRatio.action?pdgid=M004.3&home=MXXX005
But this can only be considered a consistency check. What i would like to know is if the solution I proposed makes sense, and if not, a guide on how to solve it...
I started checking for angular momentum conservation.
The initial state has ##J_{in}=S_{\phi}=1##. The pions in the final state all have 0 spin, so the total angular momentum in the final state comes only from orbital momentum. Call ##L_{\pm}## the orbital momentum of the charged pions orbiting...
I believe what is asked is impossible. Here is why.
The U(1) factors are abelian, so V and T commute with each other and with U, so i can just try to build a term containing and even number of T-s,V-s and U-s.
From the transformation laws we see that a bilinear term in the Weyl fermions must...
I noticed that ##V(\phi)## has nonzero minima, therefore I found the stationary points as ##{{\partial{V}}\over{\partial\phi}}=0##, and found the solutions:
$$\phi^0_{1,2}=-{{m}\over{\sqrt{\lambda}}}\quad \phi^0_3={{2m}\over{\sqrt{\lambda}}}$$
of these, only ##\phi^0_3## is a stable minimum...