## Wednesday, August 12, 2020

### New Tau Lepton Mass Measurement Continues To Be Consistent With Koide's Rule

The latest tau lepton mass measurement, from Belle II is:

1777.28 ± 0.75 (stat.) ± 0.33 (sys.) MeV/c^2.

The combined error is ± 0.82 MeV/c^2 (which is 0.38 sigma greater the the Koide's rule prediction).

Since it is higher than the PDG value will nudge the global PDG value towards the Koide's rule value, although not by much since the significant margin of error means it is weighted only lightly in the world average.

The current Particle Data Group value for the tau lepton mass is 1776.86 ± 0.12 (which is 0.91 sigma below the Koide's rule prediction).
Koide's rule, a formula proposed in 1981, six years after the tau lepton was discovered, when its mass was known much less accurately, predicts the mass of the tau lepton based upon the mass of the electron and the muon. This prediction using current electron and muon mass measurements is:
1776.96894 ± 0.00007 MeV/c^2.
The uncertainty is entirely due to uncertainty in the electron and muon mass measurements. The low uncertainty in the Koide's rule prediction reflects the fact that the electron and muon mass have been measured much more precisely than the tau lepton mass.
The latest measurement from BESIII, which is the most precise single experimental measurement to date (UPDATE: From 2014) is:
1776.91 ± 0.12 + 0.10/− 0.13 MeV/c^2 (the combined error is ± 0.17).
This result is 0.06 MeV less than the Koide's rule prediction which is [0.34 sigma below the Koide's rule prediction.]
From a September 28, 2017 post.

The paper is as follows:

# τ lepton mass measurement at Belle II

The reconstruction of tau-pair production, e+eτ+τ, from the subsequent 3-prong (τ+π+ππ+ν¯τ) and 1-prong (τν¯νττhντ or τππ0ντ) decays, is presented using 8.8 fb1 of e+e collision data of Belle II at the center-of-mass energy s=mΥ(4S). The pseudomass technique developed by the ARGUS experiment is used to measure the τ-lepton mass mτ in the 3-prong τ+π+ππ+ν¯τ decay, resulting in mτ=1777.28±0.75 (stat.)±0.33 (sys.) MeV/c2.
 Subjects: High Energy Physics - Experiment (hep-ex) Report number: BELLE2-CONF-PH-2020-010 Cite as: arXiv:2008.04665 [hep-ex] (or arXiv:2008.04665v1 [hep-ex] for this version)