Hidden Photons: Kinetic Mixing Parameter Limits INSPIRE search

Limits are on the kinetic mixing parameter $\chi $ which is defined by the Lagrangian $\mathit L$ = $\text{-}{1\over 4}{{\mathit F}}_{ {{\mathit \mu}} {{\mathit \nu}} }{{\mathit F}}{}^{ {{\mathit \mu}} {{\mathit \nu}} }$ $−{1\over 4}{{\mathit F}}{}^{'}_{ {{\mathit \mu}} {{\mathit \nu}} }{{\mathit F}}{}^{' {{\mathit \mu}} {{\mathit \nu}} }$ $\text{-}{\chi \over 2}{{\mathit F}}_{ {{\mathit \mu}} {{\mathit \nu}} }{{\mathit F}}{}^{' {{\mathit \mu}} {{\mathit \nu}} }$ + ${{{\mathit m}}{}^{2}_{{{\mathit \gamma}^{\,'}}}\over 2}{{\mathit A}}{}^{'}_{{{\mathit \mu}}}{{\mathit A}}{}^{'{{\mathit \mu}}}$, where ${{\mathit A}_{{\mu}}}$ and ${{\mathit A}_{{\mu}}^{\,'}}$ are the photon and hidden-photon fields with field strengths ${{\mathit F}}_{ {{\mathit \mu}} {{\mathit \nu}} }$ and ${{\mathit F}}{}^{'}_{ {{\mathit \mu}} {{\mathit \nu}} }$, respectively, and is the hidden-photon mass.
VALUE CL% DOCUMENT ID TECN  COMMENT
• • • We do not use the following data for averages, fits, limits, etc. • • •
$<1 \times 10^{-4}$ 90 1
AAIJ
2020C
LHCB ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = 214 MeV
2
AAIJ
2020C
LHCB ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $218 - 315$ MeV
3
AABOUD
2019G
ATLS ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $20 - 60$ GeV
$<6 \times 10^{-3}$ 90 4
ABLIKIM
2019A
BES3 ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $0.01 - 2.4$ GeV
$<3.4 \times 10^{-3}$ 90 5
ABLIKIM
2019H
BES3 ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $0.1 - 2.1$ GeV
$<8 \times 10^{-15}$ 90 6
AGUILAR-AREVA..
2019A
DAMC ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $1.2 - 30$ eV
$<9 \times 10^{-17}$ 90 7
APRILE
2019D
XE1T ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $0.186 - 5$ keV
$<7.5 \times 10^{-6}$ 90 8
BANERJEE
2019
NA64 ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $1 - 200$ MeV
$<2 \times 10^{-11}$ 9
BHOONAH
2019
ASTR ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $10^{-22} - 10^{-10}$ eV
$<5 \times 10^{-12}$ 95 10
BRUN
2019
SHUK ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $20.8 - 28.3$ $\mu $eV
$<4.4 \times 10^{-4}$ 90 11
CORTINA-GIL
2019
NA62 ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $60 - 110$ MeV
$<3 \times 10^{-5}$ 95 12
DANILOV
2019
TEXO ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = 20 eV - 1 MeV
$<6 \times 10^{-9}$ 95 13
HOCHBERG
2019
${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $0.8 - 4$ eV
$<1 \times 10^{-11}$ 95 14
KOPYLOV
2019
CNTR ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $9 - 40$ eV
$<1.5 \times 10^{-9}$ 15
KOVETZ
2019
COSM ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $10^{-23} - 10^{-13}$ eV
$<3 \times 10^{-14}$ 95 16
NGUYEN
2019
WDMX ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = 6 neV $-$ 2.07 $\mu $eV
$<4.5 \times 10^{-14}$ 90 17
ABE
2018F
XMAS ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $40 - 120$ keV
$<2.5 \times 10^{-3}$ 95 18
ADRIAN
2018
HPS ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $19 - 81$ MeV
$<4.4 \times 10^{-4}$ 90 19
ANASTASI
2018B
KLOE ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $519 - 987$ MeV
$<4 \times 10^{-15}$ 90 20
ARMENGAUD
2018
EDE3 ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $0.8 - 500$ keV
21
BANERJEE
2018
NA64 ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $1 - 23$ MeV
$<1.8 \times 10^{-5}$ 90 22
BANERJEE
2018A
NA64 ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $1 - 100$ MeV
$<1 \times 10^{-8}$ 90 23
KNIRCK
2018
${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $0.67 - 0.92$ meV
$<3.1 \times 10^{-14}$ 90 24
ABGRALL
2017
HPGE ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = 11.8 keV
$<6 \times 10^{-4}$ 90 25
ABLIKIM
2017AA
BES3 ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $1.5 - 3.4$ GeV
$<7 \times 10^{-15}$ 90 26
ANGLOHER
2017
CRES ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $0.3 - 0.7$ keV
$<1.2 \times 10^{-4}$ 90 27
BANERJEE
2017
NA64 ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $0.002 - 0.4$ GeV
$<2 \times 10^{-11}$ 28
CHANG
2017
ASTR ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = 15 MeV
$<4.5 \times 10^{-3}$ 90 29
DUBININA
2017
EMUL ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $1.1 - 24$ MeV
$<4 \times 10^{-4}$ 90 30
LEES
2017E
BABR ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = 4.7 GeV
