The Anomalous Magnetic Moment Of The Tau Lepton

The anomalous magnetic moment of the muon, the second generation charged lepton, has generated enormous interest because the calculated value is 3-4 standard deviations from the experimental value, about one part per million different.  A variety of theories explain this discrepancy.

The situation is different in the case of the anomalous magnetic moment of the tau, the third generation charged lepton.  It has a theoretically predicted value, as of January 30, 2007, of 117721(5)*10^-8.

This value is within the current experimental bounds on that value in a 95% confidence interval form as follows:

-0.052< 0.00117721(5) < 0.013

although tighter current experimental bound are argued to exist in the linked paper after doing a reanalysis of the data of:

-0.007 < 0.00117721(5) < 0.005

Unlike the case of the muon, the precision of the theoretical calculation is the tau anomalous magnetic moment is so much more profoundly precise than the experimentally measured value, that it is for all intents and purposes an exact value until such time as experimental measurements of the tau anomalous magnetic moment are 100,000+ times more precise than they are today in 2014.

For example, while uncertainty in the QCD contribution to the muon anomalous magnetic moment is critical (accounting for 99.1% of the uncertainty in the theoretical estimate), in the case of the tau that contribution is on the order of 3.5*10^-6, i.e. 0.0000035, which will not be relevant for a long time to come.  The electroweak contributon is on the order of 0.5*10^-6, i.e. 0.0000005, and the balance is from the QED contribution which is known with about 2.5 times as much precision as either the QCD or the electroweak contribution.

Even if the tau anomalous magnetic moment had a discrepancy between a theoretical value and experimental value similar to that of the muon, the experimental value would still be identical to the precision of 0.001177.

A co-author compares the theoretical predictions for the electron, muon and tau with the experimental results at once in a companion article.

Limits on New Physics From The Muon Anomalous Magnetic Moment

The muon and electron measurements, because they are so exquisitely precise, impose strict bounds on beyond the Standard Model physics that would tweak these measurements in any way.  But, the tau lepton measurement will be an exercise in precise experimental efforts to confirm a foregone conclusion for the foreseeable future.  A new pre-print spells out those new physics constraints (or hints, as the case may be):

We consider the contributions of individual new particles to the anomalous magnetic moment of the muon, utilizing the generic framework of simplified models. We also present analytic results for all possible one-loop contributions, allowing easy application of these results for more complete models which predict more than one particle capable of correcting the muon magnetic moment. . . . Furthermore, we derive bounds on each new particle considered, assuming either the absence of other significant contributions to a_μ or that the anomaly has been resolved by some other mechanism.

In summary we found the following particles capable of explaining the current discrepancy, assuming unit couplings: 2 TeV (0.3 TeV) neutral scalar with pure scalar (chiral) couplings, 4 TeV doubly charged scalar with pure pseudoscalar coupling, 0.3−1 TeV neutral vector boson depending on what couplings are used (vector, axial, or mixed), 0.5−1 TeV singly-charged vector boson depending on which couplings are chosen, and 3 TeV doubly-charged vector-coupled bosons.

We also derive the following 1σ lower bounds on new particle masses assuming unit couplings and that the experimental anomaly has been otherwise resolved: a doubly charged pseudoscalar must be heavier than 7~TeV, a neutral scalar than 3 TeV, a vector-coupled new neutral boson 600 GeV, an axial-coupled neutral boson 1.5TeV, a singly-charged vector-coupled W′ 1 TeV, a doubly-charged vector-coupled boson 5 TeV, scalar leptoquarks 10 TeV, and vector leptoquarks 10 TeV.

These limits, on new boson masses, are particularly relevant to SUSY theories which imply there there are at least eleven new spin-0 charged bosons (two charged Higgs bosons and nine spin-0 partners of the charged fermions) and about five new spin-0 neutral bosons (an extra scalar Higgs boson, an extra pseudo-scalar Higgs boson, and up to three partners to the neutrinos which may mix with each other).

I've also noted that the small value of the electric dipole moment (EDM) of the electron (and perhaps other particles) greatly constrains SUSY as well.

Footnote on SUSY Fermions

SUSY theories also have new spin-1/2 fermion partners to the Standard Model fundamental bosons, all but one of which (the wino) are electrically neutral.  These include partners to the gluon (neutral gluinos), electroweak bosons (the charged wino and neutral bino and/or zino, the photino), and Higgs boson (often two neutral "Higgisnos", sometimes becoming a charged "chargino" and a neutral "neutralino" after electroweak symmetry breaking).  But, limits on their masses apparently aren't implicated by the anomalous magnetic moment of the muon.