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2011

Number-Theory Dark Matter

Nakayama, Kazunori, Takahashi, Fuminobu, Yanagida, Tsutomu T.

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We propose that the stability of dark matter is ensured by a discrete subgroup of the U(1)B-L gauge symmetry, Z_2(B-L).

We introduce a set of chiral fermions charged under the U(1)B-L in addition to the right-handed neutrinos, and require the anomaly-cancellation conditions associated with the U(1)B-L gauge symmetry.
We find that the possible number of fermions and their charges are tightly constrained, and that non-trivial solutions appear when at least five additional chiral fermions are introduced.
The Fermat theorem in the number theory plays an important role in this argument.

Number-Theory Dark Matter · Around

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A. Kusenko, F. Takahashi and T. T. Yanagida, Phys. Lett. B 693

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C. F. Kausler, “Nova demonstratio theorematis nec summam, nec differentiam duorum cuborum cubum esse posse”. Novi Acta Acad. Petrop. 13 (1795/6), 1802, 245 - 253

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