Measures $\sum\vert \mathit U_{ {{\mathit \ell}} {{\mathit j}} }\vert ^2$ $\Gamma _{{{\mathit j}}}{\mathit m}_{{{\mathit j}}}{}^{-1}$, where the sum is over mass eigenstates which cannot be resolved experimentally. Some of the limits constrain the radiative decay and are based on the limit of the corresponding photon flux. Other apply to the decay of a heavier neutrino into the lighter one and a Majoron or other invisible particle. Many of these limits apply to any ${{\mathit \nu}}$ within the indicated mass range.

Limits on the radiative decay are either directly based on the limits of the corresponding photon flux, or are derived from the limits on the neutrino magnetic moments. In the later case the transition rate for ${{\mathit \nu}_{{i}}}$ $\rightarrow$ ${{\mathit \nu}_{{j}}}{+}$ ${{\mathit \gamma}}$ is constrained by $\Gamma _{ij}$ = ${1\over \tau _{ij}}$ = ${(\mathit m{}^{2}_{i} − \mathit m{}^{2}_{j}){}^{3}\over \mathit m{}^{3}_{i}}$ $\mu {}^{2}_{ij}$ where $\mu _{ij}$ is the neutrino transition moment in the mass eigenstates basis. Typically, the limits on lifetime based on the magnetic moments are many orders of magnitude more restrictive than limits based on the nonobservation of photons.

VALUE (s/eV) CL% DOCUMENT ID TECN  COMMENT $\bf{>15.4}$ 90 1 KRAKAUER 1991 CNTR ${{\mathit \nu}_{{\mu}}}$, ${{\overline{\mathit \nu}}_{{\mu}}}$ at LAMPF $\bf{>7 \times 10^{9}}$ 2 RAFFELT 1985 ASTR $\bf{>300}$ 90 3 REINES 1974 CNTR ${{\overline{\mathit \nu}}_{{e}}}$ • • We do not use the following data for averages, fits, limits, etc. • • $>8.08 \times 10^{-5}$ 90 4 AHARMIM 2019 SNO ${{\mathit \nu}_{{2}}}$ invisible nonradiative decay $>1.92 \times 10^{-3}$ 90 5 AHARMIM 2019 FIT ${{\mathit \nu}_{{2}}}$ invisible nonradiative decay $ 6 - 26 \times 10^{9}$ 95 6 ESCUDERO 2019 COSM Invisible decay ${\mathit m}_{{{\mathit \nu}}}{}\geq{}$ 0.05 eV $>\text{E5}−\text{E10}$ 95 7 CECCHINI 2011 ASTR ${{\mathit \nu}_{{2}}}$ $\rightarrow{{\mathit \nu}_{{1}}}$ radiative decay 8 MIRIZZI 2007 CMB radiative decay 9 MIRIZZI 2007 CIB radiative decay 10 WONG 2007 CNTR Reactor ${{\overline{\mathit \nu}}_{{e}}}$ $> 0.11$ 90 11 XIN 2005 CNTR Reactor ${{\mathit \nu}_{{e}}}$ 12 XIN 2005 CNTR Reactor ${{\mathit \nu}_{{e}}}$ $> 0.004$ 90 13 AHARMIM 2004 SNO quasidegen. ${{\mathit \nu}}$ masses $>4.4 \times 10^{-5}$ 90 13 AHARMIM 2004 SNO hierarchical ${{\mathit \nu}}$ masses ${ {}\gtrsim{} } \text{ 100}$ 95 14 CECCHINI 2004 ASTR Radiative decay for ${{\mathit \nu}}$ mass $>$ 0.01 eV $> 0.067$ 90 15 EGUCHI 2004 KLND quasidegen. ${{\mathit \nu}}$ masses $>1.1 \times 10^{-3}$ 90 15 EGUCHI 2004 KLND hierarchical ${{\mathit \nu}}$ masses $>8.7 \times 10^{-5}$ 99 16 BANDYOPADHYAY 2003 FIT nonradiative decay $>=4200$ 90 17 DERBIN 2002 B CNTR Solar ${{\mathit p}}{{\mathit p}}$ and ${}^{}\mathrm {Be}{{\mathit \nu}}$ $>2.8 \times 10^{-5}$ 99 18 JOSHIPURA 2002 B FIT nonradiative decay 19 