According to the documentary Particle Fever, the precise value of the Higgs boson's mass could give more credence to either SUSY or multiverse theories. If the mass had been 115 GeV or below SUSY would have been favored, whereas a mass above 140 GeV would have given preference to multiverse.
Is there a way to understand this connection? How can the mass of a particle give input to the likelihood of a particular physical theory, (and/or in particular the two discussed here}?
I'm especially interested in a graduate-level but qualitative explanation, though any level would be great.
Note: a Physics.SE question discusses Higgs, SUSY, and multiverse, but does not give an explanatory answer for the connection.
Answer
I have not seen the film. But this was not "supersymmetry versus multiverse". It was "supersymmetry without multiverse" versus "supersymmetry with multiverse".
According to quantum field theory, a light Higgs boson (light compared to "grand unification" energies) should still look heavy because of virtual particle effects, unless these effects mostly cancel each other out. This is a feature of traditional supersymmetric models, and 115 GeV was a value coming from that sort of theory.
However, it can be difficult to make such a model that gets everything right, experimentally. You may have to suppose that the various parameters of the theory assume values that are "just right", e.g. that one parameter is very small, or that two parameters are almost the same - and there will be nothing in your theory which implies this. You will just be "fine-tuning" it, in order to have certain undesirable effects not show up.
In the past, the need for such parametric fine-tuning might be regarded as reason to reject a theory, if a causal mechanism for the fine-tuning couldn't be found. But "the anthropic principle" or "environmental selection" gives us a potential new reason why physics might look fine-tuned: perhaps other values of the parameters are inconsistent with the existence of life/atoms/etc. There might be a "multiverse" in which the parameters take different values in different places, but life is only possible in those places where the parameters take values which allow, e.g., something like complex stable chemistry to develop.
140 GeV was a prediction coming from one of those arguments. Here is the paper. But you'll see that this is still a theory with supersymmetry! It's just that it's a supersymmetric model which contains some anthropic fine-tuning too.
I want to very strongly emphasize that 115 GeV and 140 GeV are in no way the predictions coming from these two approaches - they are just examples. They may have been discussed in the film, because there were some experimental false alarms (in the search for the Higgs boson) at those energies. But we are talking about two types of theory - a supersymmetric theory with untuned parameters, and a supersymmetric theory with parameters tuned by anthropic selection - and if the details are different, the predictions are different.
Indeed, go to pages 25-26 of the multiverse paper, and you will see no less than four special values of the Higgs boson mass listed, each of which they think might be indicative of anthropic selection within a multiverse. The reason is that they don't have an exact model of how physics works throughout their multiverse - they are just guessing at the principles governing what variations are allowed from place to place. In the paper they favor 140 GeV, but here they are saying that if the truly fundamental physics works in some other way, then maybe one of these other values would be favored.
They list 128 GeV, which is sort of close to the value that was ultimately found, and say (page 26) "a Higgs mass near 128 GeV would provide strong evidence for the multiverse, although not quite as strong as might occur for a value near 141 GeV". In this regard, one should consider a "secretly famous" paper by Shaposhnikov and Wetterich, which actually did predict the right value - 126 GeV - several years in advance, and which didn't use the multiverse or supersymmetry. Instead, they assumed that quantum gravity has the property of "asymptotic safety" at high energies. This is an unfashionable assumption because it seems to contradict standard ideas about black hole entropy... However, my real point is that the right mass for the Higgs boson can possibly be obtained without the use of anthropic effects. And indeed, there are now some string-theory models in which the right value is produced by a physical cause rather than an anthropic tuning.
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