What is an effective field theory (EFT)? and why all the observable interactions until one scale are only a finite number that we know? Is the standard model (SM) an EFT? till what distances? I real "introductions" to EFT, but they are examples, not an explanation what it is
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In the sense you are asking (there is also a notion of Wilsonian effective theory), an Effective Field Theory is a theory where only "light" degrees of freedom appear, while "heavier" degrees of freedom are modeled by interactions between the light elements. For instance, the Fermi theory of radioactive decay (see here) models with point-like four-fermion the interactions between things like protons neutrons electron neutrinos are resolved in the the standard model by the exchange of a massive W/Z boson between these guys. But if you don't have enough energy to resolve that interaction, it looks point-like, and you don't see that a massive object was exchanged here. So you add an interaction term in your Lagragian to account for this observed decay.
The standard model does not need extra interactions which we cannot explain by particles. People try to add terms of the form of the four-fermion coupling to the Lagrangian of the standard model and see if they fits the tiny deviations of the disintegration patterns at LHC -- so far, no success.
However, the standard model is an EFT from the gravitationnal's perspective, and from grand unification as well. The effect at which the heavier degrees of freedom start to materialize as particle is kind of linked to the mass of those particles. If you like grand unification, the fact that the magnitude of the three interactions we know seem to unify at high energies is a low energy sign of a high energy symmetry at high energies. We also know that, at the Planck scale the gravitational interaction becomes strong, so there must new degrees of freedom there. So, at worst, the standard model will need to be supplemented with new degrees of freedom at the Planck scale, because we know that gravity exist.
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$\begingroup$ But we know a scale till standard model (corrected with the Riemann geometry from gravity) is it effective? Why are the evidences? Of course, we have the SM, but we don´t know if there is another particle with low probability that it could be generated. The simmetry SU(3) SU(2) U(1) is very effective but it is ad hoc, not like gravity axioms or QFT axioms. This is the motivation for my question. We don´t know if we have enough experiments in accelerators to discard another particles at this energies $\endgroup$– user232333Commented Apr 26, 2020 at 18:10
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$\begingroup$ @Alfonso we know that at the Planck scale new degrees of freedom should emerge. Before that, it is only some sort of speculation. The hierarchy problem and very low Higgs mass kind of shout in one's hear that some piece of the puzzle is missing, but not necessarily new particles. $\endgroup$– picopCommented Apr 27, 2020 at 12:55