# ${{\boldsymbol \gamma}}$ MASS INSPIRE search

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
 2007
MHD of solar wind
• • • We do not use the following data for averages, fits, limits, etc. • • •
$<2.2 \times 10^{-14}$ 2
 2017
$<1.8 \times 10^{-14}$ 3
 2016
$<1.9 \times 10^{-15}$ 4
 2016
Ampere's Law in solar wind
$<2.3 \times 10^{-9}$ 95 5
 2014
Lensed quasar position
6
 2010
Anomalous magn. mom.
$<1 \times 10^{-26}$ 7
 2007 A
Proca galactic field
$\text{no limit feasible}$ 7
 2007 A
${{\mathit \gamma}}$ as Higgs particle
$<1 \times 10^{-19}$ 8
 2006
Torque on rotating magnetized toroid
$<1.4 \times 10^{-7}$
 2004
Dispersion of GHz radio waves by sun
$<2 \times 10^{-16}$ 9
 2004
Speed of 5-50 Hz radiation in atmosphere
$<7 \times 10^{-19}$ 10
 2003
Torque on rotating magnetized toroid
$<1 \times 10^{-17}$ 11
 1998
Torque on toroid balance
$<6 \times 10^{-17}$ 12
 1997
MHD of solar wind
$<8 \times 10^{-16}$ 90 13
 1994
Earth magnetic field
$<5 \times 10^{-13}$ 14
 1992
Ampere's Law null test
$<1.5 \times 10^{-9}$ 90 15
 1985
Coulomb's Law null test
$<3 \times 10^{-27}$ 16
 1976
Galactic magnetic field
$<6 \times 10^{-16}$ 99.7 17
 1975
Jupiter's magnetic field
$<7.3 \times 10^{-16}$
 1974
Alfven waves
$<6 \times 10^{-17}$ 18
 1971
Low freq. res. circuit
$<2.4 \times 10^{-13}$ 19
 1971 A
Dispersion in atmosphere
$<1 \times 10^{-14}$ 20
 1971
Tests Coulomb's Law
$<2.3 \times 10^{-15}$
 1968
Satellite data
1  RYUTOV 2007 extends the method of RYUTOV 1997 to the radius of Pluto's orbit.
2  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.
3  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.
4  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.
5  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.
6  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.
7  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 .
8  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 ).
9  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 .
10  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.
11  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.
12  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 [the photon mass] by approximately an order of magnitude compared with'' per DAVIS 1975 . Secure limit, best by this method'' (per GOLDHABER 2010 ).
13  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 ).
14  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 .
15  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 ).
16  CHIBISOV 1976 depends in critical way on assumptions such as applicability of virial theorem. Some of the arguments given only in unpublished references.
17  DAVIS 1975 analysis of Pioneer-10 data on Jupiter's magnetic field. Secure limit, best by this method'' (per GOLDHABER 2010 ).
18  FRANKEN 1971 method is of dubious validity (KROLL 1971A, JACKSON 1999 , GOLDHABER 2010 , and references therein).
19  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 ).
20  WILLIAMS 1971 is landmark test of Coulomb's law. Secure limit, best by this method'' (per GOLDHABER 2010 ).
References:
 BONETTI 2017
PL B768 326 FRB (fast radio burst) 121102 Casts New Light on the Photon Mass
 BONETTI 2016
PL B757 548 Photon Mass Limits from Fast Radio Bursts
 RETINO 2016
ASP 82 49 Solar Wind Test of the de Broglie-Proca Massive Photon with Cluster Multi-Spacecraft Data
 EGOROV 2014
MNRAS 437 L90 Constraining New Fundamental Physics with Multiwavelength Astrometry
 ACCIOLY 2010
PR D82 065026 Upper Bounds on the Photon Mass
PRL 98 010402 Photon-Mass Bound Destroyed by Vortices
 RYUTOV 2007
PPCF 49 B429 Using Plasma Physics to Weigh the Photon
 TU 2006
PL A352 267 Test of U(1) Local Gauge Invariance in Proca Electrodynamics
 ACCIOLY 2004
PR D69 107501 Photon Mass and Gravitational Deflection
 FULLEKRUG 2004
PRL 93 043901 Probing the Speed of Light with Radio Waves at Extremely Low Frequencies
 LUO 2003
PRL 90 081801 New Experimental Limit on the Photon Rest Mass with a Rotating Torsion Balance
 LAKES 1998
PRL 80 1826 Experimental Limits on the Photon Mass and Cosmic Magnetic Vector Potential
 RYUTOV 1997
PPCF 39 A73 The Role of Finite Photon Mass in Magnetohydrodynamics of Space Plasmas
 FISCHBACH 1994
PRL 73 514 New Geomagnetic Limits on the Photon Mass and on Long Range Forces Coexisting with Electromagnetism
 CHERNIKOV 1992
PRL 68 3383 Low Temperature Upper Limit of the Photon Mass: Experimental Null Test of Ampere's Law
 RYAN 1985
PR D32 802 Cryogenic Photon Mass Experiment
 CHIBISOV 1976
SPU 19 624 Astrophysical Upper Limits on the Photon Rest Mass
 DAVIS 1975
PRL 35 1402 Limit on the Photon Mass Deduced from Pioneer-10 Observations of Jupiter's Magnetic Fields
 HOLLWEG 1974
PRL 32 961 Improved Limit on Photon Rest Mass
 FRANKEN 1971
PRL 26 115 Photon Rest Mass
 KROLL 1971A
PRL 27 340 Concentric Spherical Cavities And Limits On The Photon Rest Mass
 WILLIAMS 1971
PRL 26 721 New Experimental Test of Coulomb's Law: A Laboratory Upper Limit on the Photon Rest Mass
 GOLDHABER 1968
PRL 21 567 New Geomagnetic Limit on the Mass of the Photon