doi:10.1016/S0550-3213(02)01012-X 
Copyright © 2002 Elsevier Science B.V. All rights reserved.
Is the lightest Kaluza–Klein particle a viable dark matter candidate?
Géraldine Servant
, a, b and Tim M. P. Tait, a
a High Energy Physics Division, Argonne National Laboratory, Argonne, IL 60439, USA
b Enrico Fermi Institute, University of Chicago, Chicago, IL 60637, USA
Received 25 June 2002;
revised 23 September 2002;
accepted 6 November 2002. ;
Available online 21 November 2002.
This article has been registered under preprint number hep-ph/0206071
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Abstract
In models with universal extra dimensions (i.e., in which all Standard Model fields, including fermions, propagate into compact extra dimensions) momentum conservation in the extra dimensions leads to the conservation of Kaluza–Klein (KK) number at each vertex. KK number is violated by loop effects because of the orbifold imposed to reproduce the chiral Standard Model with zero modes, however, a KK parity remains at any order in perturbation theory which leads to the existence of a stable lightest KK particle (LKP). In addition, the degeneracy in the KK spectrum is lifted by radiative corrections so that all other KK particles eventually decay into the LKP. We investigate cases where the Standard Model lives in five or six dimensions with compactification radius of TeV−1 size and the LKP is the first massive state in the KK tower of either the photon or the neutrino. We derive the relic density of the LKP under a variety of assumptions about the spectrum of first tier KK modes. We find that both the KK photon and the KK neutrino, with masses at the TeV scale, may have appropriate annihilation cross sections to account for the dark matter, ΩM
0.3.
PACS classification codes: 12.60.-i; 95.35.+d; 98.80.Cq
Fig. 1. Prediction for ΩB(1)h2 as a function of the KK mass (when neglecting coannihilation). The upper horizontal region delimits the values of Ωh2 above which the contribution from B(1) to the energy density would overclose the universe. The lower horizontal band denotes the region Ω=0.33±0.035 (using h=0.69±0.06) and defines the KK mass window if all the dark matter is to be accounted for by the B(1) LKP.
Fig. 2. Prediction for Ων(1)h2 as a function of the KK mass. The solid lines are for ν(1) alone (in the one and three family cases) and the dotted ones correspond to the cases where coannihilation with degenerate e(1)L is included.
Fig. 3. Prediction for ΩB(1)h2 as in Fig. 1. The solid line is the case for B(1) alone, and the dashed and dotted lines correspond to the case in which there are one (three) flavors of nearly degenerate e(1)R. For each case, the black curves (upper of each pair) denote the case Δ=0.01 and the red curves (lower of each pair) Δ=0.05.
Fig. 4. Feynman diagrams for B(1)B(1) annihilation into fermions.
Fig. 5. Feynman diagrams for B(1)B(1) annihilation into Higgs scalar bosons.
Fig. 6. Feynman diagrams for annihilation into quarks or leptons of other families.
Fig. 7. Feynman diagrams for annihilation into zero mode leptons of the same family.
Fig. 8. Feynman diagrams for annihilation into scalar Higgs bosons.
Fig. 9. Feynman diagrams for annihilation into two neutral vector bosons VV.
Fig. 10. Feynman diagrams for annihilation into two charged vector bosons W+W−.
Fig. 11. Feynman diagrams for ν(1)ν(1) annihilation into two zero mode leptons νν.
Fig. 12. Feynman diagrams for B(1)f(1) annihilation into a zero mode f and vector boson.
Table 1. Feynman diagrams for which we calculate the annihilation cross section of a KK photon into SM particles. s(x), t(x) and u(x) denote a tree-level Feynman diagram in which particle x is exchanged in the s-, t- and u-channel respectively. “Contact term” represents the scalar-gauge boson four point interaction. f denotes any zero mode fermion and φ is the scalar Higgs doublet
Table 2. Same as Table 1 but for annihilation of the KK neutrino
Table 3. Same as Table 1 but for coannihilation of e(1)R
Table 4. Same as Table 1 but for coannihilation of e(1)L
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