31
AAD
2016AG
ATLS ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $0.1 - 2$ GeV
$<4.4 \times 10^{-4}$ 90 32
ANASTASI
2016
KLOE ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $527 - 987$ MeV
$<1.7 \times 10^{-6}$ 95 33
KHACHATRYAN
2016
CMS ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = 2 GeV
$<0.04$ 95 34
AAD
2015CD
ATLS ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $15 - 55$ GeV
$<1.4 \times 10^{-3}$ 90 35
ADARE
2015
${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $30 - 90$ MeV
36
AN
2015A
${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = 12 eV - 40 keV
37
ANASTASI
2015
KLOE ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = 2${\mathit m}_{{{\mathit \mu}}}$ - 1 GeV
$<1.7 \times 10^{-3}$ 90 38
ANASTASI
2015A
KLOE ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $5 - 320$ MeV
$<4.2 \times 10^{-4}$ 90 39
BATLEY
2015A
NA48 ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = 36 MeV
40
JAEGLE
2015
BELL ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $0.1 - 3.5$ GeV
$<3 \times 10^{-13}$ 41
KAZANAS
2015
ASTR ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = 2${\mathit m}_{{{\mathit e}}}$ $-$ 100 MeV
$<6 \times 10^{-12}$ 42
SUZUKI
2015
${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $1.9 - 4.3$ eV
$<2.3 \times 10^{-13}$ 99.7 43
VINYOLES
2015
ASTR ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = 8 eV
$<2 \times 10^{-13}$ 44
ABE
2014F
XMAS ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $40 - 120$ keV
$<1.8 \times 10^{-3}$ 90 45
AGAKISHIEV
2014
HDES ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = 63 MeV
$<9.0 \times 10^{-4}$ 90 46
BABUSCI
2014
KLOE ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = 969 MeV
47
BATELL
2014
BDMP ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $10^{-3} - 1$ GeV
$<1.3 \times 10^{-7}$ 95 48
BLUEMLEIN
2014
BDMP ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = 0.6 GeV
$<3 \times 10^{-18}$ 49
FRADETTE
2014
COSM ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $50 - 300$ MeV
$<3.5 \times 10^{-4}$ 90 50
LEES
2014J
BABR ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = 0.2 GeV
$<9 \times 10^{-4}$ 95 51
MERKEL
2014
A1 ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $40 - 300$ MeV
$<3 \times 10^{-15}$ 52
AN
2013B
ASTR ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = 2 keV
$<7 \times 10^{-14}$ 53
AN
2013C
XE10 ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = 100 eV
$<8 \times 10^{-4}$ 54
DIAMOND
2013
BDMP ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $30 - 250$ MeV
$<2 \times 10^{-3}$ 90 55
GNINENKO
2013
BDMP ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $25 - 120$ MeV
$<2.2 \times 10^{-13}$ 56
HORVAT
2013
HPGE ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = 230 eV
$<8.06 \times 10^{-5}$ 95 57
INADA
2013
LSW ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = 0.04 eV$−$26 keV
$<2 \times 10^{-10}$ 95 58
MIZUMOTO
2013
${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = 1 eV
$<1.7 \times 10^{-7}$ 59
PARKER
2013
LSW ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = 53 $\mu $eV
$<5.32 \times 10^{-15}$ 60
PARKER
2013
${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = 53 $\mu $eV
$<1 \times 10^{-15}$ 61
REDONDO
2013
ASTR ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = 2 keV
$<8 \times 10^{-8}$ 90 62
GNINENKO
2012A
BDMP ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $1 - 135$ MeV
$<1 \times 10^{-7}$ 90 63
GNINENKO
2012B
CHRM ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $1 - 500$ MeV
$<1 \times 10^{-3}$ 90 64
ABRAHAMYAN
2011
${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $175 - 250$ MeV
$<9 \times 10^{-8}$ 95 65
BLUEMLEIN
2011
BDMP ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = 70 MeV
$<1 \times 10^{-7}$ 66
BJORKEN
2009
BDMP ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $2 - 400$ MeV
$<5 \times 10^{-9}$ 67
BJORKEN
2009
ASTR ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $2 - 50$ MeV
1  AAIJ 2020C look for hidden photons produced from the ${{\mathit p}}{{\mathit p}}$ collision in the decay channel ${{\mathit \gamma}^{\,'}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ . For prompt decaying hidden photons, limits at the level of $10^{-4} - 10^{-3}$ are obtained for ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $0.214 - 30$ GeV. See their Fig. 2 for mass-dependent limits.
