Citation: S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024)

I (J PC ) = 0,1(1 − − )γ (photon)γ MASS
Results prior to 2008 are critiqued in GOLDHABER 10. All experimental
results published prior to 2005 are summarized in detail by TU 05.
The following conversions are useful: 1 eV = 1.783 × 10−33 g = 1.957 ×
10−6 m e ; λ̄
¯C = (1.973 × 10−7 m)×(1 eV/m γ ).
VALUE (eV)CL%

DOCUMENT ID

COMMENT1 RYUTOV<1 × 10−1807 MHD of solar wind• • • We do not use the following data for averages, fits, limits, etc. • • •2 WANG<2.1 × 10−1568
23B Fast Radio Bursts−14
3 BONETTI<2.2 × 1017 Fast Radio Bursts, FRB 121102
4 BONETTI<1.8 × 10−14
16 Fast Radio Bursts, FRB 150418
5 RETINO<1.9 × 10−15
16 Ampere’s Law in solar wind
6 EGOROV<2.3 × 10−995
14 Lensed quasar position
7 ACCIOLY
10 Anomalous magn. mom.
8 ADELBERGER 07A Proca galactic field<1 × 10−26
8 ADELBERGER 07A γ as Higgs particle
no limit feasible−199<1 × 10TU
06 Torque on rotating magnetizedtoroid
<1.4 × 10−7
ACCIOLY
04 Dispersion of GHz radio waves bysun
10 FULLEKRUG 04 Speed of 5-50 Hz radiation in at<2 × 10−16mosphere
11 LUO<7 × 10−19
03 Torque on rotating magnetizedtoroid12 LAKES<1 × 10−17
98 Torque on toroid balance
13 RYUTOV<6 × 10−1797 MHD of solar wind−1614<8 × 1090
FISCHBACH 94 Earth magnetic field
15 CHERNIKOV 92 Ampere’s Law null test
<5 × 10−13−916 RYAN
<1.5 × 1090
85 Coulomb’s Law null test−2717<3 × 10
CHIBISOV
76 Galactic magnetic field
18 DAVIS<6 × 10−16
99.7
75 Jupiter’s magnetic field−16<7.3 × 10
HOLLWEG74 Alfven waves
19 FRANKEN<6 × 10−17
71 Low freq. res. circuit
20 KROLL<2.4 × 10−13
71A Dispersion in atmosphere
21 WILLIAMS<1 × 10−14
71 Tests Coulomb’s Law−15<2.3 × 10
GOLDHABER 68 Satellite data
1 RYUTOV 07 extends the method of RYUTOV 97 to the radius of Pluto’s orbit.
2 WANG 23B use fast radio burst photon mass dependent dispersion relation to determine
an upper limit of the photon mass.
3 BONETTI 17 uses frequency-dependent time delays of repeating FRB with welldetermined redshift, assuming the DM is caused by expected dispersion in IGM. Thereare several uncertainties, leading to mass limit 2.2 × 10−14 eV.
4 BONETTI 16 uses frequency-dependent time delays of FRB, assuming the DM is causedby expected dispersion in IGM. There are several uncertainties, leading to mass limit
1.8 × 10−14 eV, if indeed the FRB is at the initially reported redshift.

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Citation: S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024)

5 RETINO 16 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× 10−15 eV to 7.9× 10−14 eV
depending on the assumptions of the vector potential from the interplanetary magneticfield.
6 EGOROV 14 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 10 limits come from possible alterations of anomalous magnetic moment ofelectron and gravitational deflection of electromagnetic radiation. Reported limits arenot ”claimed” by the authors and in any case are not competitive.
8 When trying to measure m one must distinguish between measurements performed onlarge and small scales. If the photon acquires mass by the Higgs mechanism, the largescale 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
m < 10−26 eV, as correctly calculated by YAMAGUCHI 59 and CHIBISOV 76.
9 TU 06 continues the work of LUO 03, with extended LAKES 98 method, reporting
the improved limit µ2 A = (0.7 ± 1.7) × 10−13 T/m if A = 0.2 µG out to 4 × 1022
m. Reported result µ = (0.9 ± 1.5) × 10−52 g reduces to the frequentist mass limit
1.2 × 10−19 eV (FELDMAN 98).
10 FULLEKRUG 04 adopted KROLL 71A 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 71B,KROLL 71, and PARK 71.
11 LUO 03 extends LAKES 98 technique to set a limit on µ2 A, where µ−1 is the Compton
wavelength λ̄¯C of the massive photon and A is the ambient vector potential. The
important departure is that the apparatus rotates, removing sensitivity to the directionof A. They take A = 1012 Tm, due to “cluster level fields.” But see comment ofGOLDHABER 03 and reply by LUO 03B.
12 LAKES 98 reports limits on torque on a toroid Cavendish balance, obtaining a limit onµ2 A < 2 × 10−9 Tm/m2 via the Maxwell-Proca equations, where µ−1 is the characteristic length associated with the photon mass and A is the ambient vector potential
in the Lorentz gauge. Assuming A ≈ 1 × 1012 Tm due to cluster fields he obtainsµ−1 > 2 × 1010 m, corresponding to µ < 1 × 10−17 eV. A more conservative limit,using A ≈ (1 µG)×(600 pc) based on the galactic field, is µ−1 > 1 × 109 m orµ < 2 × 10−16 eV.
13 RYUTOV 97 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 toreduce [the photon mass] by approximately an order of magnitude compared with” perDAVIS 75. “Secure limit, best by this method” (per GOLDHABER 10).
14 FISCHBACH 94 analysis is based on terrestrial magnetic fields; approach analogous toDAVIS 75. Similar result based on a much smaller planet probably follows from more
precise B field mapping. “Secure limit, best by this method” (per GOLDHABER 10).
15 CHERNIKOV 92, 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 85.
16 RYAN 85, motivated by possibility that photon exhibits mass only below some unknown
critical temperature, sets mass limit at < (1.5 ± 1.4)×10−42 g based on Coulomb’s Law
departure limit at 1.36 K. We report the result as frequentist 90% CL (FELDMAN 98).
17 CHIBISOV 76 depends in critical way on assumptions such as applicability of virial theorem. Some of the arguments given only in unpublished references.
18 DAVIS 75 analysis of Pioneer-10 data on Jupiter’s magnetic field. “Secure limit, best bythis method” (per GOLDHABER 10).
19 FRANKEN 71 method is of dubious validity (KROLL 71A, JACKSON 99, GOLDHABER 10, and references therein).

