Nuclear and detector sensitivities for neutrinoless double beta-decay experiments
NNuclear and detector sensitivitiesfor neutrinoless double beta-decay experiments
Hiroyasu Ejiri
Research Center for Nuclear Physics, Osaka University, Osaka 567-0047, JapanE-mail [email protected]
Abstract.
Neutrinoless double beta-decay (DBD) is of current interest in high-sensitivity frontiers of particle physics. The decay is very sensitive to Majorana neu-trino masses, neutrino CP phases, right-handed weak interactions and others, whichare beyond the standard electro-weak model. DBDs are actually ultra-rare events, andthus DBD experiments with ultra-high sensitivity are required. Critical discussions arepresented on nuclear and detector sensitivities for high-sensitivity DBD experimentsto study the neutrino masses in the normal and inverted mass-hierarchies.Keyword: Neutrinoless double beta decay, nuclear sensitivity, detector sensitivity,neutrino mass, Majorana neutrino, nuclear matrix element.
1. Introduction
Neutrinoless double beta-decay (DBD) is of current interest in sensitivity frontiers ofparticle physics. The decay violates the lepton number conservation law, and thus DBDis beyond the standard electro-weak model. DBD is very sensitive to the Majorananature (neutrino=anti-neutrino) of neutrino, the absolute neutrino-mass scale andthe neutrino-mass hierarchy, the neutrino CP-phases, the possible right-handed weakinteractions and others, which are beyond the standard model. Accordingly, it has beenused to study these fundamental questions on the neutrino and the weak interaction fordecades. Recent experimental and theoretical DBD works are discussed in the reviewarticles and references therein [1, 2, 3, 4, 5].In fact, neutrinoless DBDs are due to various modes such as the light neutrino-massmode, the right-handed weak current mode, the SUSY particle exchange mode, and theothers, which are all beyond the standard model [1, 4] . In the present work, we discussmainly the neutrinoless DBD due to the light neutrino-mass mode, which is of currentinterest.DBD, however, is a very low-energy and ultra-rare decay. The energy is of theorder of E ββ ≈ − GeV and the decay rate is in the range of T νr ≈ − - 10 − per year (y), depending on the neutrino-mass and the nuclear matrix element(NME).The neutrino-mass to be studied is around m =3 meV and 30 meV in cases of the a r X i v : . [ nu c l - e x ] D ec uclear and detector sensitivities for neutrinoless double beta-decay experiments y for both Geand
Xe . The neutrino mass limits are, respectively, 600 meV/ M (76) and 230meV/ M (136) with M (76) and M (136) being the nuclear matrix elements (NMEs) for Ge and
Xe, respectively. So they are in the range of 300-100 meV if NMEs arearound 2. See section 4 for discussions on DBD experiments. Then one needs to improvethe sensitivity by factors 5 and 50 to access the IH and NH mass regions, respectively.In fact, the DBD sensitivity to the neutrino mass depends much on NME.
Femto (10 -15 m) nuclear collider
Figure 1.
Schematic views of neutrinoless double β -decay with Majorana neutrinoexchange (left hand panel) and nuclear collider (right handed panel). DBD with a light neutrino-mass mode is considered as a neutrino-exchange process,where a light Majorana neutrino is exchanged between two neutrons in the DBD nucleus.Here the nucleus acts as a high-luminosity micro-collider of two neutrons, as shown inFig.1. The neutrino-exchange cross-section for the IH neutrino is as small as σ ≈ − cm because of the second-order weak process and the small neutrino mass [4, 6, 7]. Theluminosity of one nucleus is as high as L ≈ cm − s − because of the very small ( afew fm) distance between the two neutrons in the nucleus. The summed luminosity for1 ton DBD nuclei is L ≈ cm − s − . Thus one gets 2-3 DBD signals per year for theIH neutrino exchange by using a large DBD detector with 1 ton DBD isotopes.The DBD neutrino-mass sensitivity to search for the small neutrino mass is definedas the minimum neutrino mass m m to be measured by the DBD experiment. It is givenby a product of a nuclear sensitivity and a detector sensitivity. The nuclear sensitivitydepends on nuclear parameters such as the nuclear phase space and the NME, whilethe detector sensitivity depends on the detector parameters such as the total numberof the DBD isotopes, the enrichment, the exposure time, the detection efficiency andthe backgrounds. The minimum neutrino mass to be measured and the nuclear and uclear and detector sensitivities for neutrinoless double beta-decay experiments