2  AAIJ 2020C look for hidden photons produced from the ${{\mathit p}}{{\mathit p}}$ collision in the decay channel ${{\mathit \gamma}^{\,'}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ . For hidden photons with lifetimes of order ps, limits at the level of $10^{-5}$ are obtained for ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $218 - 315$ MeV. See their Fig. 4 for mass-dependent limits.
3  AABOUD 2019G look for ${{\mathit h}}$ $\rightarrow$ ${{\mathit \gamma}^{\,'}}{{\mathit \gamma}^{\,'}}$ ( ${{\mathit \gamma}^{\,'}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ ) and exclude a kinetic mixing around $10^{-9} - 10^{-8}$ for B( ${{\mathit h}}$ $\rightarrow$ ${{\mathit \gamma}^{\,'}}{{\mathit \gamma}^{\,'}}$ ) = 0.01 and 0.1. See their Fig. 9 for mass-dependent limits.
4  ABLIKIM 2019A look for ${{\mathit J / \psi}}$ $\rightarrow$ ${{\mathit \gamma}^{\,'}}{{\mathit \eta}}$ ( ${{\mathit \gamma}^{\,'}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ ). Limits between $6 \times 10^{-3}$ and $0.05$ are obtained (see their Fig. 8).
5  ABLIKIM 2019H look for ${{\mathit J / \psi}}$ $\rightarrow$ ${{\mathit \gamma}^{\,'}}{{\mathit \eta}^{\,'}}$ ( ${{\mathit \gamma}^{\,'}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ ). Limits between $3.4 \times 10^{-3}$ and $0.026$ are obtained. See their Fig. 5 for mass-dependent limits.
6  AGUILAR-AREVALO 2019A look for the absorption signal of hidden photon dark matter by using a CCD. The quoted limit applies to ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = 17 eV. The local density $\rho _{{{\mathit \gamma}^{\,'}}}$ = 0.3 GeV/cm${}^{3}$ is assumed. See their Fig. 4 for mass-dependent limits.
7  APRILE 2019D is analogous to ABE 2014F. The quoted limit applies to ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = 0.7 keV. See their Fig. 5(f) for mass-dependent limits.
8  BANERJEE 2019 is an update of BANERJEE 2018A. The quoted limit is at ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = 1 MeV. See their Fig. 3 for mass-dependent limits.
9  BHOONAH 2019 examine heating of Galactic Center gas clouds by hidden photon dark matter. The quoted limit applies to ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ $\simeq{}$ $10^{-12}$ eV. See their Fig. 2 for mass-dependent limits.
10  BRUN 2019 is analogous to SUZUKI 2015 . The limit is derived under an assumption that hidden photons constitute the local dark matter density $\rho _{\gamma '}$ = 0.3 GeV/cm${}^{3}$.
11  CORTINA-GIL 2019 look for an invisible hidden photon in the reaction ${{\mathit K}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{0}}$ ( ${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}$ ${{\mathit \gamma}^{\,'}}$ ). The quoted limit applies to ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $62.5 - 65$ MeV. See their Figs. 6 and 7 for mass-dependent limits.
12  DANILOV 2019 examined the hidden photon production in nuclear reactors, correctly taking account of the effective photon mass in the reactor and detector. The limit gets weaker for ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ less than the effective photon mass in proportion to 1/${{\mathit m}^{2}}_{{{\mathit \gamma}^{\,'}}}$. See their Fig. 1 for mass-dependent limits.
