W Boson Vertices: Incoming vs Outgoing

[kaksmet]

Hi,

a simple question on W boson vertices (and I guess field theory in general). If I have a W boson vertex for incoming particles, i.e.

W^+ ubar d and W^- u dbar

how do I change this for outgoing W's. The first interaction contains a CKM matrix element Vud and the second a Vud^*, and I want to figure out which one of them has the complex conjugate in the case of outgoing W's.

Thanks!

 

[ofirg]

First of all remember that an interaction vertex in the lagrangian can represent several different processes in feynman diagrams.

the $W^{-}u\bar{d}$ term in the lagrangian can be the decay $W^{+}\rightarrow u\bar{d}$ or the annhilation $d\bar{u}\rightarrow W^{-}$ , both with the same coupling (including the same phase)

the conjugate decay and annihilation processes will come from the hermitian conjugate term in the lagrangian, and they will have opposite phase.

A useful way to remember which processes will have the same phase and which will not is to remember that the CPT inversed process has the same coupling (including the same phase).
In our case $W^{+}\rightarrow u\bar{d}$ is the CPT inversed process of $d\bar{u}\rightarrow W^{-}$ , since each particle is replaced by its antiparticle and the time direction is reversed.