Spectroscopy of positronium fine structure: 4.5 sigma deviation

[mfb]

TL;DR

A recent study measures a transition frequency in positronium higher than predicted.

Precision Microwave Spectroscopy of the Positronium n=2 Fine Structure

A nice compact abstract, so I'll just quote it here:

We report a new measurement of the positronium (Ps) 2³S₁→2³P₀ interval. Slow Ps atoms, optically excited to the radiatively metastable 2³S₁ level, flew through a microwave radiation field tuned to drive the transition to the short-lived 2³P₀ level, which was detected via the time spectrum of subsequent ground state Ps annihilation radiation. After accounting for Zeeman shifts we obtain a transition frequency ν₀=18501.02±0.61  MHz, which is not in agreement with the theoretical value of ν₀=18498.25±0.08  MHz.

Positronium with its two light leptons is the dream of every theorist, that keeps the uncertainties small.
The 0.61 MHz experimental uncertainty are the sum of 0.57 MHz statistical uncertainty, 0.215 MHz laser alignment and <0.1 MHz other sources.
The uncertainty on the 2.77 MHz difference is dominated by the statistical uncertainty and the significance is 4.5 standard deviations.

They produce very slow positronium excited by a laser, that suppresses uncertainties previous measurements had and improves the statistics. They also have ideas how to reduce the uncertainties that are still relevant. No indication of the measurement time that went into the study, but taking data for a longer time will certainly help even if they don't make larger upgrades.

 

[Lord Crc]

For us layfolks who don't have access to the article, what kind of mechanisms could explain such a difference? This is basically about how photons, electrons and positrons interact, no?

Also, I was a bit surprised the theoretical value was not "tighter". I mean we know the fine structure constant to a few parts per billion. Is that due to the Zeeman correction or something else?

 

[mfb]

That's the interesting thing, it is pure quantum electrodynamics - it's a system that should be understood extremely well. The theory prediction should be fine unless someone made a stupid mistake in a place no one else checked. Some experimental oversight is possible, a really weird statistical fluctuation is not ruled out.

The uncertainty on the theory prediction (free preprint) is 80 kHz or 0.3 neV, ten orders of magnitude below the positronium energy levels.

 

[ohwilleke]

When your measurement is within 0.015% of the theoretically predicted value, and the uncertainty in the theoretically predicted value is so small, I've got to think that an overlooked systemic error in the measurement or some failure to model the system you're doing the theoretical prediction for properly, is far more likely to resolve the discrepancy than any other cause.

For example (no idea if these particular examples are meaningful, but illustrating the kind of thing that I'm thinking of), perhaps some other devices in the vicinity of the experiment are emitting photons at the right frequency (perhaps a poorly shielded microwave oven in a break room in the next wing or a emergency services microwave tower's leakage) that is screwing up the measurement, or perhaps there are ground vibrations from passing delivery trucks now and then that cause the laser to be periodically much more out of alignment than estimated based on calibrations done when delivery trucks aren't rumbling through the neighborhood, or maybe you failed to consider a factor of two in the number of possibilities (perhaps related to polarization or helicity or symmetry involved) that doubles the statistical error amount from 0.57 to 1.14.

Alternately, maybe there is a higher order loop that has an overlooked QCD component similar to the one in muon g-2 that was inferred to be small enough to ignore, but actually needs to be considered because it is bigger than you would expect for some quirky reason that is easy to overlook.

It is hard to imagine any new physics that would give rise to this effect, that would be otherwise well motivated.

 

[Vanadium 50]

A few things to keep in mind:

• It's important to figure out what's going on. However...
• It is difficult to imagine new physics that affects this transition and only this transition. I'd very much like to see this in context with the 1S transitions. To (over-)simplify, if the A → C transition has the right energy, and B → C has`s the right energy, if A → B has the wrong energy, there is a measurement problem somewhere.
• Kirill Melnikov is one of the best calculators in the business.
• Combining calculations of different groups at different orders is notoriously tricky. A calculation on the muon g-2 was troubled by a sign error when inadvertently mixing conventions.

it is pure quantum electrodynamics

Actually, it's not. You have QCD loops at I think 4th order. In principle, at 6th order you have α⁴α_s² but I believe you can integrate out the α_s² parts into m(π), or actually α⁴m(e)/m(π). I think the first diagram with a "naked" α_s is a gluon between two quark loops.

 

[mfb]

Sure, with high enough orders you get everything, but is any QCD diagram notable at the positronium mass? They reference some positronium decay study saying that the weak interaction is negligible and don't even discuss the strong interaction.

Are there previous good measurements using 2³P₀? The paper only discusses 1S/2S measurements and fine-structure measurements with a way lower precision (+- several MHz).

@ohwilleke: The measurement consists of several independent points that all match a higher transition frequency, and nothing of what you mention could shift them in a systematic way. The uncertainty is taken from the fit and trivial to verify. Maybe something is wrong with their frequency reference, or something like that. But frequency measurements tend to be extremely precise.

 

[Vanadium 50]

Sure, with high enough orders you get everything, but is any QCD diagram notable at the positronium mass?

Hadronic vacuum polarization should start to come in in the hyperfine structure near α⁶. Hyperfine splitting is magnetic, so is proportional to a_e. HVP for the muon is 10^-7, and for the electron it's 40,000 times smaller or 10^-12. α⁶ is 10^-13. At this level of calculation, 12 ≈13.

I am not an expert in these calculations, but think HVP is actually down a little bit more than this because of factors of 2π and such. But this measurement is nearing the point where QCD effects are starting to become visible, if they haven't already.

But frequency measurements tend to be extremely precise.

But this is also the hardest place to do it - tiny signals. Comparting two frequencies of vastly different amplitudes is tricky because amplitude variations in the signal at the edge of sensitivity appear as phase variations with respect to the reference. Dealing with this is why you need to be a very good scientist to even attempt these measurements.

 

[vanhees71]

Couldn't it also be some subtlety in the systematic uncertainties concerning the corrections to be made due to the positronium transition being measured running through a microwave wave guide? Of course all this is discussed in the paper, including the Zeeman corrections due to the also present magnetic field.

If I reember right, the most likely solution of the notorious problem with the proton radius by measurements of usual vs. muonic hydrogen was also due to some subtle effect in fitting the lineshape with a single Breit-Wigner, though also this problem is considered in the positronium paper, arguing with the symmetry of the lineshape.

If it's sensitive to the QCD corrections it's of course also an interesting issue related to the muon $(g-2)$ problem. Maybe one can use the new positronium measurements to somehow estimate this QCD contribution experimentally in a new independent way.

 

[Vanadium 50]

Maybe one can use the new positronium measurements to somehow estimate this QCD contribution experimentally in a new independent way.

Probably not. As I argued above, they should just be becoming visible now. So call it a 100% measurement. HVP for g-2 is known to better than 1%. So it needs to be a few hundred times more precise (and to have any theory uncertainties removed) before it would contribute.

 

[PAllen]

Freely available version:

https://discovery.ucl.ac.uk/id/eprint/10107934/1/PhysRevLett.125.073002.pdf