13  HOCHBERG 2019 look for the absorption signal of hidden photon dark matter by using superconducting-nanowire single-photon detectors. The quoted limit applies to ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ $\simeq{}$ 1 eV. The local density $\rho _{{{\mathit \gamma}^{\,'}}}$ = 0.3 GeV/cm${}^{3}$ is assumed. See their Fig. 4 for mass-dependent limits.
14  KOPYLOV 2019 look for hidden-photon dark matter using a counter with an aluminum cathode and derive limits assuming it constitute all the local dark matter. The quoted limit applies to ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = 12 eV. See their Fig. 7 for mass-dependent limits.
15  KOVETZ 2019 examine heating of the early Universe plasma by hidden photon dark matter, and derive the limits by requiring that the cosmic mean 21 cm brightness temperature relative to the CMB temperature satisfy T$_{21}$ $>$ $-100$ mK. The quoted limit applies to ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ $\simeq{}$ $2 \times 10^{-14}$ eV. See their Fig. 3 for mass-dependent limits.
16  NGUYEN 2019 look for hidden photon dark matter with a resonant cavity, and set limits $\sim{}10^{-12}$ for ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $0.2 - 2.07\mu $eV. The quoted limit applies to ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = 1.3 $\mu $eV. The local density $\rho _{{{\mathit \gamma}^{\,'}}}$ = 0.3 GeV/cm${}^{3}$ is assumed. See their Fig. 19 for mass-dependent limits.
17  ABE 2018F is an update of ABE 2014F. The quoted limit applies to ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ $\simeq{}$ 40 keV. See their Fig. 5 for mass-dependent limits.
18  ADRIAN 2018 look for a hidden photon resonance in the reaction ${{\mathit e}^{-}}$ ${{\mathit Z}}$ $\rightarrow$ ${{\mathit e}^{-}}{{\mathit Z}}{{\mathit \gamma}^{\,'}}$ ( ${{\mathit \gamma}^{\,'}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ ). The quoted limit applies to ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = 40 MeV. See their Fig. 4 for mass-dependent limits.
19  ANASTASI 2018B look for a hidden photon resonance in the reaction ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \gamma}^{\,'}}{{\mathit \gamma}}$ ( ${{\mathit \gamma}^{\,'}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ ). The quoted limit is obtained by combining the result of ANASTASI 2016 and it applies to ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ $\simeq{}$ $519 - 987$ MeV. See their Fig. 9 for mass-dependent limits.
20  ARMENGAUD 2018 is analogous to ABE 2014F. The quoted limits applies to ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = 1.6 keV. See the right panel of Fig. 5 for mass-dependent limits.
21  BANERJEE 2018 look for hidden photons produced in the reaction ${{\mathit e}^{-}}$ ${{\mathit Z}}$ $\rightarrow$ ${{\mathit e}^{-}}{{\mathit Z}}{{\mathit \gamma}^{\,'}}$ ( ${{\mathit \gamma}^{\,'}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ ), and exclude $9.2 \times 10^{-5}{ {}\lesssim{} }$ $\chi $ ${ {}\lesssim{} }$ $0.01$ for ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $1 - 23$ MeV. They also set a limit on the electron coupling to a 16.7 MeV gauge boson suggested by the ATOMKI (KRASZNAHORKAY 2016 ) experiment. See their Fig. 3 for mass-dependent limits.
22  BANERJEE 2018A look for invisible decays of hidden photons produced in the reaction ${{\mathit e}^{-}}$ ${{\mathit Z}}$ $\rightarrow$ ${{\mathit e}^{-}}{{\mathit Z}}{{\mathit \gamma}^{\,'}}$ . The quoted limit is at ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = 1 MeV. See their Fig. 15 for mass-dependent limits.
23  KNIRCK 2018 is analogous to SUZUKI 2015 . See their Fig. 5 for mass-dependent limits.
24  ABGRALL 2017 is analogous to ABE 2014F using the MAJORANA DEMONSTRATOR. See their Fig. 3 for limits between 6 keV $<$ ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ $<$ 97 keV.
25  ABLIKIM 2017AA look for ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}^{\,'}}$ ( ${{\mathit \gamma}^{\,'}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ or ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ ) . Limits between $10^{-3}$ and $10^{-4}$ are obtained (see their Fig. 3).
