# ${{\boldsymbol \nu}}$ MAGNETIC MOMENT INSPIRE search

The coupling of neutrinos to an electromagnetic field is a characterized by a 3${\times }$3 matrix $\lambda$ of the magnetic ($\mu$) and electric ($\mathit d$) dipole moments ($\lambda$ = $\mu - \mathit id$). For Majorana neutrinos the matrix $\lambda$ is antisymmetric and only transition moments are allowed, while for Dirac neutrinos $\lambda$ is a general 3${\times }$3 matrix. In the standard electroweak theory extended to include neutrino masses (see FUJIKAWA 1980 ) ${{\mathit \mu}_{{\nu}}}$ = 3${{\mathit e}}{{\mathit G}_{{F}}}{\mathit m}_{{{\mathit \nu}}}/(8{{\mathit \pi}}{}^{2}\sqrt {2 }$) = 3.2${\times }10^{-19}({\mathit m}_{{{\mathit \nu}}}$/eV)${{\mathit \mu}_{{B}}}$, i.e. it is unobservably small given the known small neutrino masses. In more general models there is no longer a proportionality between neutrino mass and its magnetic moment, even though only massive neutrinos have nonvanishing magnetic moments without fine tuning.

Laboratory bounds on $\lambda$ are obtained via elastic ${{\mathit \nu}}-{{\mathit e}}$ scattering, where the scattered neutrino is not observed. The combinations of matrix elements of $\lambda$ that are constrained by various experiments depend on the initial neutrino flavor and on its propagation between source and detector (e.g., solar ${{\mathit \nu}_{{e}}}$ and reactor ${{\overline{\mathit \nu}}_{{e}}}$ do not constrain the same combinations). The listings below therefore identify the initial neutrino flavor.

Other limits, e.g. from various stellar cooling processes, apply to all neutrino flavors. Analogous flavor independent, but weaker, limits are obtained from the analysis of ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \nu}}{{\overline{\mathit \nu}}}{{\mathit \gamma}}$ collider experiments.

VALUE ($10^{-10}$ $\mu _{\mathit B}$) CL% DOCUMENT ID TECN  COMMENT
$<0.28$ 90 1
 2017 A
BORX Solar ${{\mathit \nu}}$ spectrum
$\bf{<0.29}$ 90 2
 2013
CNTR Reactor ${{\overline{\mathit \nu}}_{{e}}}$
$\bf{<6.8}$ 90 3
 2001
LSND ${{\mathit \nu}_{{e}}}{{\mathit e}}$ , ${{\mathit \nu}_{{\mu}}}{{\mathit e}}$ scattering
$\bf{<3900}$ 90 4
 2001
DONU ${{\mathit \nu}_{{\tau}}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \nu}_{{\tau}}}{{\mathit e}^{-}}$
• • • We do not use the following data for averages, fits, limits, etc. • • •
$<0.022$ 90 5
 2015
ASTR Red giants
$<0.1$ 95 6
 2014
ASTR
$<0.05$ 95 7
 2014 B
ASTR
$<0.045$ 95 8
 2013 A
ASTR Globular cluster M5
$<0.32$ 90 9
 2010
CNTR Reactor ${{\overline{\mathit \nu}}_{{e}}}$
$<2.2$ 90 10
 2010
TEXO Reactor ${{\overline{\mathit \nu}}_{{e}}}$
$\text{<0.011 - 0.027}$ 11
 2009
ASTR ${{\mathit \nu}_{{L}}}$ $\rightarrow$ ${{\mathit \nu}_{{R}}}$ in SN1987A
$<0.54$ 90 12
 2008 A
BORX Solar ${{\mathit \nu}}$ spectrum
