Has the SM predictions already considered the effect of the cosmic background microwave radiation?

Hi! Is that consistent with the uncertainties of experimental measurements and theoretical calculations? Some discussions in R.M.P. may be helpful: http://rmp.aps.org/abstract/RMP/v71/i2/pS133_1 .

Thank you for your reply, Xing-Hua. The anomaly is bigger than the measurement errors, so there must be missing something in the calculation.

I don't think the statement in the question is quite correct, if I interpret it correctly. In PRL 109, 111807 (2012) the Kinoshita group compare the currently best experimental results, a_e(HV), with the most recent theoretical calculation, a_e(theory). They cite

a_e(HV) - a_e(theory) \approx -1.05 x 10^(-12)

This difference is not significant. The theoretical prediction depends on the value of the fine structure constant alpha. However, there is no independent measurement of alpha of corresponding accuracy. At present the measurement of the electron anomaly is the most accurate way to determine alpha.

It should be mentioned that the theoretical computation include QED effects of strongly interacting particles (labelled hadronic contributions).

For the muon anomaly there is a discussion at

http://pdg.lbl.gov/2011/reviews/rpp2011-rev-g-2-muon-anom-mag-moment.pdf

It cites that

a_mu(exp) - a_mu(theory) \approx 287 x 10^(-11)

This difference is interesting, but it is not quite sufficient to say that there is a real discrepancy between theory and experiment (which could be interpreted as a signal of physics beyond the Standard Model of Particle Physics).

Since g=2+2a, the link you provided: g(exp)/g(theory)=1.00000000287

This is a difference of 3.4 standard deviations, suggesting beyond the Standard Model physics may be having an effect.

http://www.kip.uni-heidelberg.de/~ion/talks/g-factor.pdf

This is the experiment on a bound electron: g(exp)/g(theory)=1.00000000325

I have checked several other experiments on a bound electron as well, they all yielded similar conclusions. The only exception is the one on a free electron.

So your question refers to the g-factor of bound electrons.

In the presentation you link to (on page 26) only the first and second order QED corrections are included in the theoretical value. They seem to be calculated for a bound electron, since they differ a little from the free electron values. The third order QED correction is probably also rather close to the corresponding free electron value, which would add about 29.6 x 10^(-9) to g(theory), making it larger than g(exp). The discrepancy is most likely within the accuracy of the theoretical calculations for bound electrons.

Hi. I don't know of any published work on g-factor calculations (for neither free or bound electron) which assumes physics beyond the Standard Model (QED *is* part of the SM). There's probably no urgent need, since experiments and theory agree extremely well.

Anyhow, if you look at our latest published g-factor measurement (Schabinger et. al, Experimental g-factor of hydrogen-like silicon-28, Eur. Phys. J. D (2012)), you'll see that there is no deviation larger than the error bars.

Joseba,

Could you provide the link showing the data of the experiment?

The experiment results are there, can the Lee-Wick model provide an explanation?

Oh, I wasn't talking about the urgency of "correctness". I wouldn't want to have to judge what is correct. I'm saying that, in my opinion, it is probably not urgent to look for causes of discrepancies which statistically do not exist. If one goes through the literature and compares experimental and theoretical values, there are simply no discrepancies within two sigmas. A particle physicist (which I'm not) would tell you that if you need to go five sigma away for real statistical verification of a discrepancy. Table 1 in http://www.sciencedirect.com/science/article/pii/S1387380606000790 shows that measurements and theory are consistent within two sigma for 12C5+ and 16O7+. For 28Si11+ (http://prl.aps.org/abstract/PRL/v110/i3/e033003) they also agree within two sigma (and here the experimental value is lower, but that of course doesn't mean anything). For 28Si13+ (http://link.springer.com/article/10.1140%2Fepjd%2Fe2012-20610-y) they agree within one sigma. Anyways, I've been out of the g-factor business for some years, and I might be missing some of the latest news. However, as far as I know, every high-precision experimental g-factor measurement carried out on bound electrons has been in the groups of Günther Werth and later in that of Klaus Blaum. And I'm pretty sure that no discrepancy of statistical meaningfulness has been found. Which is very unfortunate, since we always hoped that we'd be able to hint at some new Physics.

By the way, Guoliang. I think your flaw is when you say

"...g(exp)/g(theory)=1.00000000287. This is a difference of 3.4 standard deviations".