DOLGOV 1999 COSM 20 BILLER 1998 ASTR ${\mathit m}_{{{\mathit \nu}}}$= $0.05 - 1$ eV $>2.8 \times 10^{15}$ 21, 22 BLUDMAN 1992 ASTR ${\mathit m}_{{{\mathit \nu}}}<$ 50 eV $\text{none } 10^{-12} − 5 \times 10^{4}$ 23 DODELSON 1992 ASTR ${\mathit m}_{{{\mathit \nu}}}=1 - 300$ keV $< 10^{-12} \text{ or > 5 }\times 10^{4}$ 23 DODELSON 1992 ASTR ${\mathit m}_{{{\mathit \nu}}}=1 - 300$ keV 24 GRANEK 1991 COSM Decaying ${{\mathit L}^{0}}$ $>6.4$ 90 25 KRAKAUER 1991 CNTR ${{\mathit \nu}_{{e}}}$ at LAMPF $>1.1 \times 10^{15}$ 26 WALKER 1990 ASTR ${\mathit m}_{{{\mathit \nu}}}$= $0.03$ $-\sim{}$2 MeV $>6.3 \times 10^{15}$ 27, 22 CHUPP 1989 ASTR ${\mathit m}_{{{\mathit \nu}}}<$ 20 eV $>1.7 \times 10^{15}$ 22 KOLB 1989 ASTR ${\mathit m}_{{{\mathit \nu}}}<$ 20 eV 28 RAFFELT 1989 RVUE ${{\overline{\mathit \nu}}}$ (Dirac, Majorana) 29 RAFFELT 1989 B ASTR $>8.3 \times 10^{14}$ 30 VONFEILITZSCH 1988 ASTR $>22$ 68 31 OBERAUER 1987 ${{\overline{\mathit \nu}}_{{R}}}$ (Dirac) $>38$ 68 31 OBERAUER 1987 ${{\overline{\mathit \nu}}}$ (Majorana) $>59$ 68 31 OBERAUER 1987 ${{\overline{\mathit \nu}}_{{L}}}$ (Dirac) $>30$ 68 KETOV 1986 CNTR ${{\overline{\mathit \nu}}}$ (Dirac) $>20$ 68 KETOV 1986 CNTR ${{\overline{\mathit \nu}}}$ (Majorana) 32 BINETRUY 1984 COSM ${\mathit m}_{{{\mathit \nu}}}\sim{}$ 1 MeV $>0.11$ 90 33 FRANK 1981 CNTR ${{\mathit \nu}}{{\overline{\mathit \nu}}}$ LAMPF $>2 \times 10^{21}$ 34 STECKER 1980 ASTR ${\mathit m}_{{{\mathit \nu}}}$= $10 - 100$ eV $>0.01$ 90 33 BLIETSCHAU 1978 HLBC ${{\mathit \nu}_{{\mu}}}$, CERN GGM $>0.017$ 90 33 BLIETSCHAU 1978 HLBC ${{\overline{\mathit \nu}}_{{\mu}}}$, CERN GGM $<3 \times 10^{-11}$ 35 FALK 1978 ASTR ${\mathit m}_{{{\mathit \nu}}}<$10 MeV $>2.2 \times 10^{-3}$ 90 33 BARNES 1977 DBC ${{\mathit \nu}}$, ANL 12-ft 36 COWSIK 1977 ASTR $>3. \times 10^{-3}$ 90 33 BELLOTTI 1976 HLBC ${{\mathit \nu}}$, CERN GGM $>0.013$ 90 33 BELLOTTI 1976 HLBC ${{\overline{\mathit \nu}}}$, CERN GGM 1  KRAKAUER 1991 quotes the limit $\tau /{\mathit m}_{{{\mathit \nu}_{{1}}}}$ $>$ ($0.75\mathit a{}^{2}$ $+$ $21.65\mathit a$ $+$ $26.3)~$s/eV, where $\mathit a$ is a parameter describing the asymmetry in the neutrino decay defined as $\mathit dN_{{{\mathit \gamma}}}/\mathit d$cos $\theta $ = (1/2)(1$~+~\mathit a$cos $\theta $) The parameter $\mathit a~=~$0 for a Majorana neutrino, but can vary from $-1$ to 1 for a Dirac neutrino. The bound given by the authors is the most conservative (which applies for $\mathit a~=~-1$). 2  RAFFELT 1985 limit on the radiative decay is from solar x- and $\gamma $-ray fluxes. Limit depends on ${{\mathit \nu}}~$flux from ${{\mathit p}}{{\mathit p}}$ , now established from GALLEX and SAGE to be $>0.5$ of expectation. 