Number-theory dark matter

Abstract

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. Focusing on one of the solutions, we show that there is indeed a good candidate for dark matter, whose stability is guaranteed by Z 2 (B − L).

General Solution to the U(1) Anomaly Equations

“…De-riving anomaly-free sets from the U (1) subgroups of a non-Abelian gauge group, such as SO(10) or E 6 , is a powerful technique [7], yet it is restricted by the choice of the larger group. Examples of chiral U (1) models can be found in [8].…”

New chiral fermions, a new gauge interaction, Dirac neutrinos, and dark matter

“…In order to develop the scenario described above, an algorithm is necessary to write chiral models that are at least anomaly-free under a U(1) gauge symmetry [22] -see also [23,24]. A general technique to do so is described in section 6, towards the end of this manuscript.…”

A new B − L model without right-handed neutrinos

“…Several attempts have also been made to incorporate the dark matter within these scenarios [16][17][18][19][20][21][22][23][24][25][26][27]. It has been known for some time, though, that the anomalies in this model can also be canceled in other ways.…”