${{\mathit \gamma}}$ MASS

INSPIRE   PDGID:
S000M
Results prior to 2008 are critiqued in GOLDHABER 2010. All experimental results published prior to 2005 are summarized in detail by TU 2005.

The following conversions are useful: 1 eV = $1.783 \times 10^{-33}$ g = $1.957 \times 10^{-6}{\mathit m}_{{{\mathit e}}}$; $ƛ_{C}$ = ($1.973 \times 10^{-7}$ m)${\times }$(1 eV/${\mathit m}_{{{\mathit \gamma}}}$).
VALUE (eV) CL% DOCUMENT ID  COMMENT
$\bf{<1 \times 10^{-18}}$ 1
RYUTOV
2007
MHD of solar wind
• • We do not use the following data for averages, fits, limits, etc. • •
$<2.1 \times 10^{-15}$ 68 2
WANG
2023B
 Fast Radio Bursts
$<2.2 \times 10^{-14}$ 3
BONETTI
2017
Fast Radio Bursts, FRB 121102
$<1.8 \times 10^{-14}$ 4
BONETTI
2016
Fast Radio Bursts, FRB 150418
$<1.9 \times 10^{-15}$ 5
RETINO
2016
Ampere's Law in solar wind
$<2.3 \times 10^{-9}$ 95 6
EGOROV
2014
Lensed quasar position
7
ACCIOLY
2010
Anomalous magn. mom.
$<1 \times 10^{-26}$ 8
ADELBERGER
2007A
 Proca galactic field
$\text{no limit feasible}$ 8
ADELBERGER
2007A
 ${{\mathit \gamma}}$ as Higgs particle
$<1 \times 10^{-19}$ 9
TU
2006
Torque on rotating magnetized toroid
$<1.4 \times 10^{-7}$
ACCIOLY
2004
Dispersion of GHz radio waves by sun
$<2 \times 10^{-16}$ 10
FULLEKRUG
2004
Speed of 5-50 Hz radiation in atmosphere
$<7 \times 10^{-19}$ 11
LUO
2003
Torque on rotating magnetized toroid
$<1 \times 10^{-17}$ 12
LAKES
1998
Torque on toroid balance
$<6 \times 10^{-17}$ 13
RYUTOV
1997
MHD of solar wind
$<8 \times 10^{-16}$ 90 14
FISCHBACH
1994
Earth magnetic field
$<5 \times 10^{-13}$ 15
CHERNIKOV
1992
Ampere's Law null test
$<1.5 \times 10^{-9}$ 90 16
RYAN
1985
Coulomb's Law null test
$<3 \times 10^{-27}$ 17
CHIBISOV
1976
Galactic magnetic field
$<6 \times 10^{-16}$ 99.7 18
DAVIS
1975
Jupiter's magnetic field
$<7.3 \times 10^{-16}$
HOLLWEG
1974
Alfven waves
$<6 \times 10^{-17}$ 19
FRANKEN
1971
Low freq. res. circuit
$<2.4 \times 10^{-13}$ 20
KROLL
1971A
 Dispersion in atmosphere
$<1 \times 10^{-14}$ 21
WILLIAMS
1971
Tests Coulomb's Law
$<2.3 \times 10^{-15}$
GOLDHABER
1968
Satellite data
1  RYUTOV 2007 extends the method of RYUTOV 1997 to the radius of Pluto's orbit.
2  WANG 2023B use fast radio burst photon mass dependent dispersion relation to determine an upper limit of the photon mass.
3  BONETTI 2017 uses frequency-dependent time delays of repeating FRB with well-determined redshift, assuming the DM is caused by expected dispersion in IGM. There are several uncertainties, leading to mass limit $2.2 \times 10^{-14}$ eV.
4  BONETTI 2016 uses frequency-dependent time delays of FRB, assuming the DM is caused by expected dispersion in IGM. There are several uncertainties, leading to mass limit $1.8 \times 10^{-14}$ eV, if indeed the FRB is at the initially reported redshift.
5  RETINO 2016 looks for deviations from Ampere's law in the solar wind, using Cluster four spacecraft data. Authors quote a range of limits from $1.9 \times 10^{-15}$ eV to $7.9 \times 10^{-14}$ eV depending on the assumptions of the vector potential from the interplanetary magnetic field.
6  EGOROV 2014 studies chromatic dispersion of lensed quasar positions (``gravitational rainbows'') that could be produced by any of several mechanisms, among them via photon mass. Limit not competitive but obtained on cosmological distance scales.
7  ACCIOLY 2010 limits come from possible alterations of anomalous magnetic moment of electron and gravitational deflection of electromagnetic radiation. Reported limits are not "claimed" by the authors and in any case are not competitive.
