Take A Moment to Remember

A few people last week were linking to this press release from Fermilab, which probably says more about the state of American particle physics than anything else: it’s about an experiment that they expect to be approved in 2012, to break ground in 2013, and start running in 2016. I guess with the Tevatron shutting down and nothing noteworthy from the LHC yet, this is what you have to talk about.

The experiment in question is an update of an experiment from Brookhaven in 2001, which measured the anomalous magnetic moment of the muon. The value they get differs from the best theoretical value by the traditional 3 standard deviations– enough to look interesting, but not enough to be concrete evidence of anything. Ten years of effort haven’t turned up an error in either experiment or theory that would conclusively close the gap, so it’s a mystery.

One of the nice things about writing up particle physics results is that everything is on the arxiv, so here’s the latest experimental value for the muon g-factor:

g/2=1.001 165 920 80(54)(33)

(The two sets of numbers in parentheses are the statistical and systematic uncertainties in the last two digits.) Meanwhile, the latest theoretical value is:

g/2=1.001 165 918 28(49)

One of the annoying things about writing about particle physics results, however, is that they tend to pretend there’s nothing other than particle physics results. In fact, as impressive as those numbers look, they’ve got a ways to go to catch a measurement from my corner of physics, namely the g-factor of the electron, whose best current value is:

g/2 = 1.001 159 652 180 73 (28)

One of the reasons the muon g-factor is interesting is that the electron g-factor has been measured to such amazing precision, and agrees perfectly with theory. In fact, that measurement is better than the best independent measure of the “fine structure constant” which is a key input to the theory, so the paper giving that result (arxiv link) casts it as a measure of the fine-structure constant. The muon’s magnetic moment is more sensitive to exotic physics (the details are a little subtle, but roughly speaking, it’s because it’s a heavier version of the electron, and couples to more things), but if the electron’s magnetic moment didn’t agree to such high precision, it would be hard to argue that the muon discrepancy was all that meaningful.

The electron measurement really is a tour de force, and the theoretical calculation is quite an achievement in its own right, involving up to eighth order Feynman diagrams. And neither side of that measurement is done– The PI on the experiment, Gerald Gabrielse of Harvard, gave a prize talk at DAMOP where he talked about the next generation experiment, and the theory team is already working on the tenth order calculation to match the expected precision of the experiment (and cut down the error bars on the current numbers). It’s worth looking at that paper just for the pages of crazy Feynman diagrams that they have to evaluate to get their result.

So, that’s an important bit of background to remember when reading about this. When it eventually happens, the measurement will be pretty impressive, but its success will build not only on the Brookhaven work, but also the exceptional work of the people making measurements and calculations of the electron’s properties.

6 thoughts on “Take A Moment to Remember

  1. Electron g factor is cool, but it’s just one measurement, what if it is simply a fluke?

    After all there are many particles with many properties, would it be so strange if one of them was particularly close to theoretical value not because the theory was so good but simply by chance?

  2. Paul @1: It’s not just one measurement. Several different labs have made measurements of the electron g-factor over the years (Chad knows the details better than I do), and at every stage, the measurement has agreed with the theory within the precision for which both were then capable. As Chad pointed out in the OP, the most recent measurement agreed with the theory to eighth order. An agreement with one number to zeroth or first order might be a fluke. Getting right to eighth order, after having been in agreement at every prior stage, is impressive. And now they are continuing the calculation to 10th order so that they will be ready for experimental data that will test the theory to that order.

    For someone like me in a field where we rarely see error bars small enough to make looking at second order effects worth the trouble, this is definitely a Big Deal.

  3. nothing noteworthy from the LHC yet

    Except a slew of important null results, which among other things pin the Higgs down into a tiny mass region if it exists. By that standard all the very precise null results of atomic physics are also “nothing noteworthy.”

  4. Eric, you misunderstood me, by “it’s just one measurement” I mean that only measurement of one parameter attains such remarkable precision (not that only one experiment). What if it is only a fluke that the real value of this particular parameter agrees so well with theoretical predictions?

  5. I get what you are saying, Paul, but at this level of precision it is unlikely to be a fluke. The parts of the theory that contribute to the g-factor of the electron are very well tested, and if you want to argue that it is a fluke, you need to come up with some alternative theory which explains this data point, as well as any others that have been measured (I’m sure that other measurements have been made, though not to this level of precision).

    If you want to argue that there is an issue with the parts of the theory that do not contribute to the electron g-factor, you are on more solid ground: the muon discrepancy is enough to suggest that there might be a there there but not big enough to confirm that the current theory is missing something. But I emphasize that whatever corrections to the theory you come up with cannot affect the electron g-factor to eighth order, which is a significant constraint on the ways in which the theory might be incomplete.

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