2. Neutrino mass sensitivity for DBD experiment
The neutrinoless DBD transition rate is expressed in terms of the axial-vector weakcoupling g A =1.27 in units of the vector coupling of g V as [1, 4] T νr = g A G ν | M ν f ( ν ) | , (1)where G ν is the phase space volume, M ν is the NME and f ( ν ) stands for the effectiveneutrino mass and the other neutrino and weak interaction parameters beyond thestandard model. These three quantities are associated with the kinematic factor, thenuclear physics factor and the particle physics factor, respectively.In case of the light neutrino-mass process, f ( ν ) is given by the effective neutrinomass of m = (cid:80) | U i | m i e α i with m i U i and α i being the ith neutrino mass, the mixingcoefficient and the phase, respectively. In case of the right-handed weak-boson process f ( ν ) includes the term k ( M LW /M RW ) with M LW and M RW being the let-handed and right-handed weak-boson masses, respectively [1, 4].The DBD NME for the light neutrino-mass mode is expressed in terms of theGamow-Teller (GT), the Fermi (F) and the tensor (T) NMEs as [1, 4, 7] M ν = ( g effA g A ) [ M ( GT ) + ( g effV g effA ) M ( F ) + M ( T )] , (2)where g effA and g effV are, respectively, the effective axial-vector and vector couplings, and g A and g V are the axial-vector and vector couplings for a free nucleon. M ( GT ), M ( F )and M ( T ) are, respectively, the model NMEs for Gamow-Teller, Fermi, and tensortransition operators.The GT and T NMEs are very sensitive to nucleonic and non-nucleonic correlationsand nuclear medium effects, and thus the ratios g effA /g A and g effV /g V stand for the re-normalization coefficients due to such correlations and nuclear medium effects that arenot explicitly included in the nuclear model. Thus they depends on the models andthe transition operators. Since the axial-vector NMEs are strongly modified by thestrong isobar (quark spin-isospin excitation) and other non-nucleonic correlations, weusually consider explicitly the re-normalization coefficient g effA , but the re-normalizationcoefficient g effV for the vector coupling should be well considered unless the modelsinclude all correlations and the medium effect [6, 7, 8]. The DBD NMEs are discussedin review articles on neutrino nuclear responses [6, 7, 8]. Theoretical works on DBDNMEs are discussed in reviews [9, 10, 11]. uclear and detector sensitivities for neutrinoless double beta-decay experiments T νr per year (y) and per ton (t) of the DBD isotope-mass is expressedby using a neutrino mass-unit m as [1, 4, 7, 8] T νr = ( mm ) , m = m (cid:48) M ν (3) m (cid:48) = 7 . A / g A ( G ν ) / , (4)where A is the mass-number of the DBD nucleus and G ν is the phase space factor inunit of 10 − /y, and m is the neutrino mass that gives the DBD rate T νr =1 per t y. Wedefine m as the nuclear sensitivity of the DBD nucleus, being inversely proportional tothe ( G ν ) / M ν . Here, high sensitivity to the neutrino mass means high capability ofmeasuring a small neutrino-mass. m (cid:48) is the neutrino mass m in case of M ν =1.The values m (cid:48) for typical DBD nuclei of Se,
Mo,
Cd and
Te, which areof current interest, are all around 40 meV, which are close to the upper bound of theIH neutrino mass. The values for Ge and
Nd are, respectively, larger and smallerby a factor 2 than the value of 40 meV because of the smaller and larger phase spacevolumes.In order to study the neutrino mass, the number of the DBD signals is required tobe larger than the fluctuation δ of the number of the background signals. Then it isexpressed as [1, 7, 8] T νr η(cid:15)N T ≥ δ, δ = δ × ( BN T ) / , (5)where N is the total DBD isotope-mass in units of t, T is the exposure in units of y, δ isaround 2 and B is the number of the backgrounds per N =1 ton per T =1 year, η is theenrichment coefficient of the DBD isotope and (cid:15) is the DBD signal detection-efficiency.Note that the actual DBD isotope-mass is ηN ton, the signal yield is T νr η(cid:15)N T , and theBG yield is BN T .Then the minimum effective neutrino-mass to be measured with 90 % confidencelevel is expressed in terms of the nuclear sensitivity m and the detector sensitivity d as m m = m × d, d = d × η − / (cid:15) − / ( N T /B ) − / , (6)where d is around 1.4. The neutrino mass to be measured is m m =2 m (cid:48) /M ν in a typicalcase of the DBD detector exposure of N T = 1 t y, the BG rate of B =1/t y, (cid:15) =0.55, and η =0.9.On the basis of the simple expression of the mass sensitivity m m as given in eq.