R-87-01.2, ETHZ - PSI - VIRGINIA - ZÜRICH
K. Assamagan³, Ch. Brönnimann° ¹, M. Daum°, H. Forrer° ², R. Frosch°, P. Gheno°, J. Löffler°, R. Horisberger°, M. Janousch° ², P.-R. Kettle°, T. Spirig° ¹, C. Wigger° ¹
| ° | Paul-Scherrer-Institut, CH-5232 Villigen-PSI |
| ¹ | Physik-Institut der Universität Zürich, CH-8057 Zürich |
| ² | Institut für Teilchenphysik, Eidgenössische Technische Hochschule, CH-5232 Villigen-PSI |
| ³ | Institute of Nuclear and Particle Physics, University of Virginia, Charlottesville, VA 22901, USA |
In 1995, the analysis of this experiment was completed [1,2]. The final result for the momentum pµ+ of muons from the decay pi+ -> µ+ + nuµ at rest is
(1)
The central value of this result is lower by 0.00007 MeV/c than that
given in our recent letter on the present experiment [3], mostly because
of the correction of a mistake found in the measurements of the distances
between the collimators and detectors of the spectrometer, and also because
of the inclusion of a few additional muon spectra.
The squared muon-neutrino mass derived from the muon momentum of
Eq. (1), the µ+-mass [4], the larger of the
two possible
pi¯-masses determined by Jeckelmann et al. [5], given by Eq. (5) below,
and the CPT-theorem (mpi+ = mpi¯
) is
(2)
consistent with a vanishing neutrino mass. The smaller of the two mpi¯-solutions of Ref. [5], given by Eq. (6) below, is still strongly excluded, since it leads to a mnuµ²-value which is negative by six standard deviations. According to the `Bayesian approach' [4] (probability density set to zero for mnuµ² < 0), Eq. (2) corresponds to the new upper limit
(3)
The uncertainty of the squared neutrino mass given by Eq. (2), and thus also the upper limit of mnuµ [Eq. (3)], is dominated by the uncertainty of mpi¯(B) [Eq. (5)].
The following pi+-mass is derived from the pµ+-value of Eq. (1), the µ+-mass [4] and the assumption mnuµ = 0 :
(4)
For muon-neutrino masses below the cosmological upper limit, mnuµ < 65 eV [6], the resulting pi+-mass is equal to that of Eq. (4). This is consistent with the larger of the two mpi¯-solutions of Ref. [5],
(5)
but differs by six standard deviations from the smaller solution,
(6)
If the cosmological upper limit of mnuµ is not
used, then
the new pµ+-result of Eq. (1) and the
µ+-mass [4]
lead either to the mpi+-result
given by Eq. (4) above
(for mnuµ = 0) or to larger
mpi+-values (for
mnuµ &neq; 0).
This information on mpi+, together with
the mpi¯(B)-value of Eq. (5) and the CPT-theorem
(mpi+ = mpi¯),
leads to a value of mpi±
which is more precise than the mpi¯(B)-result
of Eq. (5) alone.
This can be demonstrated by considering, e.g., a tentative
mpi±-value of 139.56960 MeV, which is at the
lower end
of the error bar of the mpi¯(B)-result of Eq. (5),
and thus consistent with that result, but is lower than the new
mpi+-result
obtained from pµ+ by 4.4 standard
deviations [for mnuµ = 0;
cf. Eq. (4)] or more (for mnuµ &neq; 0).
The relevant two-dimensional probability distributions (functions of
mpi± and
mnuµ²)
and the assumption
mnuµ² > 0 lead to the charged-pion mass [1]
(6)
The uncertainty of this `combined' mpi±-result without cosmology, is seen to be significantly smaller than that of the mpi¯(B) -value given by Eq. (5).
[2] C. Wigger, Ph.D. thesis, University of Zurich (1995).
[3] K. Assamagan et al., Phys. Lett. B 335 (1994) 231.
[4] Particle Data Group, Phys. Rev. D 50 (1994) 1171.
[5] B. Jeckelmann et al., Phys. Lett. B 335 (1994) 326.
[6] H. Harari and Y. Nir, Nuc. Phys. B 292 (1987) 251.
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