Recently I have started learning "Effective Field Theory". As a part of learning, I was trying to calculate the vertex factor for a process where two unknown neutral spin-1 bosons $Y$ annihilated to Standard Model (SM) gauge bosons $W^{+}$ and $W^{-}$, that is YY $\rightarrow$ $W^{+}$ $W^{-}$. The interaction vertex is "Fermi" like.

The package Feynrules has been employed to compute the vertex and it looks like the following: \begin{equation} \left\{(W^{+},1),(W^{-},2)\rightarrow (Y,1),(Y,2)\right\} = -8ia_{1}p_{1}^{\lambda}p_{2}^{\sigma}\eta_{\mu\nu}+3ip_{1}^{\sigma}p_{2}^{\lambda}\eta_{\mu\nu}+\text{similar ten more terms contaning}~p_{1}^{\mu}p_{2}^{\nu}\eta_{\lambda\sigma} \end{equation} Please note that the Wilson coefficients are not written for the sake of brevity and $p_1$, $p_2$ are the momenta for $W^{+}$ and $W^{-}$ respectively.

Here is the problem that I am dealing with: Although my intention is to calculate the vertex factor for $YY \rightarrow W^{+}W^{-}$ process but Feynrules calculated the factor for the inverse process $ W^{+}W^{-}\rightarrow YY$. In order to get the correct vertex factor for $YY \rightarrow W^{+}W^{-}$ process what change needs to be make? It will be a great help if someone shed some light on this matter.

Note: Using standard QFT techniques I tried to do the calculation but it turns out the calculation is long and prone to make errors. I don't know what techniques Feynrules has employed.


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