What is a standard deviation here? The theoretical one? Or the experimental one? You see, you need to compare both numbers with their uncertainties, and see if they overlap.

Hope that helps.

Joseba,

"...g(exp)/g(theory)=1.00000000287. This is a difference of 3.4 standard deviations".

This is the statement I copied from the link below, I am sorry that I have not checked it very carefully.

http://en.wikipedia.org/wiki/G-factor_(physics)

But the experimental results are always bigger that theoretical predictions, even on the experiment you mentioned, g(exp)/g(theory)=1.00000000033. I got the results from page110 of this long report showing on the link below.

http://pubman.mpdl.mpg.de/pubman/item/escidoc:1566155:3/component/escidoc:1566154/2012%20Dissertation%20Sven%20Sturm.pdf

By the way I got another experiment, g(exp)/g(theory)=1.00000000307

http://www.physik.uni-mainz.de/werth/g_fak/publication/19%20-%20Measurement%20of%20the%20g-factor...%20-%20Verdu.pdf

Thank you for sharing your opinions.

Hi again. For the record, it's probably interesting for you to know that all measurements are performed in the same experimental setup. I can't check pdfs now, but I would be very surprised that there is a number for lithium- like silicon in Sven Sturm's thesis, since it was measured by Anke Wagner, some time after Sven finished (Sven did hydrogen-like silicon). Still, the argument holds : you cannot compare ratios, you need to look at whether there's overlap between experimental and theoretical values or not.

If most of the ratios point to same value, then it becomes a new factor, which can be ruled out as a system error, and implies a new theoretical explanation is necessary.

Oh man, you're a stubborn one ;-)

Here goes my last (?) attempt to convince you there's no discrepancy...

Let's do it your way: let's take ratios. But let's do it properly and use the error propagation techniques we learned many years ago, as undergrads.

To each ratio r=g_exp/g_theo, let's assign an error er=\sqrt{(er_exp/g_theo)^2+(g_exp*er_theo/g_theo^2)^2}. Take the numbers from the references I gave above and find the r and er for each species and you'll find:

12C5+: rC = 1.0000000031 (22)

16O7+: rO = 1.0000000025 (23)

28Si11+: rSi11 = 0.999999990 (26)

28Si13+: rSi13 = 1.000000000 (1)

Let's give all 4 measurements the same weight, since we have no indication that one should weigh more than the others. And let's propagate errors again properly. Then the average r is:

rav = 0.9999999989 (66).

This is (very) consistent with 1.

Cheers.

The anomalous magnetic dipole moment is one of the unsolved problems in physics, I am not the one so smart to find this problem, but at least I am not the one so stubborn to ignore this problem :)

http://en.wikipedia.org/wiki/Anomalous_magnetic_dipole_moment

Cheers.

Happy Chinese new year to everyone!

Oh, I see. You referred to the MUON magnetic moment, not the electron magnetic moment!! I have absolutely no knowledge about the muon case. I would need to read about it, so I back off.

Anyways, thanks for the fun discussion and the good wishes.

What happened to my comment to this question a couple of weeks ago???

Your suggestion to the bound electron's case might be one of the possible solutions within SM, but if it cannot solve the muon's problem at the same time, then it might not be a final answer.

I think all problems might be due to SM without considering the effect of gravitational fields.

There is indeed a 3.4 sigma discrepancy right now between the best experimental measurement of the muon anomalous magnetic moment (from an experiment completed a decade ago at Brookhaven) and the best current theory. Here, sigma incorporates both experimental systematic error and theoretical systematic error estimates. This discrepancy is viewed as a tantalizing hint of possible physics beyond the Standard Model, but is not definitive until it becomes a 5 sigma discrepancy. That requires improvement of the experiment -- and a new experiment is in the planning stages at Fermilab -- and of theory. On the theory side, one of the crucial needed improvements is to the light-by-light scattering term that comes in at 4th order in QED. There are also hadronic corrections to the theory that matter at this level of precision, arising from virtual photons producing quark-antiquark loops, which have been controversial over the past decade, but seem to have settled down in recent years.

So, short answer: the discrepancy is intriguing and will be pursued further in both experimental and theoretical advances. I'm not aware of any meaningful discrepancy between electron measurements and Standard Model theory.