$<0.58$ 90 13
 2007
CNTR Reactor ${{\overline{\mathit \nu}}_{{e}}}$
$<0.74$ 90 14
 2007
CNTR Reactor ${{\overline{\mathit \nu}}_{{e}}}$
$<0.9$ 90 15
 2005
Reactor ${{\overline{\mathit \nu}}_{{e}}}$
$<130$ 90 16
 2005
CNTR Reactor ${{\mathit \nu}_{{e}}}$
$<37$ 95 17
 2004
FIT Solar ${}^{8}\mathrm {B}{{\mathit \nu}}$ (SNO NC)
$<3.6$ 90 18
 2004
SKAM Solar ${{\mathit \nu}}$ spectrum
$<1.1$ 90 19
 2004
SKAM Solar ${{\mathit \nu}}$ spectrum (LMA region)
$<5.5$ 90 20
 2003 B
CNTR Solar ${{\mathit p}}{{\mathit p}}$ and Be ${{\mathit \nu}}$
$<1.0$ 90 21
 2003
Reactor ${{\overline{\mathit \nu}}_{{e}}}$
$<1.3$ 90 22
 2003 B
CNTR Reactor ${{\overline{\mathit \nu}}_{{e}}}$
$<2$ 90 23
 2002
FIT solar + reactor (Majorana ${{\mathit \nu}}$)
$<80000$ 90 24
 2000
RVUE ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \nu}}{{\overline{\mathit \nu}}}{{\mathit \gamma}}$
$\text{<0.01 - 0.04}$ 25
 1999
ASTR ${{\mathit \nu}_{{L}}}$ $\rightarrow$ ${{\mathit \nu}_{{R}}}$ in SN$~$1987A
$<1.5$ 90 26
 1999
SKAM Solar ${{\mathit \nu}}$ spectrum
$<0.03$ 27
 1999
ASTR Red giant luminosity
$<4$ 28
 1999
ASTR Solar cooling
$<44000$ 90
 1997 J
DLPH ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \nu}}{{\overline{\mathit \nu}}}{{\mathit \gamma}}$ at LEP
$<33000$ 90 29
 1997 Q
L3 ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \nu}}{{\overline{\mathit \nu}}}{{\mathit \gamma}}$ at LEP
$<0.62$ 30
 1997
COSM Depolarization in early universe plasma
$<27000$ 95 31
 1997
RVUE $\Gamma\mathrm {( {{\mathit Z}} \rightarrow {{\mathit \nu}} {{\mathit \nu}} )}$ at LEP
$<30$ 90
 1995 B
CHM2 ${{\mathit \nu}_{{\mu}}}$ ${{\mathit e}}$ $\rightarrow$ ${{\mathit \nu}_{{\mu}}}{{\mathit e}}$
$<55000$ 90
 1994
RVUE ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \nu}}{{\overline{\mathit \nu}}}{{\mathit \gamma}}$ at LEP
$<1.9$ 95 32
 1993
CNTR Reactor ${{\overline{\mathit \nu}}}$ ${{\mathit e}}$ $\rightarrow$ ${{\overline{\mathit \nu}}}{{\mathit e}}$
$<5400$ 90 33
 1992
BEBC ${{\mathit \nu}_{{\tau}}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \nu}_{{\tau}}}{{\mathit e}^{-}}$
$<2.4$ 90 34
 1992
CNTR Reactor ${{\overline{\mathit \nu}}}$ ${{\mathit e}}$ $\rightarrow$ ${{\overline{\mathit \nu}}}{{\mathit e}}$
$<56000$ 90
 1991
RVUE ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \nu}}{{\overline{\mathit \nu}}}{{\mathit \gamma}}$
$<100$ 95 35
 1991
CHRM ${{\mathit \nu}_{{\mu}}}$ ${{\mathit e}}$ $\rightarrow$ ${{\mathit \nu}_{{\mu}}}{{\mathit e}}$
$<8.5$ 90
 1990
CNTR ${{\mathit \nu}_{{\mu}}}$ ${{\mathit e}}$ $\rightarrow$ ${{\mathit \nu}_{{\mu}}}{{\mathit e}}$
$<10.8$ 90 36
 1990
CNTR LAMPF ${{\mathit \nu}}$ ${{\mathit e}}$ $\rightarrow$ ${{\mathit \nu}}{{\mathit e}}$
$<7.4$ 90 36
 1990
CNTR LAMPF (${{\mathit \nu}_{{\mu}}}$, ${{\overline{\mathit \nu}}_{{\mu}}}$ ) ${{\mathit e}}$ elast.
