One of my preferred readings in the blogosphere is Tommaso Dorigo’s blog. I think this is a widely known blog for people interested about physics and got some citation also at New York Times. Quite recently he published a very interesting post (see here) about the fate of our loved Standard Model taking the move from a very nice paper by J.Ellis, J.R.Espinosa, G.F.Giudice, A.Hoecker, and A.Riotto (see here). These authors are well known and really smart at their work and, indeed, I have noticed this paper as it appeared in arxiv. My readers know that I work on a small part (QCD) of the whole picture arisen in sixties and seventies and I have never taken a look from outside. So, while I appreciated this paper I thought it was not the case to comment on it in my blog. But reading Tommaso’s post some thoughts come to my mind and these are really pertinent.
People put out two kind of constraints on the Higgs part of the standard model to have an idea of what to expect. I give you here the Higgs potential for your needs
and one immediately realizes that it introduces two free parameters. The critical one is and let me explain why. When one does quantum field theory, the only real tool that she has to do any meaningful computation is small perturbation theory. The word “small” is never said but it should be said in any circumstance as this technique only works if you have a small parameter in your theory (a coupling) to use as a development parameter. Otherwise we are lost and all starts to become foggy and not so well-defined. Today, nobody knows how to manage a theory with a strong coupling. Parameter is exactly such a coupling and we are able to manage a Higgs field when this parameter is small. But when you do small perturbation theory in quantum field theory you realize immediately that infinities come out and you are not able to obtain meaningful results going beyond the first order. For the most interesting theories around we are lucky: Schwinger, Tomonaga, Feynman and Dyson invented renormalization and this works to remove infinities at each order of perturbation theory in the Standard Model and also for the Higgs, if the coupling is small. We are so accustomed to such a situation that we think that this is all one needs to know to understand quantum field theory: Perturbation theory and renormalization. We think that small perturbation theory is the perturbation theory and nothing else. So, we hope also the Higgs field should fulfill such requirements. Indeed, we are already in trouble in QCD for these same reasons but I have discussed at lengthy such a situation before here and I do not want to repeat myself.
There is no reason whatsoever to believe that we know all one has to know to manage a quantum field theory. Higgs could as well be not that light and strong coupled and there is no reason to think that Nature chose the small coupling case to favor us. Of course, if things will not stay this way I will be happy as a light Higgs is favored by supersymmetry and I like supersymmetry. But I would like also to emphasize that we already have all we need to manage analytically a strong coupled Higgs field. This matter I have discussed widely here and in my published papers.
So, while we all agree that a light Higgs is favored my view is that we should not have any fear of a non-perturbative Higgs field.