# ${{\boldsymbol \pi}^{\pm}}$ MASS INSPIRE search

The most accurate charged pion mass measurements are based upon x-ray wavelength measurements for transitions in ${{\mathit \pi}^{-}}$-mesonic atoms. The observed line is the blend of three components, corresponding to different K-shell occupancies. JECKELMANN 1994 revisits the occupancy question, with the conclusion that two sets of occupancy ratios, resulting in two different pion masses (Solutions A and B), are equally probable. We choose the higher Solution$~$B since only this solution is consistent with a positive mass-squared for the muon neutrino, given the precise muon momentum measurements now available (DAUM 1991 , ASSAMAGAN 1994 , and ASSAMAGAN 1996 ) for the decay of pions at rest. Earlier mass determinations with pi-mesonic atoms may have used incorrect K-shell screening corrections.

Measurements with an error of $>0.005$ MeV have been omitted from this Listing.
VALUE (MeV) DOCUMENT ID TECN CHG  COMMENT
$\bf{ 139.57061 \pm0.00024}$ 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
 2016
CNTR X-ray transitions in pionic N2
$139.57071$ $\pm0.00053$ 2
 1998
CNTR - pionic -atoms gas target
$139.56995$ $\pm0.00035$ 3
 1994
CNTR - ${{\mathit \pi}^{-}}$ atom, Soln.$~$B
• • • We do not use the following data for averages, fits, limits, etc. • • •
$139.57022$ $\pm0.00014$ 4
 1996
SPEC + ${{\mathit \pi}^{+}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \nu}_{{\mu}}}$
$139.56782$ $\pm0.00037$ 5
 1994
CNTR - ${{\mathit \pi}^{-}}$ atom, Soln.$~$A
$139.56996$ $\pm0.00067$ 6
 1991
SPEC + ${{\mathit \pi}^{+}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \nu}}$
$139.56752$ $\pm0.00037$ 7
 1986 B
CNTR - Mesonic atoms
$139.5704$ $\pm0.0011$ 6
 1984
SPEC + See DAUM 1991
$139.5664$ $\pm0.0009$ 8
 1980
CNTR - Mesonic atoms
$139.5686$ $\pm0.0020$
 1976
CNTR - Mesonic atoms
$139.5660$ $\pm0.0024$ 8, 9
 1976
CNTR - Mesonic atoms
1  TRASSINELLI 2016 use the muonic oxygen line for online energy calibration of the pionic line.
2  LENZ 1998 result does not suffer K-electron configuration uncertainties as does JECKELMANN 1994 .
3  JECKELMANN 1994 Solution B (dominant 2-electron K-shell 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 2-electron K-shell 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 K-shell 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 wavelength-energy 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 inner-shell 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).

${{\mathit \pi}^{\pm}}$ mass (MeV)
References:
 TRASSINELLI 2016
PL B759 583 Measurement of the Charged Pion Mass using X-ray Spectroscopy of Exotic Atoms
 LENZ 1998
PL B416 50 A New Determination of the Mass of the Charged Pion
 ASSAMAGAN 1996
PR D53 6065 Upper Limit of the ${{\mathit \nu}_{{\mu}}}$ Mass and Charged Pion Mass from Momentum Analysis of a Surface Muon Beam
 JECKELMANN 1994
PL B335 326 The Mass of the Negative Pion
 DAUM 1991
PL B265 425 New Precision Measurement of the Muon Momentum in Pion Decay at Rest
 JECKELMANN 1986B
NP A457 709 New Precision Determination of the ${{\mathit \pi}^{-}}$ Mass from Pionic X Rays
 ABELA 1984
PL 146B 431 Precision Measurement of the Muon Momentum in Pion Decay at Rest
 LU 1980
PRL 45 1066 New High Accuracy Measurement of the Pionic Mass
 CARTER 1976
PRL 37 1380 A New Determination of the ${{\mathit \pi}^{-}}$ Mass from Pionic Atom Transition Energies
 MARUSHENKO 1976
JETPL 23 72 New Measurement of ${{\mathit \pi}^{-}}$ Mass