8  When trying to measure ${\mathit m}_{\mathrm {}}$ one must distinguish between measurements performed on large and small scales. If the photon acquires mass by the Higgs mechanism, the large-scale behavior of the photon might be effectively Maxwellian. If, on the other hand, one postulates the Proca regime for all scales, the very existence of the galactic field implies ${\mathit m}_{\mathrm {}}$ $<$ $10^{-26}$ eV, as correctly calculated by YAMAGUCHI 1959 and CHIBISOV 1976.
9  TU 2006 continues the work of LUO 2003, with extended LAKES 1998 method, reporting the improved limit ${{\mathit \mu}^{2}}{{\mathit A}}$ = ($0.7$ $\pm1.7$) $ \times 10^{-13}$ T/m if ${{\mathit A}}$ = 0.2 ${{\mathit \mu}}$G out to $4 \times 10^{22}$ m. Reported result ${{\mathit \mu}}$ = ($0.9$ $\pm1.5$) $ \times 10^{-52}$ g reduces to the frequentist mass limit $1.2 \times 10^{-19}$ eV (FELDMAN 1998). While the results of the torsion balance method give a value for the local limit on ${{\mathit \mu}^{2}}{{\mathit A}}$, the deduced limit on the photon mass ${{\mathit \mu}}$ is open to question. See the discussions in TU 2005 and GOLDHABER 2003.
10  FULLEKRUG 2004 adopted KROLL 1971A method with newer and better Schumann resonance data. Result questionable because assumed frequency shift with photon mass is assumed to be linear. It is quadratic according to theorem by GOLDHABER 1971B, KROLL 1971, and PARK 1971.
11  LUO 2003 extends LAKES 1998 technique to set a limit on ${{\mathit \mu}^{2}}{{\mathit A}}$, where $\mu {}^{-1}$ is the Compton wavelength $ƛ_{C}$ of the massive photon and ${{\mathit A}}$ is the ambient vector potential. The important departure is that the apparatus rotates, removing sensitivity to the direction of ${{\mathit A}}$. They take ${{\mathit A}}$ = $10^{12}$ Tm, due to ``cluster level fields.'' But see comment of GOLDHABER 2003 and reply by LUO 2003B.
12  LAKES 1998 reports limits on torque on a toroid Cavendish balance, obtaining a limit on $\mu {}^{2}\mathit A~<2 \times 10^{-9}~$Tm/m${}^{2}$ via the Maxwell-Proca equations, where $\mu {}^{-1}$ is the characteristic length associated with the photon mass and $\mathit A$ is the ambient vector potential in the Lorentz gauge. Assuming $\mathit A$ $\approx{}1 \times 10^{12}~$Tm due to cluster fields he obtains $\mu {}^{-1}$ $>2 \times 10^{10}~$m, corresponding to $\mu <$ $1 \times 10^{-17}$ eV. A more conservative limit, using $\mathit A$ $\approx{}$(1 $\mu G){\times }$(600 pc) based on the galactic field, is $\mu {}^{-1}$ $>$ $1 \times 10^{9}~$m or $\mu $ $<$ $2 \times 10^{-16}$ eV.
13  RYUTOV 1997 uses a magnetohydrodynamics argument concerning survival of the Sun's field to the radius of the Earth's orbit. ``To reconcile observations to theory, one has to reduce $\lbrack{}$the photon mass] by approximately an order of magnitude compared with'' per DAVIS 1975. ``Secure limit, best by this method'' (per GOLDHABER 2010).
14  FISCHBACH 1994 analysis is based on terrestrial magnetic fields; approach analogous to DAVIS 1975. Similar result based on a much smaller planet probably follows from more precise ${{\mathit B}}$ field mapping. ``Secure limit, best by this method'' (per GOLDHABER 2010).
15  CHERNIKOV 1992, motivated by possibility that photon exhibits mass only below some unknown critical temperature, searches for departure from Ampere's Law at 1.24 K. See also RYAN 1985.
16  RYAN 1985, motivated by possibility that photon exhibits mass only below some unknown critical temperature, sets mass limit at $<$ ($1.5$ $\pm1.4$) $ \times 10^{-42}$ g based on Coulomb's Law departure limit at 1.36 K. We report the result as frequentist 90$\%$ CL (FELDMAN 1998).
17  CHIBISOV 1976 depends in critical way on assumptions such as applicability of virial theorem. Some of the arguments given only in unpublished references.
18  DAVIS 1975 analysis of Pioneer-10 data on Jupiter's magnetic field. ``Secure limit, best by this method'' (per GOLDHABER 2010).
19  FRANKEN 1971 method is of dubious validity (KROLL 1971A, JACKSON 1999, GOLDHABER 2010, and references therein).
20  KROLL 1971A used low frequency Schumann resonances in cavity between the conducting earth and resistive ionosphere, overcoming objections to resonant-cavity methods (JACKSON 1999, GOLDHABER 2010, and references therein). ``Secure limit, best by this method'' (per GOLDHABER 2010).
21  WILLIAMS 1971 is landmark test of Coulomb's law. ``Secure limit, best by this method'' (per GOLDHABER 2010).
References