26  ANGLOHER 2017 is analogous to ABE 2014F. The quoted limit is at ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = 0.7 keV. See their Fig. 8 for mass-dependent limits.
27  BANERJEE 2017 look for invisible decays of hidden photons produced in the reaction ${{\mathit e}^{-}}$ ${{\mathit Z}}$ $\rightarrow$ ${{\mathit e}^{-}}{{\mathit Z}}{{\mathit \gamma}^{\,'}}$ . The quoted limit applies to ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = 2 MeV. See their Fig. 3 for mass-dependent limits.
28  CHANG 2017 examine the hidden photon emission from SN1987A, including the effects of finite temperature and density on $\chi $ and obtain limits $\chi $ (${\mathit m}_{{{\mathit \gamma}^{\,'}}}$/MeV) ${ {}\lesssim{} }$ $3 \times 10^{-9}$ for ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ $<$ 15 MeV and $\chi $ ${ {}\lesssim{} }$ $10^{-9}$ for ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $15 - 120$ MeV.
29  DUBININA 2017 look for ${{\mathit \mu}^{+}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\overline{\mathit \nu}}_{{\mu}}}{{\mathit \nu}_{{e}}}{{\mathit \gamma}^{\,'}}$ ( ${{\mathit \gamma}^{\,'}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ ) in a nuclear photoemulsion. The quoted limit applies to ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = 1.1 MeV. Limits between $4.5 \times 10^{-3}$ and are obtained (see their Fig. 3).
30  LEES 2017E look for invisible decays of hidden photons produced in the reaction ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}^{\,'}}$ . See their Fig. 5 for limits in the mass range ${\mathit m}_{{{\mathit \gamma}^{\,'}}}{}\leq{}$ 8 GeV.
31  AAD 2016AG look for hidden photons promptly decaying into collimated electrons and/or muons, assuming that they are produced in the cascade decays of squarks or the Higgs boson. See their Fig. 10 and Fig.13 for their limits on the cross section times branching fractions.
32  ANASTASI 2016 look for the decay ${{\mathit \gamma}^{\,'}}$ $\rightarrow$ ${{\mathit \pi}^{+}}$ ${{\mathit \pi}^{-}}$ in the reaction ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}^{\,'}}$ . Limits between $4.3 \times 10^{-3}$ and $4.4 \times 10^{-4}$ are obtained for 527 $<$ ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ $<$ 987 MeV (see their Fig. 9).
33  KHACHATRYAN 2016 look for ${{\mathit \gamma}^{\,'}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ in a dark SUSY scenario where the SM-like Higgs boson decays into a pair of the visible lightest neutralinos with mass 10 GeV, both of which decay into ${{\mathit \gamma}^{\,'}}$ and a hidden neutralino with mass 1 GeV. See the right panel in their Fig. 2.
34  AAD 2015CD look for ${{\mathit H}}$ $\rightarrow$ ${{\mathit Z}}{{\mathit \gamma}^{\,'}}$ $\rightarrow$ 4 ${{\mathit \ell}}$ with the ATLAS detector at LHC and find $\chi $ $<$ $4 - 17$ for ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $15 - 55$ GeV. See their Fig. 6.
35  ADARE 2015 look for a hidden photon in ${{\mathit \pi}^{0}}$, ${{\mathit \eta}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit e}^{+}}{{\mathit e}^{-}}$ at the PHENIX experiment. See their Fig. 4 for mass-dependent limits.
36  AN 2015A derived limits from the absence of ionization signals in the XENON10 and XENON100 experiments, assuming hidden photons constitute all the local dark matter. Their best limit is $\chi $ $<$ $1.3 \times 10^{-15}$ at ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = 18 eV. See their Fig. 1 for mass-dependent limits.
37  ANASTASI 2015 look for a production of a hidden photon and a hidden Higgs boson with the KLOE detector at DA$\Phi $NE, where the hidden photon decays into a pair of muons and the hidden Higgs boson lighter than ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ escape detection. See their Figs. 6 and 7 for mass-dependent limits on a product of the hidden fine structure constant and the kinetic mixing.
38  ANASTASI 2015A look for the decay ${{\mathit \gamma}^{\,'}}$ $\rightarrow$ ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ in the reaction ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}{{\mathit \gamma}}$ . Limits between $1.7 \times 10^{-3}$ and $0.01$ are obtained for ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $5 - 320$ MeV (see their Fig. 7).
