Monday, 6 January 2014

Higgs ... Numerology?

The Christmas season is generally a quiet time in terms of new research papers.  The reason's pretty obvious; with so many people taking time off, anything you put out won't be read as much.  And that's assuming you haven't dashed off somewhere yourself.  Still, things don't drop to a complete halt, and you get odd little papers like this one on the Higgs decay.

First, some context.  The Higgs discovery has raised a lot of theoretical problems with it looking very Standard Model-like, and with nothing else showing up at the LHC yet.  For experimentalists, however, the Higgs is pretty much at the ideal mass.  If the Higgs were only slightly heavier, it would have only a couple of observable decays; to the W and Z gauge bosons, plus tops if it was heavy enough.  This is due to the Higgs coupling proportional to mass; it likes to decay to the heaviest thing possible, with an additional enhancement for gauge bosons from the structure of the coupling.

At the actual Higgs mass, we have already seen decays to WW and ZZ (with one of the gauge bosons a "virtual" state); to diphotons (essential for the actual discovery); and strong evidence for decays to bottom quarks and pairs of taus.  There's even the possibility of eventually measuring the decay to muons, and maybe charm if we are very optimistic, at a successor to the LHC.

Generally, there's no clear reason why this should be true.  One possibility is given by Mini-Split Supersymmetry, based on the recognition that the Higgs mass is below the Supersymmetry bound and the absence of various rare decays.  Alves, Barreto and Dias offer a somewhat more speculative alternative in this paper: they propose that for some reason, the branching ratio for the Higgs to decay to two photons is maximised.

The reason I called this numerology is because they don't suggest why that branching ratio should be maximised.  They do, however, clearly show that it is, at least to current accuracy.  This is illustrated in the following plot:
The horizontal axis here is the Higgs mass.  The blue bars/red lines show what fraction of the allowed SM parameter space maximises the branching ratio for Higgs to γγ.  This was found by varying the SM parameters within the range corresponding to experimental uncertainties.  As noted on the plot, the distribution is centred at a Higgs mass of 126 GeV with a width of about a third of a GeV.  The observed mass is shown in black, well within the distribution.

The authors go on to note several other things.  No other Higgs branching ratio is anywhere near maximal at the observed mass.  Similarly, varying parameters like the W or top quark mass even by a few percent radically changes the location of the maximal diphoton branching ratio.  Minimal alterations of the Standard Model also cause large changes the optimal mass.  So we do seem to be in an unusual point of parameter space.

What they don't seem to do, that I can see, is offer a reason why this should be important.  We are, after all, talking about a rare decay mode in a short-lived state that does not seem to be connected to any observable outside the LHC.  Usually, when people look at stuff like this, there's some kind of anthropic argument to explain the parameters.  I'm not a fan of those kinds of explanations, but they would be an improvement on what we have.

Still, I can't dismiss this paper.  With so few clues about what, if any, new physics might exist, even something as apparently unmotivated as this must be considered.  So in that sense we have something useful.

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