(6), key points for high sensitivity DBD experiments are as follows.1. The neutrino mass to be measured is proportional to 1/ M ν and ( B/N T ) / .Therefore the DBD nucleus with larger M ν by a factor 2 is equivalent to the DBDisotope-mass ( N ) larger by a factor 16. Then the detector volume gets more than anorder of magnitude larger if M ν gets smaller by 40 %.2. The minimum mass to be measured depends on the ratio of ( B/N ) / . Then theneutrino mass sensitivity is improved by a factor 2 by increasing the DBD isotope-mass uclear and detector sensitivities for neutrinoless double beta-decay experiments N ) by a factor 16, or by decreasing the BG rate by a factor 16, or by increasing theDBD isotope-mass by a factor 4 and decreasing the BG rate by a factor 4.3. The effective neutrino mass depends on the neutrino mixing-phases, and is inthe regions of m ≈ m ≈ M ν =2, one needs the DBD detectors with the masssensitivities around the nuclear sensitivity of m ≈
20 meV and one tenth of that,respectively, in cases of IH and NH. Then one needs DBD detectors with N ≈ B ≈ N ≈
100 t and B ≈ −
90% enriched DBD isotopes.
3. DBD nuclear and detector sensitivities
In this section we discuss DBD nuclear and detector sensitivities as given in eq. (6) forDBD experiments to access the IH and NH neutrino masses.
The nuclear sensitivity m is a ratio of the unit mass m (cid:48) and the NME M ν . In fact, M ν is so sensitive to the details of the nuclear structures that accurate evaluation for M ν is very hard. So we discuss in the present work mainly m (cid:48) , and assume that M ν is in the region of 1-3. See the recent review on DBD NMEs [7] and references thereinfor detailed discussions on M ν .The unit mass m (cid:48) is proportional to A / ( G ν ) − / . The phase space factor G ν increases with increase of the DBD Q value. Thus double β − nuclei with the large Q around 3 MeV are used. The large Q is also effective to reduce much BGs from Tl and
Bi, which are two major BGs. The mass-number A dependence reflects the numberof the DBD nuclei per ton of the total DBD isotope-mass. The mass sensitivities for atypical DBD nucleus with m (cid:48) =40 meV are plotted as a function of the exposure N T in Fig. 2. In order to access the IH mass of 20 meV, one needs a DBD exposure
N T of around 16 t y , i.e. N ≈ T ≈ M ν =2 and BG rate of B =1/t y. On the other hand, one needs N T ofaround 3 t y, i.e. N ≈ T ≈ M ν =3,and N T of around 250 t y, i.e. N ≈
60 ton DBD isotopes and T ≈ M ν =1. So, it is very crucial to know the NME even for designing the DBDdetector.The mass sensitivities for the enrichment factors of η =10, 50, 100 % are plotted asa function of the total DBD isotope-mass N in Fig. 3In order to access the IH mass of 20 meV, one needs N =3.4 t and 4.1 t of the totalDBD isotopes, respectively, in case of η =100% and 90%, while it is N =14 t in case of uclear and detector sensitivities for neutrinoless double beta-decay experiments Neutrino mass sensitivity m m meV NT ton year
IHNH
M=3 B=1 M=2 B=0.01
M=2 B=1
M=1 B=1
Figure 2.
Neutrino mass sensitivities m m as a function of the exposure N T . M and B are the NME and the BG rate per t y. d =1.4, (cid:15) =0.55, η =0.9. See eq. (6). . Mass sensitivity m m meV DBD isotope mass N ton
Figure 3.
Neutrino mass sensitivities m m for η =1.0, 0.5, and 0.1 as a function ofthe total isotope-mass N . The exposure time is T =5 y, and the nuclear sensitivity of m =20 meV, (cid:15) =0.55, d =1.4, and B =1 /t y. η =50% ( ηN = 7 t), and N =340 t in case of η =10% ( ηN = 34 t). Therefore, enrichmentaround η ≥
80% is very effective . The 1 ton DBD total isotope-mass with η ≈
90% is uclear and detector sensitivities for neutrinoless double beta-decay experiments Mass sensitivity m m meV N/B M= M= M= Figure 4.