39  BATLEY 2015A look for ${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}^{\,'}}$ ( ${{\mathit \gamma}^{\,'}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ ) at the NA48/2 experiment. Limits between $4.2 \times 10^{-4}$ and $8.8 \times 10^{-3}$ are obtained for ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $9 - 120$ MeV (see their Fig. 4).
40  JAEGLE 2015 look for the decay ${{\mathit \gamma}^{\,'}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ , ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ , or ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ in the dark Higgstrahlung channel, ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \gamma}^{\,'}}{{\mathit H}^{\,'}}$ ( ${{\mathit H}^{\,'}}$ $\rightarrow$ ${{\mathit \gamma}^{\,'}}{{\mathit \gamma}^{\,'}}$ ) at the BELLE experiment. They set limits on a product of the branching fraction and the Born cross section as well as a product of the hidden fine structure constant and the kinetic mixing. See their Figs. 3 and 4.
41  KAZANAS 2015 set limits by studying the decay of hidden photons ${{\mathit \gamma}^{\,'}}$ $\rightarrow$ ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ inside and near the progenitor star of SN1987A. See their Fig. 6 for mass-dependent limits.
42  SUZUKI 2015 looked for hidden-photon dark matter with a dish antenna and derived limits assuming they constitute all the local dark matter. Their limits are $\chi $ $<$ $6 \times 10^{-12}$ for ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $1.9 - 4.3$ eV. See their Fig. 7 for mass-dependent limits.
43  VINYOLES 2015 performed a global fit analysis based on helioseismology and solar neutrino observations, and set the limits $\chi {\mathit m}_{{{\mathit \gamma}^{\,'}}}$ $<$ $1.8 \times 10^{-12}$ eV for ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $3 \times 10^{-5} - 8$ eV. See their Fig. 11.
44  ABE 2014F look for the photoelectric-like interaction in the XMASS detector assuming the hidden photon constitutes all the local dark matter. Limits between $2 \times 10^{-13}$ and $1 \times 10^{-12}$ are obtained, where the relation $\chi {}^{2}$ = $\alpha $'/$\alpha $ is used to translate the original bound on the ratio of the hidden and EM fine-structure constants. See their Fig. 3 for mass-dependent limits.
45  AGAKISHIEV 2014 look for hidden photons ${{\mathit \gamma}^{\,'}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ at the HADES experiment, and set limits on ${{\mathit \chi}}$ for ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $0.02 - 0.6$ GeV. See their Fig. 5 for mass-dependent limits.
46  BABUSCI 2014 look for the decay ${{\mathit \gamma}^{\,'}}$ $\rightarrow$ ${{\mathit \mu}^{+}}$ ${{\mathit \mu}^{-}}$ in the reaction ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}{{\mathit \gamma}}$ . Limits between $4 \times 10^{-3}$ and $9.0 \times 10^{-4}$ are obtained for 520 MeV $<$ ${\mathit m}_{{{\mathit \gamma}^{\,'}}}<$ 980 MeV (see their Fig. 7).
47  BATELL 2014 derived limits from the electron beam dump experiment at SLAC (E-137) by searching for events with recoil electrons by sub-GeV dark matter produced from the decay of the hidden photon. Limits at the level of are obtained for ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ = $10^{-3} - 1$ GeV, depending on the dark matter mass and the hidden gauge coupling (see their Fig. 2).
48  BLUEMLEIN 2014 analyzed the beam dump data taken at the U-70 accelerator to look for ${{\mathit \gamma}^{\,'}}$-bremsstrahlung and the subsequent decay into muon pairs and hadrons. See their Fig. 4 for mass-dependent excluded region.
49  FRADETTE 2014 studied effects of decay of relic hidden photons on BBN and CMB to set constraints on very small values of the kinetic mixing. See their Figs. 4 and 7 for mass-dependent excluded regions.
50  LEES 2014J look for hidden photons in the reaction ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}^{\,'}}$ ( ${{\mathit \gamma}^{\,'}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ , ${{\mathit \mu}^{+}}$ ${{\mathit \mu}^{-}}$ ). Limits at the level of $10^{-4} - 10^{-3}$ are obtained for 0.02 GeV $<$ ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ $<$ 10.2 GeV. See their Fig. 4 for mass-dependent limits.
