Supersymmetry vs minimalism: what is the Higgs mass telling us?

[mitchell porter]

We have had several threads that discuss the 2009 prediction of the Higgs boson mass by Shaposhnikov and Wetterich, which used the assumption that quantum gravity is "asymptotically safe".

But it's also true that the observed value is within a range predicted by some orthodox supersymmetric models. For example, in Carena et al, dating from 2000, on the first page we read that, if the stop squarks have a mass of 1 TeV or less, then the Higgs boson mass will be 125 GeV or less. Two years later, Witten writes (final page) that in the MSSM, the Higgs mass "should be below about 130 GeV". Closer to the present, we have Kane et al claiming, on the eve of the first rumors from the LHC, that 129 GeV is an upper bound in their version of the MSSM; in his talks, Arkani-Hamed says that the observed value is squarely in the middle of supersymmetric territory; and so forth.

It would be good to be able to think clearly about what this means. For example:

At some level, these hypotheses are mutually exclusive: nothing but standard model, all the way to the Planck scale, versus stop squarks at 1 TeV, and other superparticles somewhere beyond. So, assuming for the moment that one is true, would we then dismiss the success of the other hypothesis as merely a coincidence?

Or could it be that the arguments advanced by these opposing schools of thought, actually have something in common, at a very abstract level? I don't quite see it, but neither can I rule it out. I believe the key consideration in the supersymmetric argument is naturalness - a lack of finetuning. Supersymmetry is there so that the Higgs mass isn't finetuned, and a heavy Higgs gets its mass from the stop loops; but if the stops are too heavy, some finetuning will need to be reintroduced, and I think that's where this folklore of 125-130 GeV as an upper bound came from.

Meanwhile, on the minimalist side, the philosophy employed was asymptotic safety, but the boundary condition which actually produced the prediction, is that the quartic self-coupling of the Higgs goes gently towards zero at high energies. A variety of other papers are now appearing, which try to realize (or which just assume) this boundary condition, without assuming asymptotic safety as well.

That's as far as I've come, in trying to compare and contrast the two ideas. Something I can say is that the "top sector" - top quark and associated particles - plays a role in both arguments. The Shaposhnikov-Wetterich prediction required the measured mass of the top quark as an input; and it's the stop squarks, plus naturalness, which produce the upper bound on the Higgs mass in the MSSM. Perhaps this is the key to finding a bigger perspective that encompasses both.

 

[mitchell porter]

I've tried to think more about this issue, which is really central to the question of how seriously one should take the quest for low-scale supersymmetry (reviewed today by Nathaniel Craig).

In the original post, I posed it as a comparison between the very precise prediction of the Higgs mass from SM + asymptotic safety, versus the vague expectation of a Higgs mass in the 120-130 GeV range, that some susy advocates had. To make the comparison sharper, it would be good to know, on the one hand, what the SM "by itself" implied about possible or likely values of the Higgs mass, and on the other hand, exactly where the susy "prediction" came from, and to what extent it depended e.g. on experimental exclusion of the range below 115 GeV having already occurred.

When I say the SM by itself... I suppose I would allow the use of some extra physical principle, just not one as specific as asymptotic safety. The fact that asymptotic safety predicted the mass is a highly significant fact, but I would like to know if there was some other, more general argument, which already favored masses in that vicinity, under the assumption of no low-scale susy, and a desert extending at least to the grand unification scale.