$<0.02$ 37
 1990
ASTR Red giant luminosity
$<0.1$ 38
 1989 B
ASTR Cooling helium stars
39
 1988
COSM Primordial magn. fields
$<40000$ 90 40
 1988
RVUE ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \nu}}{{\overline{\mathit \nu}}}{{\mathit \gamma}}$
$<=.3$ 38
 1988 B
ASTR ${}^{}\mathrm {He}$ burning stars
$<0.11$ 38
 1987
ASTR Cooling helium stars
$<0.0006$ 41
 1987
ASTR Cosmic EM backgrounds
$\text{<0.1 - 0.2}$
 1981
COSM ${}^{4}\mathrm {He}$ abundance
$<0.85$
 1978
ASTR Stellar plasmons
$<0.6$ 42
 1976
ASTR Red giants + degenerate dwarfs
$<81$ 43
 1974
RVUE ${{\overline{\mathit \nu}}_{{\mu}}}$ ${{\mathit e}}$ $\rightarrow$ ${{\overline{\mathit \nu}}_{{\mu}}}{{\mathit e}}$
$<1$
 1963
ASTR Solar cooling
$<14$
 1957
CNTR Reactor ${{\overline{\mathit \nu}}}$
1  AGOSTINI 2017A obtained this limit using the shape of the recoil electron energy spectrum from the Borexino Phase-II 1291.5 live days of solar neutrino data and the constraints on the sum of the solar neutrino fluxes from the radiochemical gallium experiments SAGE, Gallex, and GNO. Without radiochemical constraints, the 90$\%$ C.L. limit of $<4.0 \times 10^{-11}\mu _{B}$ is obtained.
2  BEDA 2013 report ${{\overline{\mathit \nu}}_{{e}}}{{\mathit e}^{-}}$ scattering results, using the Kalinin Nuclear Power Plant and a shielded ${}^{}\mathrm {Ge}$ detector. The recoil electron spectrum is analyzed between 2.5 and 55 keV. Supersedes BEDA 2007 . Supersedes BEDA 2010 . This is the most stringent limit on the magnetic moment of reactor ${{\overline{\mathit \nu}}_{{e}}}$.
3  AUERBACH 2001 limit is based on the LSND ${{\mathit \nu}_{{e}}}$ and ${{\mathit \nu}_{{\mu}}}$ electron scattering measurements. The limit is slightly more stringent than KRAKAUER 1990 .
4  SCHWIENHORST 2001 quote an experimental sensitivity of $4.9 \times 10^{-7}$.
5  ARCEO-DIAZ 2015 constrains the neutrino magnetic moment from observation of the tip of the red giant branch in the globular cluster $\omega$-Centauri.
6  CORSICO 2014 constrains the neutrino magnetic moment from observations of white drarf pulsations.
7  MILLER-BERTOLAMI 2014B constrains the neutrino magnetic moment from observations of the white dwarf luminosity function of the Galactic disk.
8  VIAUX 2013A constrains the neutrino magnetic moment from observations of the globular cluster M5.
9  BEDA 2010 report ${{\overline{\mathit \nu}}_{{e}}}{{\mathit e}^{-}}$ scattering results, using the Kalinin Nuclear Power Plant and a shielded ${}^{}\mathrm {Ge}$ detector. The recoil electron spectrum is analyzed between 2.9 and 45 keV. Supersedes BEDA 2007 . Superseded by BEDA 2013 .
10  DENIZ 2010 observe reactor ${{\overline{\mathit \nu}}_{{e}}}{{\mathit e}}$ scattering with recoil kinetic energies $3 - 8$ MeV using CsI(Tl) detectors. The observed rate and spectral shape are consistent with the Standard Model prediction, leading to the reported constraint on ${{\overline{\mathit \nu}}_{{e}}}$ magnetic moment.
11  KUZNETSOV 2009 obtain a limit on the flavor averaged magnetic moment of Dirac neutrinos from the time averaged neutrino signal of SN1987A. Improves and supersedes the analysis of BARBIERI 1988 and AYALA 1999 .
12  ARPESELLA 2008A obtained this limit using the shape of the recoil electron energy spectrum from the Borexino 192 live days of solar neutrino data.
13  BEDA 2007 performed search for electromagnetic ${{\overline{\mathit \nu}}_{{e}}}-{{\mathit e}}$ scattering at Kalininskaya nuclear reactor. A ${}^{}\mathrm {Ge}$ detector with active and passive shield was used and the electron recoil spectrum between 3.0 and 61.3 keV analyzed. Superseded by BEDA 2010 .
