# How to understand the Lagrangian of the standard model, effective or "fundamental"?

I have a question about understanding the Lagrangian of standard model, should we view it as a "fundamental" or effective theory? The "fundamental" theory here means the theory with physical cutoff (maybe Planck scale) $\Lambda$; the effective theory here means the theory given by lowering the cutoff $\Lambda'<\Lambda$, (Wilsonian renormalization), and we pick up the leading terms as we saw in the action.

The reason to think the standard model Lagrangian is an effective action

We haven't tested the physics up to the physical cutoff (Planck scale?), this is an extra assumption that the standard model is valid up to physical cutoff. To the contrary, in the effective theory, the cutoff is much more reasonable (e.g. LHC scale).

The reason to think the standard model Lagrangian is a "fundamental" action

If we follow the renormalization flow, the coupling constant of QCD will grow in low energy scale, then the perturbation breaks down. We know from lattice calculations of hardron mass, that even in low energy, QCD works. The Wilsonian renormalization group transformation is formulated from perturbative expansion (may be this is just my limited knownledge, correct me if I am wrong). Since QCD agree with experiment beyond the regiom of perturbation, it has to be a "fundamental" action, than effective action. Similar attitude applies to the standard model.

It seems the question is rather a mental setup. Since standard model works very well so far at LHC, it seems hard to distinguish these two opinions: whether viewing standard model action as "fundamental" or effective.

• The Standard Model has "input data" (free parameters), so it is not a fundamental theory. Sep 16, 2013 at 18:21
• "fundamental" here means the theory with a physical cutoff $\Lambda$, I follows the terminology from my course of QFT, maybe that's a misnomer... I edited the post with "" on fundamental Sep 16, 2013 at 18:26
• Well there are neutrino masses so there is a dimension 5 term already. And that's not even talking about dark matter, dark energy, gravity... Sep 17, 2013 at 0:26
• how to see neutrino mass term has dimension 5? thx Sep 17, 2013 at 0:34
• It's not true that the Wilsonian renormalization group transformation is defined using the perturbative expansion. It can be done on the lattice. Dec 3, 2013 at 20:59

The Standard Model isn't consistent up to arbitrarily high energy scales – because of the Landau pole for the $U(1)$ part of the gauge group at an exponentially high scale – which is one of the reasons why it can't be a fundamental description of Nature.