3  REINES 1974 looked for ${{\mathit \nu}}$ of nonzero mass decaying radiatively to a neutral of lesser mass + ${{\mathit \gamma}}$. Used liquid scintillator detector near fission reactor. Finds lab lifetime $6 \times 10^{7}~$s or more. Above value of (mean life)/mass assumes average effective neutrino energy of 0.2 MeV. To obtain the limit $6 \times 10^{7}~$s REINES 1974 assumed that the full ${{\overline{\mathit \nu}}_{{e}}}$ reactor flux could be responsible for yielding decays with photon energies in the interval 0.1 MeV $-$ 0.5 MeV. This represents some overestimate so their lower limit is an over-estimate of the lab lifetime (VOGEL 1984 ). If so, OBERAUER 1987 may be comparable or better. 4  AHARMIM 2019 quotes the limit $\tau /{\mathit m}_{{{\mathit \nu}_{{2}}}}$ for invisible nonradiative decay of ${{\mathit \nu}_{{2}}}$. They obtained this result by analyzing the entire SNO dataset, allowing for the decay of ${{\mathit \nu}_{{2}}}$ which would cause an energy-dependent distortion of the survival probability of electron-type solar neutrinos. 5  AHARMIM 2019 quotes the limit $\tau /{\mathit m}_{{{\mathit \nu}_{{2}}}}$ for invisible nonradiative decay of ${{\mathit \nu}_{{2}}}$. They obtained this result by combining the $\tau /{\mathit m}_{{{\mathit \nu}_{{2}}}}$ measurements from SNO and other solar neutrino experiments (Super-Kamiokande, KamLAND, and Borexino ${}^{8}\mathrm {B}$ results; Borexino and KamLAND ${}^{7}\mathrm {Be}$ results; the combined gallium interaction rate from GNO, GALLEX, and SAGE; and the chlorine interaction rate from Homestake). The quoted limit at 99$\%$ CL is $>1.04 \times 10^{-3}$. 6  ESCUDERO 2019 sets limits on invisible neutrino decays using Planck 2018 data of $\tau $ $>$ $1.3 - 0.3 \times 10^{9}$ s at 95$\%$ C.L. Values in the range $\tau $ = $2 - 16 \times 10^{9}$ s are preferred at 95$\%$ C.L. when Planck polarization data is included. Limits scale as (${\mathit m}_{{{\mathit \nu}}}$/0.05 eV)${}^{3}$. 7  CECCHINI 2011 search for radiative decays of solar neutrinos into visible photons during the 2006 total solar eclipse. The range of (mean life)/mass values corresponds to a range of ${{\mathit \nu}_{{1}}}$ masses between $10^{-4}$ and 0.1 eV. 8  MIRIZZI 2007 determine a limit on the neutrino radiative decay from analysis of the maximum allowed distortion of the CMB spectrum as measured by the COBE/FIRAS. For the decay ${{\mathit \nu}_{{2}}}$ $\rightarrow$ ${{\mathit \nu}_{{1}}}$ the lifetime limit is ${ {}\lesssim{} }4 \times 10^{20}$ s for ${ {}\lesssim{} }$ 0.14 eV. For transition with the $\vert \Delta \mathit m_{31}\vert $ mass difference the lifetime limit is $\sim{}2 \times 10^{19}$ s for ${ {}\lesssim{} }$ 0.14 eV and $\sim{}5 \times 10^{20}$ s for ${ {}\gtrsim{} }$ 0.14 eV. 9  MIRIZZI 2007 determine a limit on the neutrino radiative decay from analysis of the cosmic infrared background (CIB) using the Spitzer Observatory data. For transition with the $\vert \Delta \mathit m_{31}\vert $ mass difference they obtain the lifetime limit $\sim{}10^{20}$ s for ${ {}\lesssim{} }0.14~$eV. 10  WONG 2007 use their