Belle II Measurement Makes World Average Tau Mass Match Koide's Rule

[ohwilleke]

TL;DR Summary

Koide's Rule predicted the tau lepton mass from the electron and muon mass in 1981. The latest Belle II measurement makes the world average measurement of the tau lepton mass perfectly match this prediction.

We present a measurement of the τ-lepton mass using a sample of about 175 million e+e−→τ+τ− events collected with the Belle II detector at the SuperKEKB e+e− collider at a center-of-mass energy of 10.579GeV. This sample corresponds to an integrated luminosity of 190fb^−1.

We use the kinematic edge of the τ pseudomass distribution in the decay τ−→π−π+π−ντ and measure the τ mass to be 1777.09±0.08±0.11MeV/c^2, where the first uncertainty is statistical and the second systematic. This result is the most precise to date.

Belle II Collaboration, "Measurement of the τ-lepton mass with the Belle~II experiment" arXiv:2305.19116 (May 30, 2023).

Combining the uncertainties in quadrature, the newly measured tau quark mass is 1777.09 ± 0.136 MeV/c^2.

This is a big improvement over the previous Belle II tau lepton mass measurement of 1777.28 ± 0.82 MeV/c^2 from August of 2020.

This will eventually pull up the Particle Data Group value which is currently 1776.86 ± 0.12 MeV/c^2. The new measurement is consistent with the Particle Data Group value at the 1.62 sigma level. The Particle Data Group value is considering only measurements in 2014 and earlier. The new inverse error weighted PDG value should be about 1776.97 ± 0.11. This is a precision of one part per 16,154.

The Koide's rule prediction is 1776.968 94 ± 0.000 07 MeV/c^2. To the nearest 10 keV it is 1776.97 ± 0.00 MeV/c^2.

The Koide's rule prediction is consistent with the new measurement at the 0.89 sigma level and is consistent with the PDG value at the 0.91 sigma level. The Belle II result pulls the global average closer to the Koide's rule prediction based upon a formula stated in 1981 (42 years ago when the charged lepton masses were known much less precisely) and also is closer to the Koide's rule prediction than its previous less precise measurement from August of 2020.

Before the new Belle II measurement, the most precise single measurement of the tau lepton mass was the BESIII measurement from 2014 which was 1776.91 ± 0.12 + 0.10/− 0.13 MeV/c^2 (the combined error was ± 0.17).

 

[malawi_glenn]

Is Koide's Rule A Coincidence Or A Missing Rule Of Physics

Yes

No

It is like "Do you want coffee or tea?" all over again, and people will hate you if you answer "yes" on that question xD

 

[ohwilleke]

Is Koide's Rule A Coincidence Or A Missing Rule Of Physics

Yes

No

It is like "Do you want coffee or the?" all over again, and people will hate you if you answer "yes" on that question xD

I knew there was a reason I didn't go into market research.

 

[arivero]

I wonder how much of the revival of Koide formula is because of physicsforums :-D

The oldest post I see is 2005, May 23, and same day I did a posting to s.p.r that got less traction. Two days later Gsponer and myself did a commit to the arxiv, with an assortment of crude ideas. I have lost my email exchange with André, surely because it was in my academic account.

 

[mitchell porter]

As far as I know, there has never been a conference, or even a conference session, specifically about Koide's formula. In the era of Zoom, surely this can be done...

 

[arivero]

String theory was a theory of the XXIth century that fell accidentally in the XXth century. Koide's was a formula of the XXth century that fell accidentally in a forum in the XXIth.

 

[arivero]

They went with 1776.93±0.09 MeV only

 

[ohwilleke]

The new PDG value is 1776.93±0.09 MeV https://pdglive.lbl.gov/Particle.action?node=S035&init=0

I had predicted that the new PDG value would be about 1776.97 ± 0.11. So, I had the best fit value 0.04 MeV too high, and the uncertainty 0.02 MeV too high.

The old PDG value was 1776.86 ± 0.12 MeV which was a 0.9 sigma fit to Koide's prediction.

Koide's prediction is 1776.968 94 ± 0.000 07 MeV

So, the difference between Koide's prediction and the new PDG value is 0.0394 ± 0.09 MeV which is 0.4 sigma with improved precision, which is still very close and is 0.07 MeV closer than it was before Belle II.

This isn't shabby for a prediction made in 1981 which has no fudge factors!

 

[arivero]

Belle is now in long stop, isnt? So it will to take 10 years to get another digit.

 

[Vanadium 50]

Belle is now in long stop, isnt?

No. (Technically, all I know is that KEK-B is running, but I assume that means Belle II is as well)

So it will to take 10 years to get another digit.

More, I am sure. Statistically, a factor of 10 in precision means a factor of 100 more data. But this measurement is systeamatics limited. The best you can hope for is that your ability to control the systematics is driven by statistics (e.g. from a control data set), but it can be worse than that. Even much worse.

I don't think this will ever get settled. The Koide cheerleaders/numerologists or whatever you want to call them are far more prevalent on the internet than in physics departments. His paper gets ~5 cites per year. (And declining) These also tend to be conference procedings and lower-impact journals.

I will make a prediction. If an experiment gets a result inconsistent with the relationship, the internet numerology fans will: first, claim the experiment got it wrong; next, call the deviation an "anomaly that must be explored" and finally say "well, the real question is why this almost works."

 

[ohwilleke]

No. (Technically, all I know is that KEK-B is running, but I assume that means Belle II is as well)

More, I am sure. Statistically, a factor of 10 in precision means a factor of 100 more data. But this measurement is systeamatics limited. The best you can hope for is that your ability to control the systematics is driven by statistics (e.g. from a control data set), but it can be worse than that. Even much worse.

I don't think this will ever get settled. The Koide cheerleaders/numerologists or whatever you want to call them are far more prevalent on the internet than in physics departments. His paper gets ~5 cites per year. (And declining) These also tend to be conference procedings and lower-impact journals.

I will make a prediction. If an experiment gets a result inconsistent with the relationship, the internet numerology fans will: first, claim the experiment got it wrong; next, call the deviation an "anomaly that must be explored" and finally say "well, the real question is why this almost works."

What would get Koide's rule accepted would be to fit it into a larger theory that also explains the quark masses and perhaps all of the Higgs Yukawa derived masses of the SM. I could see that happening.

 

[Vanadium 50]

Yes, and if we had some ham we could have some ham and eggs - if we had eggs.

 

[arivero]

I will make a prediction. If an experiment gets a result inconsistent with the relationship, the internet numerology fans will: first, claim the experiment got it wrong; next, call the deviation an "anomaly that must be explored" and finally say "well, the real question is why this almost works."

Well, that is my situation with c-b-t (claimed by Rodejohann and Zhang in the preprint, deleted in the PhysLetB publication) and s-c-b... So it is a easy prediction, it is happening.