One of the main objectives for the Large Hadron Collider (LHC) was to solve the problem of naturalness. More precisely, the standard model contains a scalar field, the Higgs field, that does not have a mechanism to stabilize its mass. Radiative corrections are expected to cause the mass to grow all the way to the cut-off scale, which is assumed to be the Planck scale. If the Higgs boson has a finite mass far below the Planck scale (as was found to be the case), then it seems that there must exist some severe fine tuning giving cancellations among the different orders of the radiative corrections. Such a situation is considered to be unnatural. Hence, the concept of naturalness.
It was believed, with a measure of certainty, that the LHC would give answers to the problem of naturalness, telling us how nature maintains the mass of the Higgs far below the cut-off scale. (I also held to such a conviction, as I recently discovered reading some old comments I made on my blog.)
Now, after the LHC has completed its second run, it seems that the notion that it would provide answers for the naturalness problem is confronted with some disappointment (to put it mildly). What are we to conclude from this? There are those saying that the lack of naturalness in the standard model is not a problem. It is just the way it is. It is stated that the requirement for naturalness is an unjustified appeal to beauty.
No, no, no, it has nothing to do with beauty. At best, beauty is just a guide that people sometimes use to select the best option among a plethora of options. It falls in the same category as Occam’s razor.
On the other hand, naturalness is associated more with the understanding of scale physics. The way scales govern the laws of nature is more than just an appeal to beauty. It provides us with a means to guess what the dominant behavior of a phenomenon would be like, even when we don’t have an understanding of the exact details. As a result, when we see a mechanism that deviates from our understanding of scale physics, it gives a strong hint that there are some underlying mechanisms that we have not yet uncovered.
For example, in the standard model, the masses of the elementary particles range over several orders of magnitude. We cannot predict these mass values. They are dimension parameters that we have to measure. There is no fundamental scale parameter close to the masses that can give any indication of where they come from. Our understanding of scale physics tells us that there must be some mechanism that gives rise to these masses. To say that these masses are produced by the Yukawa couplings to the Higgs field does not provide the required understanding. It replaces one mystery with another. Why would such Yukawa couplings vary over several orders of magnitude? Where did they come from?
So the naturalness problem, which is part of a bigger mystery related to the mass scales in the standard model, still remains. The LHC does not seem to be able to give us any hints to solve this mystery. Perhaps another larger collider will.