## Thursday, February 01, 2018

### Earth's gravity correction removes muon's $$g-2$$ anomaly: wrong papers

Hours later, I got suspicious that the claimed effect is proportional to the gravitational potential, therefore violates the equivalence principle, and has to be rubbish

By Saturday evening, I got sufficiently certain that the papers are plain wrong and the effect must be zero. The text below was written well before this convergence of my views.

As you know very well, the electron magnetic moment $$\vec \mu$$ is proportional to the electron's spin $$\vec S$$:$\Delta E = -\vec \mu\cdot \vec B,\quad \vec \mu = g \frac{e}{2m}\vec S.$ Simple first-quantized Dirac equation tells you that $$g=-2$$: the Dirac magnetic moment is twice as strong as what you would expect from a spinning classical gyroscope of the same mass whose current creates the magnetic field as coils do. In quantum electrodynamics, there are loop corrections and the value of $$g$$ measured by my ex-colleague Gerry Gabrielse is$g_e\approx –2.00231930436182(52).$ The accuracy is some 13 decimal points. All these 13 digits are predicted by theory – which needs up to five-loop diagrams (it's some power law expansion involving powers of the fine structure constant $$\alpha\approx 1/137.036$$) – and all these 13 theoretical digits perfectly match Gabrielse's experiment.

By this agreement, the ageing and dwindling field of physics maintains the most accurate experimentally verified prediction in all of science. Well, some of the other, more dynamic disciplines of science only verify 1 or 2 figures and sometimes less than that (e.g. in the case of the most cited scholar, Moravian Jewish German Sigmund Freud who didn't really know what a digit was). ;-)

The same Dirac equation and QED should apply to electron's heavier siblings, muons and tau leptons, too. Tau is too unstable etc. but it's interesting to look at the measured value for the muon,$g_\mu \approx -2.0023318418(13).$ It's naively the same value as the electron's value except that some special, flavor-sensitive loop diagrams matter so it's not quite the same.

You see that the number of significant figures is lower than in the electron's case. Moreover, despite this significantly larger error margin, the experiments' agreement with theory is less impressive. There has been some tantalizing 3.6-sigma disagreement. It's been argumentatively exploited as a weak hint of some new physics beyond the Standard Model.

In recent days, three Japanese authors, Takahiro Morishima, Toshifumi Futamase, and (in 2/3 of the papers) Hirohiko M. Shimizu released three articles:
Japan 1, Japan 2, Japan 3
which claim that the 3.6-sigma anomaly is removed because some neglected term in the theoretical prediction has been identified, computed, and corrected.

The neglected term is due to an object you must have encountered in your life. It's blue, not green. And despite the environmentalists' misinformation about the color and their deceitful claims that there is no Planet B, there exist tons of alternatives to that object (e.g. those discovered by the Kepler mission). What is it? Yes, it's Planet Earth. And its gravity.

These Japanese physicists say that gravity does influence the magnetic moments a priori, but for the electron, the previous calculations have been basically done in such a way that it's consistent to neglect the Earth's gravitational contribution. Other things have been gauged so that the Earth doesn't matter.

But when you do it, you can no longer neglect the gravitational effect for the heavier particle, the muon. Correct the problem and... if they are right, the 3.6-sigma anomaly goes away.

I was busy today and my energy is limited now (probably below the level of the laziness) but I hope to think about their argument later. If they're right, the lesson for theorists is simple: During your important calculations, don't forget you live on Earth and there are clouds and the Sun above you – and sometimes, don't even forget the Moon which is sometimes above you and sometimes below the horizon, as the brain-dead Bitcoin hodlers are learning in the hard way these days. ;-)

Tommaso Dorigo wrote another popular text about the papers.