TY - JOUR

T1 - Number-theory dark matter

AU - Nakayama, Kazunori

AU - Takahashi, Fuminobu

AU - Yanagida, Tsutomu T.

N1 - Funding Information:
We would like to thank Satoshi Kondo for useful discussions and particularly for his interdisciplinary colloquium on Number Theory at IPMU, where the basic idea of the present Letter occurred to us. This work was supported by the Grant-in-Aid for Scientific Research on Innovative Areas (No. 21111006 ) [K.N. and F.T.], Scientific Research (A) (No. 22244030 [F.T.] and 22244021 [T.T.Y.]), and JSPS Grant-in-Aid for Young Scientists (B) (No. 21740160 ) [F.T.]. This work was also supported by World Premier International Center Initiative (WPI Program), MEXT, Japan .

PY - 2011/5/23

Y1 - 2011/5/23

N2 - We propose that the stability of dark matter is ensured by a discrete subgroup of the U(1)B-L gauge symmetry, Z2(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 Z2(B-L).

AB - We propose that the stability of dark matter is ensured by a discrete subgroup of the U(1)B-L gauge symmetry, Z2(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 Z2(B-L).

KW - Dark matter

UR - http://www.scopus.com/inward/record.url?scp=79960165179&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79960165179&partnerID=8YFLogxK

U2 - 10.1016/j.physletb.2011.04.035

DO - 10.1016/j.physletb.2011.04.035

M3 - Article

AN - SCOPUS:79960165179

VL - 699

SP - 360

EP - 363

JO - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

JF - Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

SN - 0370-2693

IS - 5

ER -