14  WONG 2007 performed search for non-standard ${{\overline{\mathit \nu}}_{{e}}}-{{\mathit e}}$ scattering at the Kuo-Sheng nuclear reactor. Ge detector equipped with active anti-Compton shield is used. Most stringent laboratory limit on magnetic moment of reactor ${{\overline{\mathit \nu}}_{{e}}}$. Supersedes LI 2003B.
15  DARAKTCHIEVA 2005 present the final analysis of the search for non-standard ${{\overline{\mathit \nu}}_{{e}}}-{{\mathit e}}$ scattering component at Bugey nuclear reactor. Full kinematical event reconstruction of both the kinetic energy above 700 keV and scattering angle of the recoil electron, by use of TPC. Most stringent laboratory limit on magnetic moment. Supersedes DARAKTCHIEVA 2003 .
16  XIN 2005 evaluated the ${{\mathit \nu}_{{e}}}$ flux at the Kuo-Sheng nuclear reactor and searched for non-standard ${{\mathit \nu}_{{e}}}-{{\mathit e}}$ scattering. Ge detector equipped with active anti-Compton shield was used. This laboratory limit on magnetic moment is considerably less stringent than the limits for reactor ${{\overline{\mathit \nu}}_{{e}}}$, but is specific to ${{\mathit \nu}_{{e}}}$.
17  GRIFOLS 2004 obtained this bound using the SNO data of the solar ${}^{8}\mathrm {B}$ neutrino flux measured with deuteron breakup. This bound applies to ${{\mathit \mu}}_{{\mathrm {eff}}}$ = (${{\mathit \mu}}{}^{2}_{21}$ + ${{\mathit \mu}}{}^{2}_{22}$ + ${{\mathit \mu}}{}^{2}_{23}){}^{1/2}$.
18  LIU 2004 obtained this limit using the shape of the recoil electron energy spectrum from the Super-Kamiokande-I 1496 days of solar neutrino data. Neutrinos are assumed to have only diagonal magnetic moments, ${{\mathit \mu}_{{\nu1}}}$ = ${{\mathit \mu}_{{\nu2}}}$. This limit corresponds to the oscillation parameters in the vacuum oscillation region.
19  LIU 2004 obtained this limit using the shape of the recoil electron energy spectrum from the Super-Kamiokande-I 1496 live-day solar neutrino data, by limiting the oscillation parameter region in the LMA region allowed by solar neutrino experiments plus KamLAND. ${{\mathit \mu}_{{\nu1}}}$ = ${{\mathit \mu}_{{\nu2}}}$ is assumed. In the LMA region, the same limit would be obtained even if neutrinos have off-diagonal magnetic moments.
20  BACK 2003B obtained this bound from the results of background measurements with Counting Test Facility (the prototype of the Borexino detector). Standard Solar Model flux was assumed. This ${{\mathit \mu}_{{\nu}}}$ can be different from the reactor ${{\mathit \mu}_{{\nu}}}$ in certain oscillation scenarios (see BEACOM 1999 ).
21  DARAKTCHIEVA 2003 searched for non-standard ${{\overline{\mathit \nu}}_{{e}}}$-e scattering component at Bugey nuclear reactor. Full kinematical event reconstruction by use of TPC. Superseded by DARAKTCHIEVA 2005 .
22  LI 2003B used Ge detector in active shield near nuclear reactor to test for nonstandard ${{\overline{\mathit \nu}}_{{e}}}-{{\mathit e}}$ scattering.
23  GRIMUS 2002 obtain stringent bounds on all Majorana neutrino transition moments from a simultaneous fit of LMA-MSW oscillation parameters and transition moments to global solar neutrino data + reactor data. Using only solar neutrino data, a 90$\%$ CL bound of $6.3 \times 10^{-10}\mu _{{{\mathit B}}}$ is obtained.
24  TANIMOTO 2000 combined ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \nu}}{{\overline{\mathit \nu}}}{{\mathit \gamma}}$ data from VENUS, TOPAZ, and AMY.
25  AYALA 1999 improves the limit of BARBIERI 1988 .
26  BEACOM 1999 obtain the limit using the shape, but not the absolute magnitude which is affected by oscillations, of the solar neutrino spectrum obtained by Superkamiokande (825 days). This $\mu _{{{\mathit \nu}}}$ can be different from the reactor $\mu _{{{\mathit \nu}}}$ in certain oscillation scenarios.