Neutrino mass sensitivities m m for η =0.9, (cid:15) =0.55, d =1.4 as a function ofthe ratio of the total isotope-mass N to the BG rate B . The exposure time is T =5 y,and the unit mass m (cid:48) =40 meV .equivalent to the N ≈
10 ton of the total DBD isotope-mass with η ≈ DBD experiment requires an ultra-low BG detector since the DBD signal is very lowin energy and the event rate is very rare. The neutrino mass-sensitivity for a typicalexposure time of T =5 y and η = 0.9, (cid:15) =0.55, d =1.4 is rewritten in therms of the ratioof the DBD isotope-mass N and the BG rate B as m m ≈ . m (cid:48) M ν ( N/B ) / . (7)The mass sensitivities for the m (cid:48) = 40 meV with typical NMEs of M ν =2 and M ν =3 are simply given as m m ≈
27 meV/(
N/B ) / and m m ≈
18 meV/(
N/B ) / . Theyare shown as a function of N/B in Fig. 4. So, in case of M ν ≈
2, DBD detectors tosearch for the IH mass of 20-30 meV and the NH mass of 2-3 meV are required to belarge isotope-mass and low-BG detectors with
N/B ≈ N/B ≈ , respectively.Let us see how the mass sensitivity changes if one gets a BG free ( B =0) detector.In this case, the mass sensitivity is derived by requiring the signal yield ≥ m m = 1 . × m (cid:15) − / η − / ( N T ) − / . (8)The mass sensitivities for three BG cases of B =1, 0.01, and 0 are compared in Fig. 5.Then the DBD isotope-mass N required to access the IH mass of 20 meV is 1 t, whilethe DBD isotope-mass to access the NH mass of 2 meV is 100 t. They are a factor 3 uclear and detector sensitivities for neutrinoless double beta-decay experiments Mass sensitivity m m meV DBD isotope mass N ton
B=1/t/y
B=0.01B= Figure 5.
Neutrino mass sensitivities m m as a function of the DBD isotope-mass N in cases of B =1, 0.01, and 0. The exposure time is T =5 y. The unit mass m (cid:48) =40 meVand M ν =2, (cid:15) =0.55 and η =0.9. smaller than those for the detectors with B =1 and 0.01. Thus one needs 1ton-scale and100 ton-scale DBD isotope-masses to access the IH and NH neutrino masses even byusing the BG-free detectors.The DBD signal is expected to appear as a sharp peak at the energy of E = Q inthe energy spectrum. The peak width is around the FWHM (full width half maximum)of the detector. Thus one usually sets the energy window of ∆ E = 2 FWHM as theregion of interest, ROI.BGs in ROI are mostly due to β -rays and Compton-scattered γ rays, which arecontinuum spectra. Backgrounds due to the solar-neutrino interaction, which get seriousin the NH mass search, are also continuum [12, 13]. Then the BG rate at the energywindow of ROI is proportional to FWHM. Since the mass sensitivity is proportional to( B/N ) / , improvement of the energy resolution by an order of magnitude is equivalentto increase of the DBD isotope-mass by the same order of magnitude.The mass sensitivity depends on the detection efficiency as m m = k(cid:15) − / . Theefficiency includes all efficiencies associated with the energy and PSA windows/cuts andanalyses to select the DBD signals and to reject BG ones. It is around (cid:15) ≈ (cid:15) and the BG rate B . The decreaseof (cid:15) by 20% is compensated if B gets smaller by 40 %.
4. Remarks and discussions on DBD detectors
There are many high-sensitivity DBD experiments and future plans to access the IHmass around 20 meV and the NH mass around 2 meV. The detailed reports on the uclear and detector sensitivities for neutrinoless double beta-decay experiments Se,
Mo and
Xe are very useful isotopes because ofthe small m (cid:48) ≈
40 meV due to the large phase space G ν and the large Q value andmulti-ton scale enriched isotopes with N ≈
10 and η ≈
90% are available by centrifugalseparation.Cryogenic Se- and
Mo- bolometers with both thermal and scintillation signalsare promising detectors with high energy resolution and low BG rate. See refs.[15, 16, 17, 18].
