#
The Neutrino Mass Problem: From Double Beta Decay to Cosmology^{ †}

^{†}

## Abstract

**:**

## 1. Introduction

## 2. About the Formalism

#### Neutrinoless Double-Beta-Decay Rates

## 3. Some Results

- (2): by fixing the value of ${\tilde{m}}_{\nu}$ at the maximum value ${m}_{\nu}$ allowed by the non-observation of the neutrinoless double beta decay. This is done by taking the average resulting from the theoretical estimates of the ratios between the half-lives and the coefficients ${C}_{mm}$ for the double beta decay emitters listed in Ref. [18]. This choice of ${\tilde{m}}_{\nu}$ is arbitrary, because of the uncertainties affecting the values of the different nuclear matrix elements, but it should be taken as a demonstration of the feasibility of the method.

- The non-observation of the neutrinoless double beta decay provides limits on the effective neutrino mass ${m}_{\nu}$, which are compatible with values determined from the coupling of neutrinos with axions.
- The values (${m}_{a}$ and ${g}_{a}$), which are consistent with ${m}_{\nu}$, can be taken as reference values for dark-matter studies.

## 4. Conclusions

## 5. Some Final Remarks

## Funding

## Conflicts of Interest

## Notes

1 | Which is equivalent to the Mexican hat potential of the conventional Higgs mechanism. |

2 | See also these references for the meaning of the factors which appear in Equation (19), such as $\u03f5,\gamma ,\beta ,\zeta ,\xi $. |

## References

- Vergados, J.D. Modulation effect for supersymmetric dark matter detection with asymmetric velocity dispersion. Phys. Rev. D
**2000**, 62, 023519. [Google Scholar] [CrossRef][Green Version] - Vergados, J.D. Lepton physics beyond the standard model. Phys. Atom. Nucl.
**2003**, 66, 1981. [Google Scholar] - Vergados, J.D. Searching for dark matter—Theoretical rates and exclusion plots due to the spin. Nucl. Phys. B
**2010**, 829, 383. [Google Scholar] [CrossRef][Green Version] - Vergados, J.D.; Semertzidis, Y. Modulation, asymmetry and the diurnal variation in axionic dark matter searches. Nucl. Phys. B
**2015**, 897, 821. [Google Scholar] - Vergados, J.D.; Semertzidis, Y. Axionic dark matter signatures in various halo models. Nucl. Phys. B
**2017**, 915, 10. [Google Scholar] [CrossRef] - Peccei, R.D.; Quinn, H.R. CP conservation in the presence of pseudoparticles. Phys. Rev. Lett.
**1977**, 38, 1440. [Google Scholar] [CrossRef][Green Version] - Peccei, R.D.; Quinn, H.R. Constraints imposed by CP conservation in the presence of pseudoparticles. Phys. Rev.
**1977**, D16, 1791. [Google Scholar] - Mohapatra, R.; Senjanović, G. Neutrino Masses and Mixings in Gauge Models with Spontaneous Parity Violation. Phys. Rev. D
**1981**, 23, 165. [Google Scholar] [CrossRef] - Bilenky, S.M.; Petcov, S. Massive neutrinos and neutrino oscillations. Rev. Mod. Phys.
**1987**, 59, 671. [Google Scholar] [CrossRef] - Vergados, J.D. The neutrinoless double beta decay from a modern perspective. Phys. Rep.
**2002**, 361, 1–56. [Google Scholar] [CrossRef][Green Version] - Penacchioni, A.V.; Civitarese, O. Extragalactic neutrinos as tracers of dark matter? arXiv
**2020**, arXiv:1904.04355. [Google Scholar] [CrossRef][Green Version] - Penacchioni, A.V.; Civitarese, O.; Arguelles, C.P. Testing dark matter distributions by neutrino—Dark matter interactions. Eur. Phys. J.
**2020**, C80, 183. [Google Scholar] [CrossRef] - Penacchioni, A.V.; Civitarese, O. Constraining the axion mass from the nonobservation of 0νββ decay. Int. J. Mod. Phys. E
**2022**, 31, 2250038. [Google Scholar] [CrossRef] - Mosquera, M.E.; Civitarese, O. The Neutrino Mass Problem: From Double Beta Decay to Cosmology. Int. J. Mod. Phys. E
**2022**, 31, 2250082. [Google Scholar] [CrossRef] - Mosquera, M.E.; Civitarese, O. The Neutrino Mass Problem: From Double Beta Decay to Cosmology. Int. J. Mod. Phys. E, 2023; in press. [Google Scholar]
- Ryder, L.H. Quantum Field Theory; Cambridge University Press: Cambridege, UK, 1985. [Google Scholar]
- Weinberg, S. The Quantum Theory of Fields; Cambridge University Press: Cambridege, UK, 1995. [Google Scholar]
- Suhonen, J.; Civitarese, O. Weak-interaction and nuclear-structure aspects of nuclear double beta decay. Phys. Rep.
**1998**, 300, 123. [Google Scholar] [CrossRef]

**Figure 1.**The effective neutrino mass ${m}_{\nu}$, as a function of ${m}_{a}$ and ${g}_{a}$. The results of Equation (19) are given for the largest value of ${\tilde{m}}_{\nu}$ (0.3 eV).

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**MDPI and ACS Style**

Civitarese, O.
The Neutrino Mass Problem: From Double Beta Decay to Cosmology. *Universe* **2023**, *9*, 275.
https://doi.org/10.3390/universe9060275

**AMA Style**

Civitarese O.
The Neutrino Mass Problem: From Double Beta Decay to Cosmology. *Universe*. 2023; 9(6):275.
https://doi.org/10.3390/universe9060275

**Chicago/Turabian Style**

Civitarese, Osvaldo.
2023. "The Neutrino Mass Problem: From Double Beta Decay to Cosmology" *Universe* 9, no. 6: 275.
https://doi.org/10.3390/universe9060275