Muon g-2 and Supersymmetry

I spent part of the morning reading an interesting review preprint by D.Stockinger ( http://xxx.lanl.gov/ps/hep-ph/0609168) which discusses the implications of the current measurement of the Brookhaven determination of the anomalous magnetic moment of the muon for Supersymmetry.

So what is this about ? First of all, let me make an attempt at not losing by force my three non-physicist readers here by explaining what is an anomalous magnetic moment, why should we care to measure it for muons, how it is done, and what it teaches us.

A magnetic moment is a property of charged particles with a non-zero spin. Although quantum mechanics prevents us from drawing a perfect analogy, a spinning charged sphere develops a magnetic field, and so do charged elementary particles. This magnetic moment is easily computed from the three fundamental quantities involved: for particles with s=1/2 (electrons or muons, for instance) it is nothing more than the product of charge by spin divided by mass.

The agreement of that simple formula with experiment is good, but not perfect. Quantum mechanics does predict, indeed,  that tiny corrections have to be applied to the above calculation before a comparison with experimental results becomes meaningful. What happens is basically that not just electrodynamics, but also quantum chromodynamics -the theory of strong interactions, responsible of binding quarks into protons and neutrons- and electroweak processes -those responsible for radioactivity- modify the result.

It is as if the magnetic field of the elementary particle – whose carriers are photons, the quanta of the electromagnetic field – were affected by a cloud of virtual particles into which the propagating photons can materialize by borrowing the necessary energy from the vacuum. These are quantum fluctuations, affecting the life of our subatomic friends in a way we have learned how to compute.

The anomalous magnetic moment of the muon is interesting to measure because these quantum fluctuations have an effect which increases with the square of the mass of the particle: and since muons weigh 200 times as much as electrons, the quantistic effects are 40 thousand times larger.

An experiment at the Brookhaven National Laboratory (http://www.g-2.bnl.gov/index.shtml)has been measuring the precession of muon spin in a magnetic field while they travel inside a ring. From the precession frequency of their magnetic moment – which can be determined by the angular distribution of the electrons that muons emit when they decay – an extremely precise measurement of the anomaly has been obtained, with an error of less than a billionth.  

Now, the measured quantity (called “g-2” because what is measured is the deviation, or anomaly, of the gyromagnetic ratio from the value 2 expected for spin-1/2 particles) is in fair agreement with standard model predictions – which include all quantum fluctuation effects known from the known particles. Only fairly so: there is a discrepancy at the 2-sigma level.

What that means is that the measured value, 11659184.1 +- 8.0 (x10^-10) (red point marked as “Avg.” in the graph on the left), is higher by 23.9+-9.9 (x10^-10) from theoretical predictions (blue point on the left). Such a discrepancy is a mild signal that something is wrong in the calculation or in the experimental determination: a mere statistical fluctuation of the data, departing from the prediction by chance, would happen only once or twice every hundred such experiments.

The paper cited above is a long discussion of the implications for supersymmetric theories of the 2-sigma discrepancy. Indeed, if one allowed new particles hypothesized by SUSY models to contribute to the anomaly, one could explain the discrepancy.

Mind you: SUSY is not one single theory, but a hundred theories, with several tunable parameters. Depending on the unknown, un-predictable value of the SUSY particles masses, one could explain away the 2-sigma discrepancy, or create a much worse disagreement. The paper is very nice because it takes into account several possible values of the tunable parameters, along with experimental determinations of other measurable quantities, to produce a picture of the sustainability of SUSY theories in the present experimental landscape.

The nice thing about this g-2 measurement is in fact that the dependency of the measured quantity on this unknown realm of new particles will eventually help us a lot in determining whether they exist or not. Indeed, by a combination of lower limits on the unknown mass of the Higgs boson (which is also predicted by SUSY to exist, but whose mass cannot be higher than some 135 GeV), on some rare decays of B mesons, and on determinations of the anomalous magnetic moment of the muon, we might be able to get strong hints at whether SUSY is the right theory or not, even before SUSY particles start popping up at the Large Hadron Collider at CERN.

Or, as some of us believe (see my 1000$ bet below), the 2-sigma discrepancy will fizzle out, SUSY will not be discovered, and theorists will get yet one more headache from the consistency of a necessarily incomplete, but utterly successful theory: the standard model of electroweak interactions.