51  MERKEL 2014 look for ${{\mathit \gamma}^{\,'}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ at the A1 experiment at the Mainz Microtron (MAMI). See their Fig. 3 for mass-dependent limits.
52  AN 2013B examined the stellar production of hidden photons, correcting an important error of the production rate of the longitudinal mode which now dominates. See their Fig. 2 for mass-dependent limits based on solar energy loss.
53  AN 2013C use the solar flux of hidden photons to set a limit on the atomic ionization rate in the XENON10 experiment. They find $\chi $ ${\mathit m}_{{{\mathit \gamma}^{\,'}}}$ $<$ $3 \times 10^{-12}$ eV for ${\mathit m}_{{{\mathit \gamma}^{\,'}}}<$ 1 eV. See their Fig. 2 for mass-dependent limits.
54  DIAMOND 2013 analyzed the beam dump data taken at the SLAC millicharge experiment to constrain a hidden photon invisibly decaying into lighter long-lived particles, which undergo elastic scattering off nuclei in the detector. Limits between $8 \times 10^{-4} - 0.02$ are obtained. The quoted limit is applied when the dark gauge coupling is set equal to the electromagnetic coupling. See their Fig.4 for mass-dependent limits.
55  GNINENKO 2013 used the data taken at the SINDRUM experiment to constrain the decay, ${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}^{\,'}}$ ( ${{\mathit \gamma}^{\,'}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ ) to derive limits. See their Fig. 2 for their mass-dependent excluded region.
56  HORVAT 2013 look for hidden-photo-electric effect in HPGe detectors induced by solar hidden photons. See their Fig. 3 for mass-dependent limits.
57  INADA 2013 search for hidden photons using an intense X-ray beamline at SPring-8. See their Fig. 4 for mass-dependent limits.
58  MIZUMOTO 2013 look for solar hidden photons. See their Fig. 5 for mass-dependent limits.
59  PARKER 2013 look for hidden photons using a cryogenic resonant microwave cavity. See their Fig.5 for mass-dependent limits.
60  PARKER 2013 derived a limit for the hidden photon CDM with a randomly oriented hidden photon field.
61  REDONDO 2013 examined the solar emission of hidden photons including the enhancement factor for the longitudinal mode pointed out by AN 2013B, and also updated stellar-energy loss arguments. See their Fig.3 for mass-dependent limits, including a review of the currently best limits from other arguments.
62  GNINENKO 2012A obtained bounds on B( ${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}^{\,'}}$ ) $\cdot{}$ B( ${{\mathit \gamma}^{\,'}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ ) from the NOMAD and PS191 neutrino experiments, and derived limits between $8 \times 10^{-8} - 2 \times 10^{-4}$. See their Fig.4 for mass-dependent excluded regions.
63  GNINENKO 2012B used the data taken at the CHARM experiment to constrain the decay, ${{\mathit \eta}}({{\mathit \eta}^{\,'}}$) $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}^{\,'}}$ ( ${{\mathit \gamma}^{\,'}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ ), and derived limits between $1 \times 10^{-7} - 1 \times 10^{-4}$. See their Fig.4 for mass-dependent excluded region.
64  ABRAHAMYAN 2011 look for ${{\mathit \gamma}^{\,'}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ in the electron-nucelon fixed-target experiment at the Jefferson Laboratory (APEX). See their Fig. 5 for mass-dependent limits.
65  BLUEMLEIN 2011 analyzed the beam dump data taken at the U-70 accelerator to look for ${{\mathit \pi}^{0}}$ $\rightarrow$ ${{\mathit \gamma}}{{\mathit \gamma}^{\,'}}$ ( ${{\mathit \gamma}^{\,'}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ ). See their Fig. 5 for mass-dependent limits.
66  BJORKEN 2009 analyzed the beam dump data taken at E137, E141, and E774 to constrain a hidden photon produced by bremsstrahlung, subsequently decaying into ${{\mathit e}^{+}}{{\mathit e}^{-}}$ , and derived limits between $10^{-7}$ and . See their Fig. 1 for mass-dependent excluded region.
67  BJORKEN 2009 required the energy loss in the ${{\mathit \gamma}^{\,'}}$ emission from the core of SN1987A not to exceed $10^{53}$ erg/s, and derived limits between $5 \times 10^{-9}$ and $2 \times 10^{-6}$. See their Fig. 1 for mass-dependent excluded region.
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