I am currently working on a BSM model for unification where I am adding scalars for unification. I add many scalars, so finding the most general gauge invariant lagrangian is becoming difficult. Is there a tool kit where I can enter the particle content, and under what representation of the gauge group they transform and get out the most general gauge invariant lagrangian? I have heard SARAH can do it, but I am unsuccessful with it. If anyone knows how to implement this in SARAH, that would be helpful, too.
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$\begingroup$ Obtaining the most general lagrangian given only a gauge invariance constraint is impossibile. You will get an infinite series of terms if they are gauge invariant. You need also other conditions which could be such as admitting only renormalizable $D=4$ operators, admitting only stable solutions constraining the number of derivatives, asking for Lorentz-invariant operators and so on $\endgroup$– LolloBoldoCommented Sep 11, 2023 at 16:07
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$\begingroup$ Sorry, I didn't mention it. I am requesting a Lagrangian renormalizable in D = 4 and Lorentz invariant. I think now the number of allowed terms will be constrained. And derivatives only appear in the kinetic term. More generally, I just want the potential which has no derivatives in D = 4. $\endgroup$– Suriyah R KCommented Sep 11, 2023 at 16:21
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