limit on the neutrino magnetic moment together with the assumed experimental value of $\Delta \mathit m{}^{2}_{13}\sim{}2 \times 10^{-3}$ eV${}^{2}$ to obtain ${{\mathit \tau}_{{13}}}/\mathit m{}^{3}_{1}>3.2 \times 10^{27}$ s/eV${}^{3}$ for the radiative decay in the case of the inverted mass hierarchy. Similarly to RAFFELT 1989 this limit can be violated if electric and magnetic moments are equal to each other. Analogous, but numerically somewhat different limits are obtained for ${{\mathit \tau}_{{23}}}$ and ${{\mathit \tau}_{{21}}}$. 11  XIN 2005 search for the ${{\mathit \gamma}}$ from radiative decay of ${{\mathit \nu}_{{e}}}$ produced by the electron capture on ${}^{51}\mathrm {Cr}$. No events were seen and the limit on $\tau /{\mathit m}_{{{\mathit \nu}}}$ was derived. This is a weaker limit on the decay of ${{\mathit \nu}_{{e}}}$ than KRAKAUER 1991 . 12  XIN 2005 use their limit on the neutrino magnetic moment of ${{\mathit \nu}_{{e}}}$ together with the assumed experimental value of $\Delta $ $\sim{}$ $2 \times 10^{-3}~$eV${}^{2}$ to obtain $\tau _{13}/\mathit m{}^{3}_{1}$ $>$ $1 \times 10^{23}~$s/eV${}^{3}$ for the radiative decay in the case of the inverted mass hierarchy. Similarly to RAFFELT 1989 this limit can be violated if electric and magnetic moments are equal to each other. Analogous, but numerically somewhat different limits are obtained for $\tau _{23}$ and $\tau _{21}$. Again, this limit is specific for ${{\mathit \nu}_{{e}}}$. 13  AHARMIM 2004 obtained these results from the solar ${{\overline{\mathit \nu}}_{{e}}}$ flux limit set by the SNO measurement assuming ${{\mathit \nu}_{{2}}}$ decay through nonradiative process ${{\mathit \nu}_{{2}}}$ $\rightarrow$ ${{\overline{\mathit \nu}}_{{1}}}{{\mathit X}}$ , where ${{\mathit X}}$ is a Majoron or other invisible particle. Limits are given for the cases of quasidegenerate and hierarchical neutrino masses. 14  CECCHINI 2004 obtained this bound through the observations performed on the occasion of the 21 June 2001 total solar eclipse, looking for visible photons from radiative decays of solar neutrinos. Limit is a $\tau /{\mathit m}_{{{\mathit \nu}_{{2}}}}$ in ${{\mathit \nu}_{{2}}}$ $\rightarrow$ ${{\mathit \nu}_{{1}}}{{\mathit \gamma}}$ . Limit ranges from $\sim{}$ 100 to $10^{7}~$s/eV for 0.01 $<$ ${\mathit m}_{{{\mathit \nu}_{{1}}}}$ $<$ 0.1 eV. 15  EGUCHI 2004 obtained these results from the solar ${{\overline{\mathit \nu}}_{{e}}}$ flux limit set by the KamLAND measurement assuming ${{\mathit \nu}_{{2}}}$ decay through nonradiative process ${{\mathit \nu}_{{2}}}$ $\rightarrow$ ${{\overline{\mathit \nu}}_{{1}}}{{\mathit X}}$ , where ${{\mathit X}}$ is a Majoron or other invisible particle. Limits are given for the cases of quasidegenerate and hierarchical neutrino masses. 