SciPost Submission Page

The mass of the 4\pi^+$

by M. Daum and P.-R. Kettle

Submission summary

As Contributors: Manfred Daum
Preprint link: scipost_202106_00035v1
Date accepted: 2021-07-14
Date submitted: 2021-06-19 08:19
Submitted by: Daum, Manfred
Submitted to: SciPost Physics Proceedings
Proceedings issue: Review of Particle Physics at PSI
Academic field: Physics
  • High-Energy Physics - Experiment
Approach: Experimental


At the Paul Scherrer Institute, the most precise pion mass value was obtained from a precision determination of the muon momentum, $p_{\mu^+}$, in pion decay at rest, $\pi^+ \rightarrow \mu^+ + \nu_{\mu}$. We find $p_{\mu^+} = (29.792\,00 \pm 0.000\,11$ MeV/c and $m_{\pi^+}$ = (139.570\,21 $\pm$ 0.000\,14) MeV/c$^2$. This value is more precise, however, in agreement with the recent compilation of the Particle Data Group for $m_{\pi^-}$. The agreement of $m_{\pi^+}$ with the most precise and recent single measurement, $m_{\pi^-}$ = (139.570\,77 $\pm$ 0.000\,18) MeV/c$^2$ is only fair (2.43 $\sigma$). From our $p_{\mu^+}$ value and using the above mentioned $m_{\pi^-}$ mass and the mass of the muon, $m_{\mu^+} = (105.658\,374\,5 \pm 0.000\,002\,4)$ MeV/c$^2$ we obtain an upper limit for the muon neutrino mass with 90 \%confidence, $m_{\mu_{\nu}} \leq 230$ keV/c$^2$. One also obtains a new quantitative measure of CPT invariance in the pion sector: $(m_{\pi^+} - m_{\pi^-})/m_{\pi}(\mbox{av}) = (-2.9 \pm 2.0)\cdot 10^{-6}$, an improvement by two orders of magnitude.

Published as SciPost Phys. Proc. 5, 011 (2021)

Submission & Refereeing History

Reports on this Submission

Anonymous Report 2 on 2021-7-5 (Invited Report)

  • Cite as: Anonymous, Report on arXiv:scipost_202106_00035v1, delivered 2021-07-05, doi: 10.21468/SciPost.Report.3196


1. detailed and well written review on the measurements at PSI of the \mu⁺ momentum after \pi⁺ decay at rest
2. very informative figures 11.1 & 11.2 about the p_\mu⁺ experiments
3. clear argumentation about neutrino mass upper limits and how to extract m_\pi⁺ from p_\mu⁺
4. good figure 11.3 showing the time development of \pi⁺ / \pi⁻ mass results


1. the determinations of m_\pi⁻ are essentially only referenced and not much discussed.
2. solution A and B only understandable for insiders. It is understood that PDG made the choice of B.


The authors present a good review on the experiments resulting in high precision mass determinations of the charged pion masses m_\pi⁺ and m_\pi⁻. It is fascinating that by comparison of the two final values a measurement of CPT invariance at the 3 ppm level is obtained.
A discussion of the \pi⁻ mass measurements by pionic X ray experiments would be interesting, but is clearly beyond the scope of this paper.
This paper fits the criteria of the SciPost journal.

  • validity: good
  • significance: good
  • originality: high
  • clarity: good
  • formatting: good
  • grammar: perfect

Report 1 by Adrian Signer on 2021-7-5 (Invited Report)

  • Cite as: Adrian Signer, Report on arXiv:scipost_202106_00035v1, delivered 2021-07-05, doi: 10.21468/SciPost.Report.3189


We (the editors Cy Hoffman, Klaus Kirch, Adrian Signer) had the
opportunity to review an earlier draft of the article and were in
communication with the authors before the submission. All our comments
and suggestions have been taken into account. Hence, we think the
paper can now be published in the current form.

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

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