$\bf{
139.57061 \pm0.00024}$

OUR FIT
Error includes scale factor of 1.6.

$\bf{
139.57061 \pm0.00023}$

OUR AVERAGE
Error includes scale factor of 1.5.

$139.57077$ $\pm0.00018$ 
^{ 1} 

CNTR 

$139.57071$ $\pm0.00053$ 
^{ 2} 

CNTR 
 
$139.56995$ $\pm0.00035$ 
^{ 3} 

CNTR 
 
• • • We do not use the following data for averages, fits, limits, etc. • • • 
$139.57022$ $\pm0.00014$ 
^{ 4} 

SPEC 
+ 
$139.56782$ $\pm0.00037$ 
^{ 5} 

CNTR 
 
$139.56996$ $\pm0.00067$ 
^{ 6} 

SPEC 
+ 
$139.56752$ $\pm0.00037$ 
^{ 7} 

CNTR 
 
$139.5704$ $\pm0.0011$ 
^{ 6} 

SPEC 
+ 
$139.5664$ $\pm0.0009$ 
^{ 8} 

CNTR 
 
$139.5686$ $\pm0.0020$ 


CNTR 
 
$139.5660$ $\pm0.0024$ 
^{ 8}^{, 9} 

CNTR 
 
^{1}
TRASSINELLI 2016 use the muonic oxygen line for online energy calibration of the pionic line.

^{2}
LENZ 1998 result does not suffer Kelectron configuration uncertainties as does JECKELMANN 1994 .

^{3}
JECKELMANN 1994 Solution B (dominant 2electron Kshell occupancy), chosen for consistency with positive ${{\mathit m}^{2}}_{{{\mathit \nu}_{{\mu}}}}$.

^{4}
ASSAMAGAN 1996 measures the ${{\mathit \mu}^{+}}$ momentum ${{\mathit p}_{{\mu}}}$ in ${{\mathit \pi}^{+}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \nu}_{{\mu}}}$ decay at rest to be $29.79200$ $\pm0.00011$ MeV/$\mathit c$. Combined with the ${{\mathit \mu}^{+}}$ mass and the assumption ${\mathit m}_{{{\mathit \nu}_{{\mu}}}}$ = 0, this gives the ${{\mathit \pi}^{+}}$ mass above; if ${\mathit m}_{{{\mathit \nu}_{{\mu}}}}>~$0, ${\mathit m}_{{{\mathit \pi}^{+}}}$ given above is a lower limit. Combined instead with ${\mathit m}_{{{\mathit \mu}}}$ and (assuming $\mathit CPT$) the ${{\mathit \pi}^{}}$ mass of JECKELMANN 1994 , $\mathit p_{{{\mathit \mu}}}$ gives an upper limit on ${\mathit m}_{{{\mathit \nu}_{{\mu}}}}$ (see the ${{\mathit \nu}_{{\mu}}}$).

^{5}
JECKELMANN 1994 Solution A (small 2electron Kshell occupancy) in combination with either the DAUM 1991 or ASSAMAGAN 1994 pion decay muon momentum measurement yields a significantly negative ${{\mathit m}^{2}}_{{{\mathit \nu}_{{\mu}}}}$. It is accordingly not used in our fits.

^{6}
The DAUM 1991 value includes the ABELA 1984 result. The value is based on a measurement of the ${{\mathit \mu}^{+}}$ momentum for ${{\mathit \pi}^{+}}$ decay at rest, ${{\mathit p}_{{\mu}}}$ = $29.79179$ $\pm0.00053$ MeV, uses ${\mathit m}_{{{\mathit \mu}}}$ = $105.658389$ $\pm0.000034$ MeV, and assumes that ${\mathit m}_{{{\mathit \nu}_{{\mu}}}}$ = 0. The last assumption means that in fact the value is a lower limit.

^{7}
JECKELMANN 1986B gives ${\mathit m}_{{{\mathit \pi}}}/{\mathit m}_{{{\mathit e}}}$ = 273.12677(71). We use ${\mathit m}_{{{\mathit e}}}$ = 0.51099906(15) MeV from COHEN 1987 . The authors note that two solutions for the probability distribution of Kshell occupancy fit equally well, and use other data to choose the lower of the two possible ${{\mathit \pi}^{\pm}}$ masses.

^{8}
These values are scaled with a new wavelengthenergy conversion factor $\mathit V\lambda $ = $1.23984244(37){\times }10^{6}$ eV m from COHEN 1987 . The LU 1980 screening correction relies upon a theoretical calculation of innershell refilling rates.

^{9}
This MARUSHENKO 1976 value used at the authors' request to use the accepted set of calibration ${{\mathit \gamma}}$ energies. Error increased from 0.0017 MeV to include QED calculation error of 0.0017 MeV (12 ppm).