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Citation: S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024)

20 KROLL 71A used low frequency Schumann resonances in cavity between the conducting earth and resistive ionosphere, overcoming objections to resonant-cavity methods(JACKSON 99, GOLDHABER 10, and references therein). “Secure limit, best by thismethod” (per GOLDHABER 10).
21 WILLIAMS 71 is landmark test of Coulomb’s law. “Secure limit, best by this method”(per GOLDHABER 10).

γ CHARGE
OKUN 06 has argued that schemes in which all photons are charged areinconsistent. He says that if a neutral photon is also admitted to avoidthis problem, then other problems emerge, such as those connected withthe emission and absorption of charged photons by charged particles. Heconcludes that in the absence of a self-consistent phenomenological basis,interpretation of experimental data is at best difficult.
VALUE (e)CHARGE× 10−46
× 10−35

DOCUMENT ID

TECNCOMMENT

1 ALTSCHUL
2 CAPRINI<1mixed07B VLBI Aharonov-Bohm effect<1single
05 CMB Isotropy constraint• • • We do not use the following data for averages, fits, limits, etc. • • •1 ALTSCHUL<1 × 10−32 single
07B VLBI Aharonov-Bohm effect−333<3 × 10mixed
KOBYCHEV 05 VLBI Smear as function of B·E
× 10−31<8.5 × 10−17<3 × 10−28<5 × 10−30<2 × 10−28<2 × 10−32<4singlesingle

3 KOBYCHEV

05

4 SEMERTZIDIS 03
5 SIVARAM
95
6 RAFFELT
94
7 COCCONI
92γ
VLBI Deflection as function of B·Eγ
Laser light deflection in B-field
CMB For ΩM = 0.3, h2 = 0.5
TOF Pulsar f1 −f2
VLBA radio telescope resolution
TOF Pulsar f1 − f2 TOF

COCCONI88
1 ALTSCHUL 07B looks for Aharonov-Bohm phase shift in addition to geometric phaseshift in radio interference fringes (VSOP mission).
2 CAPRINI 05 uses isotropy of the cosmic microwave background to place stringent limitson possible charge asymmetry of the Universe. Charge limits are set on the photon,
neutrino, and dark matter particles. Valid if charge asymmetries produced by different
particles are not anticorrelated.
3 KOBYCHEV 05 considers a variety of observable effects of photon charge for extragalactic
compact radio sources. Best limits if source observed through a foreground cluster ofgalaxies.
4 SEMERTZIDIS 03 reports the first laboratory limit on the photon charge in the last
30 years. Straightforward improvements in the apparatus could attain a sensitivity of
10−20 e.
5 SIVARAM 95 requires that CMB photon charge density not overwhelm gravity. Result
scales as ΩM h2 .
6 RAFFELT 94 notes that COCCONI 88 neglects the fact that the time delay due to dispersion by free electrons in the interstellar medium has the same photon energy dependence
as that due to bending of a charged photon in the magnetic field. His limit is based on
the assumption that the entire observed dispersion is due to photon charge. It is a factorof 200 less stringent than the COCCONI 88 limit.
7 See COCCONI 92 for less stringent limits in other frequency ranges. Also see RAFFELT 94 note.

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Citation: S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024)

γ REFERENCES
WANG
23B
BONETTI
17BONETTI
16
RETINO
16
EGOROV
14
ACCIOLY
10
GOLDHABER 10
ADELBERGER 07A
ALTSCHUL
07B
Also
RYUTOV
07
OKUN
06
TU
06
CAPRINI
05
KOBYCHEV
05
TU
05
ACCIOLY
04
FULLEKRUG 04
GOLDHABER 03
LUO
03
LUO
03B
SEMERTZIDIS 03
JACKSON
99
FELDMAN98
LAKES
98
RYUTOV97
SIVARAM95
FISCHBACH
94
RAFFELT94
CHERNIKOV 92
Also
COCCONI92
COCCONI88
RYAN
85
CHIBISOV76
DAVIS
HOLLWEGFRANKEN
GOLDHABER
KROLL
KROLL
PARK
WILLIAMSGOLDHABER
YAMAGUCHI

75
74
71
71B
71
71A
71
71
68
59

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