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).

12 pages, no figure. v2: references added

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• The GeV-scale dark matter with B-L asymmetry
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• A new B-L model without right-handed neutrinos
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• Chiral Abelian gauge theories with few fermions
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• Degenerate Fermion Dark Matter from a Broken $U(1{)}_{\mathrm{B}-\mathrm{L}}$ Gauge Symmetry
• Revisiting the Number-Theory Dark Matter Scenario and the Weak Gravity Conjecture
• Hypercharge Quantisation and Fermat's Last Theorem
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• Tree level Majorana neutrino mass from Type-1 $\times$ Type-2 Seesaw mechanism with Dark Matter
• Anomaly-free chiral $U(1{)}_D$ and its scotogenic implication
• Anomaly-free Abelian gauge symmetries with Dirac seesaws
• QCD Axion From a Spontaneously Broken B-L Gauge Symmetry
• Model of the quintessence axion
• Notes on anomalies, elliptic curves and the BS-D conjecture
• U(1)${}_{B-L}$ Symmetry Restoration and Effective Neutrino Species