Cd with m (cid:48) ≈
40 mev is also interesting. See refs. [19, 20].
Xe can be easily enriched to get a 10 t scale isotope-mass and thus is possible toaccess the IH and NH masses. Various kinds of
Xe detectors are under progress. Seerefs. [21, 22, 23, 24, 25, 26, 27]. Ge with Q =2.039 MeV has the unit mass of m (cid:48) =80 meV, a factor 2 larger thanthe others given above. Ton scale enriched DBD isotopes are possible by centrifugalseparation, and the energy resolution of 10 − in FWHM is very good. Accordingly theGe BG rate is almost an order of magnitude smaller than others to get the neutrinomass sensitivity comparable with other detectors. See refs. [28, 29, 30, 31, 32].The natural abundance of Te is 34%, and thus multi-ton scale natural Te isotopesmay be used although the mass sensitivity m m gets larger by a factor 1.6 than the masssensitivity with enriched Te-isotope detectors. See ref. [18, 33]
Nd has a large phase space factor because of the large Q value of 3.4 MeV andthe large Z number of 60. Thus the m (cid:48) =18 meV is a half of the others [7, 8]. Thenatural abundance, however, is only 5.6 % and the enrichment is not easy. See ref.[34].Tracking detectors have been used to study DBDs on Mo,
Cd, Se, and manyother DBD nuclei as discussed in review articles and references therein [1, 2, 4, 5].They measure individual two β -rays to identify the DBD signals and to reject single- β background signals. The measured energy and angular correlations are used todifferentiate the DBD processes due to the left-handed and right-handed weak currents.See refs. [35, 36, 37].Finally it should be remarked that the NME is one of key ingredients for the DBDmass sensitivity, and thus selection of DBD isotopes with a large NME is very crucialfor getting high-sensitivity DBD experiments [6, 7]. It is however very hard to evalu-ate accurately the DBD NMEs. So various experiments are under progress to providenuclear parameters, the effective axial-vector weak couplings and nuclear structures tohelp theoretical evaluations of the neutrinoless DBD NMEs. These are discussed inrecent articles [8, 38]. Acknowledgement uclear and detector sensitivities for neutrinoless double beta-decay experiments th birthday. [1] H. Ejiri, Double beta decays and neutrino masses, J. Phys. Soc. Jpn. , 2101 (2005).[2] F. Avignone, S. Elliott, J. Engel, Double beta dcay, Majorana neutrino, and neutrino mass, Rev.Mod. Phys. , 481 (2008).[3] H. Ejiri, Double β -decays and neutrino nuclear responses, Prog. Part. Nucl. Phys. , 249 (2010)[4] J. Vergados, H. Ejiri, F. ˇSimkovic, Theory of neutrinoless double- β decay, Rep. Prog. Phys. ,106301 (2012).[5] J. Vergados, H. Ejiri, F. ˇSimkovic, Neutrinoless double β -decay and neutrino mass, Internat. J.Modern Phys. E , 1630007 (2016).[6] H. Ejiri, Nuclear spin isospin responses for low-energy neutrinos, Phys. Rep. , 265 (2000).[7] H. Ejiri, J. Suhonen and K. Zuber, Neutrino nuclear responses for astro-neutrinos, single β -decays,and double β -decays Phys. Rep. , 1 (2019).[8] H. Ejiri, Neutrino-mass sensitivity and nuclear matrix element for neutrinoless double beta decay,
Universe
225 (2020). doi:103390/universe 6120225.[9] J. Suhonen, O. Civitarese, Weak interaction and nuclear structure aspect of nuclear double betadecay
Phys. Rep. , 123 (1998).[10] J. Suhonen, O. Civitarese, Double-beta decay nuclear matrix elements in the QRPA framework,
J. Phys. G: Nucl. Part. Phys. , 035105 (2012).[11] J. Engel and J. Men´endez, Status and future of nuclear matrix elements for neutrinoless double β -decay: a review, Rep. Prog. Phys. , 046301 (2017).[12] H. Ejiri and S. R. Elliott, Charged current neutrino cross section for solar neutrinos, andbackground to the ββ (0 ν ) experiments, Phys. Rev. C. , 055501 (2014).[13] H. Ejiri and S. R. Elliott, Solar neutrino interactions with the double- β nuclei Se,