16  The ratio of the lifetime over the mass derived by BANDYOPADHYAY 2003 is for ${{\mathit \nu}_{{2}}}$. They obtained this result using the following solar-neutrino data: total rates measured in Cl and Ga experiments, the Super-Kamiokande's zenith-angle spectra, and SNO's day and night spectra. They assumed that ${{\mathit \nu}_{{1}}}$ is the lowest mass, stable or nearly stable neutrino state and ${{\mathit \nu}_{{2}}}$ decays through nonradiative Majoron emission process, ${{\mathit \nu}_{{2}}}$ $\rightarrow$ ${{\overline{\mathit \nu}}_{{1}}}$ , or through nonradiative process with all the final state particles being sterile. The best fit is obtained in the region of the LMA solution. 17  DERBIN 2002B (also BACK 2003B) obtained this bound for the radiative decay from the results of background measurements with Counting Test Facility (the prototype of the Borexino detector). The laboratory gamma spectrum is given as $\mathit dN_{\gamma }/\mathit d$ cos $\theta $= (1/2) (1 + $\alpha $cos $\theta $) with $\alpha $=0 for a Majorana neutrino, and $\alpha $ varying to $-1$ to 1 for a Dirac neutrino. The listed bound is for the case of $\alpha $=0. The most conservative bound $1.5 \times 10^{3}~$s$~$eV${}^{-1}$ is obtained for the case of $\alpha =-1$. 18  The ratio of the lifetime over the mass derived by JOSHIPURA 2002B is for ${{\mathit \nu}_{{2}}}$. They obtained this result from the total rates measured in all solar neutrino experiments. They assumed that ${{\mathit \nu}_{{1}}}$ is the lowest mass, stable or nearly stable neutrino state and ${{\mathit \nu}_{{2}}}$ decays through nonradiative process like Majoron emission decay, ${{\mathit \nu}_{{2}}}$ $\rightarrow$ ${{\mathit \nu}_{{1}}^{\,'}}$ where ${{\mathit \nu}_{{1}}^{\,'}}$ state is sterile. The exact limit depends on the specific solution of the solar neutrino problem. The quoted limit is for the LMA solution. 19  DOLGOV 1999 places limits in the (Majorana) ${{\mathit \tau}}$-associated$~{{\mathit \nu}}$ mass-lifetime plane based on nucleosynthesis. Results would be considerably modified if neutrino oscillations exist. 20  BILLER 1998 use the observed TeV ${{\mathit \gamma}}$-ray spectra to set limits on the mean life of any radiatively decaying neutrino between $0.05$ and 1$~$eV. Curve shows $\tau _{{{\mathit \nu}}}/B_{{{\mathit \gamma}}}>0.15 \times 10^{21}~$s at $0.05~$eV, $>1.2 \times 10^{21}~$s at $0.17~$eV, $>3 \times 10^{21}~$s at $1~$eV, where B$_{{{\mathit \gamma}}}$ is the branching ratio to photons. 21  BLUDMAN 1992 sets additional limits by this method for higher mass ranges. Cosmological limits are also obtained. 22  Limit on the radiative decay based on nonobservation of ${{\mathit \gamma}}$'s in coincidence with ${{\mathit \nu}}$'s from SN$~$1987A. 23  DODELSON 1992 range is for wrong-helicity keV mass Dirac ${{\mathit \nu}}$'s from the core of neutron star in SN$~$1987A decaying to ${{\mathit \nu}}$'s that would have interacted in KAM2 or IMB detectors. 