Large-scale nuclear-structure calculation for constraining neutrino masses

Y. Iwata1), N. Shimizu1), T. Otsuka1), Y. Utsuno2), J. Menéndez1), M. Honma1) and T. Abe1)1) : Univ. Tokyo 2):. R. G. for Heavy Element Nuclear Science, JAEANeutrinos are quite “abundant” elementary particles in theuniverse because they are emitted from a nucleus (with mass
number A and proton number Z) during its β decay:
𝐴𝑍 → 𝐴(𝑍 − 1) + 𝑒 − + 𝜈̅𝑒 ,−where 𝑒 and 𝜈̅𝑒 are an electron and a (electron-) antineutrino,
respectively. Nevertheless, many of the neutrino properties arestill unknown. This is because these particles are quite hard to
detect due to very weakly interacting nature. While neutrinos
are proven to be massive particles by the Super-Kamiokande
experiment on the basis of neutrino oscillation, it is impossible
to measure their absolute masses using the same principle.
Among several possible methods to measure neutrino masses,
ββ decay is regarded to be a promising probe. ββ decay occurs
for nuclides which are stable or very long-lived against single βdecay but are unstable against two simultaneous β decays:
𝐴𝑍 → 𝐴(𝑍 − 2) + 2𝑒 − + 2𝜈̅𝑒 .
The ββ decay is so far observed for about ten nuclides. Inaddition to this normal ββ decay mode which emits twoneutrinos, another ββ decay mode without emitting neutrinos
expressed as𝐴
𝑍 → 𝐴(𝑍 − 2) + 2𝑒 −is possible if neutrinos are Majorana particles, i.e., the particles
which are identical with their own antiparticles. Although thisdecay mode, called zero-neutrino ββ decay, has not beenobserved yet, Majorana neutrinos are an attractive scenario toaccount for the extremely small neutrino masses and thedominance of matter over antimatter in the universe, andtherefore many experimental projects are running to detect zeroneutrino ββ decay. Once the half-life of zero-neutrino ββ decay
is measured, neutrino masses can be derived through0𝜈[𝑇1/2]−1= 𝐺 0𝜈 |𝑀0𝜈 |2 (0𝜈
where 𝑇1/2and 〈𝑚𝛽𝛽 〉/𝑚𝑒 are〈𝑚𝛽𝛽 〉 2𝑚𝑒) ,the half-life and the effective
neutrino mass in the unit of the electron mass, respectively.
While 𝐺 0𝜈 is the phase-space factor which is unambiguously
given when the masses of the parent and daughter nuclei areprovided, 𝑀0𝜈 , called nuclear matrix element, cannot be
determined without precise information on nuclear many-bodyproperties. Namely, nuclear input is needed to extract theeffective neutrino mass from the half-life of zero-neutrino ββ
decay. Since the quantity of the nuclear matrix element cannot
be directly measured from nuclear experiment, its determinationmust rely on nuclear-structure theory. In the present study [1],we provide a reliable nuclear matrix element for the zeroneutrino ββ decay in 48Ca, performing a very large-scale
nuclear-structure calculation using the K supercomputer.
The nucleus is a quantum many-body system composed ofprotons and neutrons which interact with one another via thenuclear forces. Since the A=48 system (i.e., 48Ca and 48Ti) arestill beyond the applicability of the ab-initio (first-principles)
calculations, one should adopt effective models for the present
purpose. Among them, the nuclear shell model (or configurationinteraction in terms of quantum chemistry) is usually conceived
to provide the most precise nuclear wave function because thismodel is able to fully include nucleon-nucleon correlation near
the Fermi surface, which is essential for describing nuclear
structure. In the previous shell-model calculations for the zero-Fig. 1 Nuclear matrix element 𝑴𝟎𝝂 for the zero-neutrino ββ decay of48
Ca compared among various theoretical models in the literature (see[1] and references therein). SM (sdpf) and SM (pf) stand for thepresent shell-model calculations and the previous ones, respectively.
Two different Hamiltonians are used and compared for EDF, SM (pf),and SM (sdpf).

neutrino ββ decay in 48Ca, only the last eight nucleons near theFermi surface can be explicitly treated as the active model space
due to computational limitation at that time. In the present
calculation, the degrees of freedom below this active model
space are partially treated, and the resulting dimension of theHamiltonian matrix becomes approximately two billion. We aresuccessful in diagonalizing this large matrix by using the Ksupercomputer.
In Fig. 1, the nuclear matrix element obtained in this study iscompared with other theoretical calculations. The calculated
values range from ~0.5 to ~3, indicating large theoreticaluncertainty. The previous and present shell-model calculations
correspond to SM (pf) and SM (sdpf), respectively. The
comparison between these shell-model calculations shows thatthe nuclear matrix element enhances by about 30% by taking
more nucleon degrees of freedom. Since the present calculation
includes the leading correction to the previous calculation, theresult should be rather reliable. In fact, nuclear structures in theA~40 region are well described with the same setup as thepresent study [2]. Unlike the shell model, other models (QRPA,IBM and EDF) do not have a systematic way to improve theresult.
References[1] Y. Iwata, N. Shimizu, T. Otsuka, Y. Utsuno et al., Phys.
Rev. Lett. 116, 112502 (2016).
[2] Y. Utsuno et al., Phys. Rev. C 86, 051301(R) (2012); Y.
Utsuno et al., Phys. Rev. Lett. 114, 032501 (2015).