Hi Francesco,
I'm afraid that if you need to work with 4-fermion vertices
where all particles are identical, there is no silver bullet to
avoid the mess.
Whatever you do, at some point you will have to get your hands dirty.
However, if there are really just 6 tree-level diagrams, I wonder if it
would not be simpler to stick to the explicit 4-fermion operators (as
you tried at the beginning) and then determine the correct relative
signs by hand. By that I mean writing down the Dyson-Schwinger series
and applying Wick's theorem (c.f. Peskin, chapter 4.7) or use the path
integral approach (depending on your taste). At least this is probably
something I would do in this case.
For a more automatic solution one might start looking at
<https://github.com/djukanovic/qct>
in order to automatize Wick contractions, but this might take more time
than just doing the sign determination by pen and paper. At the end it
all depends on how much time one is willing to spend on that.
Cheers,
Vladyslav
frankly speaking, I'm not very familiar with the method of
using heavy particles to avoid 4-fermion vertices.
Am 03.07.2016 um 13:43 schrieb Francesco:
> Hi Vladyslav,
> Do you know if there is a simple way to restore the couplings of the effective theory with 4-fermions operators?
> I mean, If I use an auxiliary field, I get a propagator (even if I would like to have a constant propagator ) then I have to correct manually each "auxiliary" propagator and also the factors of 2 coming from the matching… and also the correct sign for each propagator… and try to express the amplitude in terms of the coupling of the effective theory. Then, the probability to make a mistake is very high.
>
> if you want to have a look, here https://www.dropbox.com/sh/hm77oyedcb3p055/AABzBlEPZvcPjAstjoclCR3ya?dl=0 you find the model and my notebook that is totally a mess.
>
> Thank you,
> Francesco
>
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