Mo, and
Nd,
Phys. Rev. C. , 055501 (2017).[14] J. Detwiler, Future neutrino-less double-beta decay experiments, Proc. Neutrino 2020 (2020).[15] D. R. Artusa et al., The LUCIFER/CUPID-0 demonstrator: searching for the neutrinoless double-beta decay with Zn Se scintillating bolometers,
J. Phys. Conf. Ser . , 012077 (2017).[16] H. Park et al., The AMoRE: Search for neutrinoless double beta decay in Mo,
Nucl. Part. Phys.Proc . , 2630 (2016).[17] D. Poda, A. Giuliani, Low background techniques in bolometers for double-beta-decay search, Int.J. Mod. Phys . A , 1743012 (2017).[18] T.O. Donnell et al., (CUORE collaboration), CUORE results and CUPID Project, Proc. Neutrino2020 , (2020).[19] K. Zuber, COBRA: Double β -decay searches using CdTe detectors, Phys. Lett. B , 1 (2001).[20] F. A. Danevich et al. (Aurora experiment), Search for double beta decay of Cd with enriched
CdWO crystal scintillators, J. Phys. Conf. Ser . , 062009 (2016) .[21] A. Gando et al. (KamLAND collaboration), Search for Majorana neutrinos near the inverted masshierarchy region with KamLAND-Zen, Phys. Rev. Lett. 117 (2016) 082503, Addendum: Phys.Rev. Lett. , 109903 (2016).[22] J. B. Albert et al. (EXO-200 collaboration), Search for neutrinoless double- β -decay with theupgraded EXO-200 detector, Phys. Rev. Lett . , 072701 (2018).[23] L. Yang et al., Status and prospects for the EXO-200 and nEXO experiments, J. Phys. Conf. Ser. , 012032 (2017).[24] G. Anton et al., (EXO-200 Collaboration), Search for neutrinoless double- β decay with thecomplete EXO-200 data set, Phys. Rev. Lett. , 161802 (2019).[25] C. Grant, Results from KamLAND-ZEN and SON+,
Proc. Neutrino 2020 (2020).[26] J.J. Gomez Cadenas, Xe-136 experiments, present and future,
Proc. Neutrino 2020 (2020).[27] N. Lopez March et al., The NEXT high pressure xenon gas TPC for neutrinoless double β -decay uclear and detector sensitivities for neutrinoless double beta-decay experiments searches, JINST, , C01048 (2018).[28] M. Agostini et al., Improved limit on neutrinoless double β -decay of Ge from GERDA Phase II,
Phys. Rev. Lett. , , 132503 ( 2018).[29] C.E. Aalseth et al. (MAJORANA-collaboration), Search for neutrinoless double- β decay in Gewith the Majorana demonstrator,
Phys. Rev. Lett. , 132502 (2018).[30] S.I. Alvis, et al., (MAJORANA-Collaboration), Search for neutrino-less double- β decay in Gewith 26 kgy of exposure from the Majorana demonstrator,
Phys. Rev. C , 025501 (2019).[31] N. Abgrall et al. (LEGEND-collaboration), The large enriched germanium experiment forneutrinoless double beta decay (LEGEND), AIP Conf. Proc. , 020027 (2017).[32] Y. Kermaidic, GERDA, Majorana and LEGEND towards a background-free ton-scale Ge76experiment,
Proc. Neutrino 2020 (2020).[33] D.Q. Adams et al. (CUORE Collaboration), Improved limit on neutrinoless double-beta decay in
Te with CUORE,
Phys. Rev. lett. , 122501 (2019).[34] S. Andringa et al. (SNO+-collaboration), Current status and future prospects of the SNO+experiment,
Adv. High Energy Phys. , 6194250 (2016).[35] H. Ejiri, J. Engel, R. Hazama, P. Kurastev, N. Kudomi, and R.G.H. Robertson, Spectroscopy ofdouble-beta decays from
Mo for neutrinos,
Phys. Rev. Lett. , 2917 (2000).[36] H. Ejiri et al., MOON (Molybdenum Observatory Of Neutrinos) for neutrinoless double β -decays, Eur. Phys. J. , 239 (2008).[37] D. Waters et al. (NEMO-3 and Super NEMO collaboration), Latest results from NEMO-3 andstatus of the superNEMO experiment,
J. Phys. Conf. Ser. , 012033 (2017).[38] H. Ejiri, Perspectives on neutrino nuclear-response studies for double beta decays and astroneutrinos,