27  RAFFELT 1999 is an update of RAFFELT 1990 . This limit applies to all neutrino flavors which are light enough ($<5~$keV) to be emitted from globular-cluster red giants. This limit pertains equally to electric dipole moments and magnetic transition moments, and it applies to both Dirac and Majorana neutrinos.
28  RAFFELT 1999 is essentially an update of BERNSTEIN 1963 , but is derived from the helioseismological limit on a new energy-loss channel of the Sun. This limit applies to all neutrino flavors which are light enough ($<1~$keV) to be emitted from the Sun. This limit pertains equally to electric dipole and magnetic transition moments, and it applies to both Dirac and Majorana neutrinos.
29  ACCIARRI 1997Q result applies to both direct and transition magnetic moments and for $\mathit q{}^{2}$=0.
30  ELMFORS 1997 calculate the rate of depolarization in a plasma for neutrinos with a magnetic moment and use the constraints from a big-bang nucleosynthesis on additional degrees of freedom.
31  Applies to absolute value of magnetic moment.
32  DERBIN 1993 determine the cross section for $0.6 - 2.0$ MeV electron energy as ($1.28$ $\pm0.63){\times }\sigma _{{\mathrm {weak}}}$. However, the (reactor on -- reactor off)/(reactor off) is only $\sim{}$1/100.
33  COOPER-SARKAR 1992 assume $\mathit f_{{{\mathit D}_{{s}}}}/\mathit f_{{{\mathit \pi}}}$ = 2 and ${{\mathit D}_{{s}}}$, ${{\overline{\mathit D}}_{{s}}}$ production cross section = $2.6$ $\mu$b to calculate ${{\mathit \nu}}$ flux.
34  VIDYAKIN 1992 limit is from a ${{\mathit e}}{{\overline{\mathit \nu}}_{{e}}}$ elastic scattering experiment. No experimental details are given except for the cross section from which this limit is derived. Signal/noise was 1/10. The limit uses sin$^2\theta _{\mathit W}$ = $0.23$ as input.
35  DORENBOSCH 1991 corrects an incorrect statement in DORENBOSCH 1989 that the ${{\mathit \nu}}$ magnetic moment is $<~1 \times 10^{-9}$ at the 95$\%$CL. DORENBOSCH 1989 measures both ${{\mathit \nu}_{{\mu}}}{{\mathit e}}$ and ${{\overline{\mathit \nu}}}{{\mathit e}}$ elastic scattering and assume $\mu\mathrm {({{\mathit \nu}})}$ = $\mu\mathrm {({{\overline{\mathit \nu}}})}$.
36  KRAKAUER 1990 experiment fully reported in ALLEN 1993 .
37  RAFFELT 1990 limit applies for a diagonal magnetic moment of a Dirac neutrino, or for a transition magnetic moment of a Majorana neutrino. In the latter case, the same analysis gives $<1.4 \times 10^{-12}$. Limit at 95$\%$CL obtained from $\delta \mathit M_{\mathit c}$.
38  Significant dependence on details of stellar models.
39  FUKUGITA 1988 find magnetic dipole moments of any two neutrino species are bounded by $\mu$ $<$ $10^{-16}$ [$10^{-9}~\mathit G/{{\mathit B}}_{0}$] where ${{\mathit B}}_{0}$ is the present-day intergalactic field strength.
40  GROTCH 1988 combined data from MAC, ASP, CELLO, and Mark$~$J.
41  For ${\mathit m}_{{{\mathit \nu}}}$ = 8$-$200 eV. NUSSINOV 1987 examines transition magnetic moments for ${{\mathit \nu}_{{\mu}}}$ $\rightarrow$ ${{\mathit \nu}_{{e}}}$ and obtain $<$ $3 \times 10^{-15}$ for ${\mathit m}_{{{\mathit \nu}}}$ $>$ 16 eV and $<$ $6 \times 10^{-14}$ for ${\mathit m}_{{{\mathit \nu}}}$ $>$ 4 eV.
42  We obtain above limit from SUTHERLAND 1976 using their limit $\mathit f$ $<$ 1/3.
43  KIM 1974 is a theoretical analysis of ${{\overline{\mathit \nu}}_{{\mu}}}$ reaction data.
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 ARCEO-DIAZ 2015
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