It happened last week, in the course of putting together a meaningful discussion of the state of the art in global electroweak fits to standard model observables, and their implications for the unknown mass of the Higgs boson: by skimming the hep-ph folder I found a very recent paper by a colleague in Padova, which I had shamefully failed to notice in the last couple of careless visits.
The paper, titled "The muon g-2 discrepancy: new physics or a relatively light Higgs ?" by Massimo Passera, W.Marciano, and A.Sirlin, discusses the current status of the discrepancy between the experimentally measured value of the muon magnetic moment and the state-of-the-art of theoretical predictions, and then moves to determine what the difference would imply for the mass of the Higgs boson in case one were to attribute it entirely to a mismeasurement of QCD corrections. In order to explain what connects the two things, I need to provide a minimum of background on the topic. If you know the details, you may well skip the following section.
Determinations of the Muon Anomaly
I have discussed the basic physics of the muon magnetic moment in a couple of recent posts. My wish to repeat myself is limited, so please visit those pages for a zeroth-order introduction, and to figure out what the muon magnetic moment is.
The muon magnetic moment receives significant corrections from quantum loop effects due to all the three forces of nature affecting elementary particles: electromagnetic, weak, and strong interactions. These effects are calculable within the standard model with great precision, thanks to the development of very sophisticated calculation tools, plus an ounce or two of black magic.

You might have noticed that I picked a very particular value for the momentum of a muon in the example above. Indeed, the momentum of 3.09 GeV/c is "magic", because of a peculiarity in the formula which connects the spin precession frequency to the muon anomaly and the electric and magnetic field in which the particle is traveling. The difference between precession frequency and cyclotron frequency,
where B and E are magnetic and electric field vectors, and
The Discrepancy and QCD Effects
The experimental measurement of the muon anomalous moment performed at the Brookhaven laboratories a few years ago yielded
These QCD effects are non calculable with perturbation theory, because they occur at very low energy, where the value of the strong coupling constant is very large: a series of terms in powers of
Given the trouble with perturbation series, theorists revert to quantities that are closely connected to the QCD correction to the diagrams describing the interaction of the muon with the electromagnetic field, which allow to determine its magnetic moment. There are two ways to do this: extrapolating from the measured value of the cross section of electron-positron annihilations yielding pion pairs (a simple-to-measure process) or taking into account tau-lepton decays involving hadrons in the final state. These are the methods that provide the two different theoretical estimates quoted above.
Despite the fact that the electron-positron cross section method provides a much more discrepant value from the experimental estimate than the one based on hadronic tau decays, the two in some way "agree to disagree" with experiment; in addition, recent investigations have demonstrated that the two theoretical calculations are not as discrepant with one another as once thought.
Blaming it on the Hadronic Cross Section
There are many hypotheses to explain the discrepancy between experiment and theory on the muon anomaly. However, one can take the stand that it is entirely due to a underestimate of the hadronic cross section, which is at the heart of the QCD correction.
This hypothesis has a very interesting consequence. The standard model, in fact, is a complex system, in which a small modification anywhere brings consequences everywhere else. Increasing the hadronic cross section produces an increase of the hadronic contribution to the fine-structure constant, and this -in case some not unreasonable assumptions are made- may make the upper limit on the allowed mass range for the Higgs boson from global electroweak fits become smaller than the 114.4 GeV lower limit experimentally established by LEP II! Other assumptions instead move the 95% CL upper limit on the Higgs mass up to a more reasonable 135 GeV.
The authors consider a number of different possibilities to try and bridge the discrepancy between theory and experiment on the muon anomaly. If tau-decay data are used as a basis, the shift in the hadronic parameters bring the upper limit on the Higgs boson to 138 GeV, still much smaller than the one from the "official" one of 158 GeV.
The authors conclude, evidently showing they caress the idea that new physics is actually the source of the discrepancy on the muon anomaly:
If thediscrepancy is real, it points to "new physics", like low-energy supersymmetry where Da_mu is reconciled by the additional contributions of supersymmetric partners and one expects
for the mass of the lightest scalar. If, instead, the deviaton is caused by an incorrect leading-order hadronic contribution, it leads to reduced upper bounds for the Higgs mass. This reduction, together with the LEP lower bound, leaves a narrow window for the mass of this fundamental particle.
It seems to me that we are in a risky game: either there is supersymmetry -which we may soon discover at the LHC, bringing a new renaissance in particle physics- or we are going to have to wait for at least four years for a Higgs boson discovery, since the Higgs boson, if it is there, is light -exactly what makes it hard to be seen by the ATLAS and CMS experiments.
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