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Neutrinoless double beta decay has not been observed so far, and its existence cannot be disproved. Therefore the question whether neutrinos are Majorana particles is still inconclusive. In this paper, we hope to investigate the possibility of distinguishing neutrino fermion types by gravitational fields from the perspective of gravitational scattering of fermions. The Levi-Civita connection is decomposed according to the parity transformation. Under the perturbation therory of gravitational field to fermion quantum scattering and weak gravitational approximation, it is found that the difference between Dirac and Majorana fermion quantum scattering matrix elements of general metric gravitational field comes from similar vector parts under parity transformation; the scattering of the gravitational field on the Kerr metric confirms that the difference in scattering among different types of fermions is related to the angular momentum of the Kerr gravitational source, whose scattering matrix elements are proportional to the square of the product of the mass of the gravitational source and the angular momentum. The above results provide another possible way to distinguish fermion types by gravitational fields.
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Keywords:
- Majorana fermion /
- torsion /
- teleparallel gravity /
- Kerr metric
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[1] Majorana E 1937 Nuovo Cim. 14 171
Google Scholar
[2] Furry W H 1939 Phys. Rev. 56 1184
Google Scholar
[3] Oberauer L, Ianni A, Serenelli A 2020 Solar Neutrino Physics: The Interplay between Particle Physics and Astronomy (Wiley-VCH) pp120–127
[4] Ng K L 1993 Phys. Rev. D 47 5187
Google Scholar
[5] Ng K L 1994 Nuovo Cim. B 109 1143
Google Scholar
[6] Singh D, Mobed N, Papini G 2006 Phys. Rev. Lett. 97 041101
Google Scholar
[7] Menon A, Thalapillil A M 2008 Phys. Rev. D 78 667
Google Scholar
[8] Alavi S A, Abbasnezhad A 2012 Grav. Cosmol. 22 288
Google Scholar
[9] Nieves J F, Pal P B 2007 Phys. Rev. Lett. 98 288
Google Scholar
[10] Lai J H, Xue X 2021 arXiv: 2112.10590[gr-qc]
[11] Arcos H I, Andrade V D, Pereira J G 2004 Int. J. Mod. Phys. D 13 807
Google Scholar
[12] Aldrovandi R, Pereira J G 2013 Teleparallel Gravity: An Introduction (Dordrecht: Springer)
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