24  GRANEK 1991 considers heavy neutrino decays to ${{\mathit \gamma}}{{\mathit \nu}_{{L}}}$ and 3 ${{\mathit \nu}_{{L}}}$ , where ${\mathit m}_{{{\mathit \nu}_{{L}}}}<$100 keV. Lifetime is calculated as a function of heavy neutrino mass, branching ratio into ${{\mathit \gamma}}{{\mathit \nu}_{{L}}}$ , and ${\mathit m}_{{{\mathit \nu}_{{L}}}}$. 25  KRAKAUER 1991 quotes the limit for ${{\mathit \nu}_{{e}}}$, $\tau /{\mathit m}_{{{\mathit \nu}}}$ $>$ ($0.3\mathit a{}^{2}$ $+$ $9.8\mathit a$ $+$ $15.9)~$s/eV, where $\mathit a$ is a parameter describing the asymmetry in the radiative neutrino decay defined as $\mathit dN_{{{\mathit \gamma}}}/\mathit d$cos $\theta $ = (1/2)(1$~+~\mathit a$cos $\theta $) $\mathit a~=~$0 for a Majorana neutrino, but can vary from $-1$ to 1 for a Dirac neutrino. The bound given by the authors is the most conservative (which applies for $\mathit a~=~-1$). 26  WALKER 1990 uses SN 1987A ${{\mathit \gamma}}$ flux limits after 289 days. 27  CHUPP 1989 should be multiplied by a branching ratio (about 1) and a detection efficiency (about 1/4), and pertains to radiative decay of any neutrino to a lighter or sterile neutrino. 28  RAFFELT 1989 uses KYULDJIEV 1984 to obtain $\tau \mathit m{}^{3}$ $>$ $3 \times 10^{18}~$s eV${}^{3}$ (based on ${{\overline{\mathit \nu}}_{{e}}}{{\mathit e}^{-}}$ cross sections). The bound for the radiative decay is not valid if electric and magnetic transition moments are equal for Dirac neutrinos. 29  RAFFELT 1989B analyze stellar evolution and exclude the region $3 \times 10^{12}$ $<$ $\tau \mathit m{}^{3}$ $<$ $3 \times 10^{21}~$s$~$eV${}^{3}$. 30  Model-dependent theoretical analysis of SN$~$1987A neutrinos. Quoted limit is for $\sum_{j}\vert \mathit U_{ {{\mathit \ell}} {{\mathit j}} }\vert ^2$ $\Gamma _{{{\mathit j}}}{\mathit m}_{{{\mathit j}}}{}^{-1}$, where ${{\mathit \ell}}$ ${{\mathit \mu}}$ , ${{\mathit \tau}}$. Limit is $3.3 \times 10^{14}$ s/eV for ${{\mathit \ell}}$ ${{\mathit e}}$ . 31  OBERAUER 1987 looks for photons and ${{\mathit e}^{+}}{{\mathit e}^{-}}$ pairs from radiative decays of reactor neutrinos. 32  BINETRUY 1984 finds $\tau <10^{8}~$s for neutrinos in a radiation-dominated universe. 33  These experiments look for ${{\mathit \nu}_{{k}}}$ $\rightarrow$ ${{\mathit \nu}_{{j}}}$ ${{\mathit \gamma}}$ or ${{\overline{\mathit \nu}}_{{k}}}$ $\rightarrow$ ${{\overline{\mathit \nu}}_{{j}}}{{\mathit \gamma}}$ . 34  STECKER 1980 limit based on UV background; result given is $\tau >4 \times 10^{22}~$s at ${\mathit m}_{{{\mathit \nu}}}=20~$eV. 35  FALK 1978 finds lifetime constraints based on supernova energetics. 36  COWSIK 1977 considers variety of scenarios. For neutrinos produced in the big bang, present limits on optical photon flux require $\tau >10^{23}~$s for ${\mathit m}_{{{\mathit \nu}}}\sim{}$1 eV. See also COWSIK 1979 and GOLDMAN 1979 .

References:

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