DDark Matter Interference
Eugenio D el N obile , ∗ Chris K ouvaris , † Francesco S annino , ‡ and Jussi V irkaj ¨ arvi § CP -Origins & D anish I nstitute f or A dvanced S tudy DIAS ,University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark
Abstract
We study di ff erent patterns of interference in WIMP-nuclei elastic scattering that can accommodate theDAMA and CoGeNT experiments via an isospin violating ratio f n / f p = − .
71. We study interferencebetween the following pairs of mediators: Z and Z (cid:48) , Z (cid:48) and Higgs, and two Higgs fields. We show underwhat conditions interference works. We also demonstrate that in the case of the two Higgs interference, anexplanation of the DAMA / CoGeNT is consistent with Electroweak Baryogenesis scenarios based on twoHiggs doublet models proposed in the past.
Preprint: CP -Origins-2011-39 & DIAS-2011-32. ∗ [email protected] † [email protected] ‡ [email protected] § [email protected] a r X i v : . [ h e p - ph ] J u l . INTRODUCTION Asymmetric dark matter has emerged as a competitive paradigm to thermally produced darkmatter. Instead of having a mechanism where the population of Weakly Interacting MassiveParticles (WIMPs) is controlled by annihilations, it is possible to have an initial asymmetry betweenparticles and antiparticles. The existence of a conserved quantum number associated with theWIMPs can protect them from decay or co-annihilation. If the particle-antiparticle annihilationis su ffi ciently strong, antiparticles are eliminated by equal number of particles, and due to theasymmetry, the dark matter (DM) consists of the remaining particles. If annihilations are notstrong enough, a mixed case with a substantial number of antiparticles present today is alsopossible [1]. Obviously in this mixed scenario DM consists of both particles and antiparticles. Thefact that the asymmetry in the DM sector resembles the baryonic asymmetry, makes asymmetricDM easily incorporated in extensions of the Standard Model. It also means that the asymmetriesin the baryonic and dark sector might be related. Although the idea of asymmetric DM is not new[2–5], it has recently attracted a lot of interest [6–22].The current status of experimental direct detection of DM is quite intriguing. A signal withannual modulation possibly attributed to DM has been solidly established in DAMA [23], and morerecently in CoGeNT [24]. In addition CRESST-II [25] has recently released results compatible withthe existence of a light WIMP too. However, experiments such as CDMS [26], and Xenon10 /
100 [27,28] find null evidence for DM, imposing thus severe constraints on WIMP-nucleons cross sections.The fact that some experiments detect DM and some other do not is not the only experimentaldiscrepancy one faces. Upon assuming spin-independent interactions between WIMPs and nuclei,it is clear that DAMA and CoGeNT are at odds, if WIMPs couple to protons and neutrons withequal strength. However if the relative couplings of WIMPs to neutrons and protons satisfy f n / f p (cid:39) − .
71 [29, 30], an agreement of DAMA and CoGeNT is possible, and it indicates a DM-proton cross section σ p ∼ × − cm and a DM mass m DM ≈ f n / f p (cid:39) − .
71 can beeasily accommodated using Standard Model mediators, via interference of two di ff erent channelsin elastic WIMP-nuclei collisions (see also [32, 33]). Interfering DM can thus naturally explainthe above phenomenological ratio. We showed that if Interfering DM is made of compositeasymmetric WIMPs (with electroweak compositeness scale), a simple interference in the WIMP-nucleus collision between a photon exchange (via a dipole type interaction) and a Higgs exchangecan produce the required isospin violation. Interestingly this candidate has been proven to arise2n strongly interacting models using first principle lattice computations [19]. (cid:45) (cid:45) (cid:45) (cid:45) m DM in GeV Σ p i n c m (cid:45) (cid:45) (cid:45) m DM in GeV Σ p i n c m FIG. 1:
Favored regions and exclusion contours in the ( m DM , σ p ) plane for the standard case f n / f p = (left panel)and the case f n / f p = − . (right panel). The green contour is the σ favored region by DAMA [34] assuming nochanneling [35] and that the signal arises entirely from Na scattering; the blue region is the CL favoredregion by CoGeNT; the cyan contour is the σ favored region by CRESST-II [25]; the dashed line is the exclusionplot by CDMS II Soudan [26]; and the black and blue lines are respectively the exclusion plots from the Xenon10[27] and Xenon100 [28] experiments. The CoGeNT and DAMA overlapping region passing the constraints isshown in red. In this paper we extend the idea of interfering DM by presenting three general interferencepatterns for fermionic DM that can accommodate the experimental findings. More specificallywe show under what conditions interference between Z and a Z (cid:48) ; Z (cid:48) and Higgs, and two Higgsdoublets can provide the appropriate isospin violation. In the last case we show that the in-terference between the two Higgs scalars can also be compatible with Electroweak Baryogene-sis [36–38]. We should also mention that observations of neutron stars put severe constraints onthe spin-dependent cross section of fermionic asymmetric WIMPs [39], and bosonic asymmetricWIMPs [40]. In our study here we avoid these constraints because our fermionic asymmetricWIMP candidates do not have significant spin-dependent cross section. II. Z INTERFERING WITH Z (cid:48) First we will consider a scenario where a fermionic DM particle ψ couples to the Z -boson andto a spin-1 state Z (cid:48) . 3he Z -DM and Z -nucleon interaction Lagrangian, including only renormalizable terms, reads L Z = g θ W Z µ ¯ ψ ( v ψ − a ψ γ ) γ µ ψ + (1) g θ W Z µ (cid:104) ¯ p γ µ ( v p − a p γ ) p + ¯ n γ µ ( v n − a n γ ) n (cid:105) , where the Z -DM couplings v ψ (vector) and a ψ (axial-vector) are normalized to the usual weakcoupling strength. p and n refer respectively to protons and neutrons and the Z -nucleon vectorand axial-vector couplings are v p = − θ W , v n = − , a p = . , a n = − . , where we have used the numerical values from [41] to estimate a p and a n . However, we arenot concerned with the axial-vector couplings, since their contribution to the cross section issuppressed with respect to the one given by the vector couplings. Similarly the Z (cid:48) -DM and Z (cid:48) -nucleon interaction Lagrangian can be written as L Z (cid:48) = g θ W Z (cid:48) µ ¯ ψ ( v (cid:48) ψ − a (cid:48) ψ γ ) γ µ ψ + (2) g θ W Z (cid:48) µ (cid:104) ¯ p γ µ ( v (cid:48) p − a (cid:48) p γ ) p + ¯ n γ µ ( v (cid:48) n − a (cid:48) n γ ) n (cid:105) . As for the Z , also in this case the axial-vector couplings contribution to the cross section isnegligible. Possible constraints from colliders on Z (cid:48) can be safely avoided assuming a leptophobic Z (cid:48) . As long as the Z (cid:48) couplings to leptons are small enough, no bounds can be set at present. UsingEqs. (1) and (2), we can write the spin-independent cross section in the zero momentum transferlimit as σ = G F µ A π (cid:12)(cid:12)(cid:12) f p Z + f n ( A − Z ) (cid:12)(cid:12)(cid:12) , (3)where G F is the Fermi constant, µ A is the DM-nucleus reduced mass, and the dimensionlesscouplings to protons and neutrons are defined as f p = v ψ v p + v (cid:48) ψ v (cid:48) p m Z m Z (cid:48) , f n = v ψ v n + v (cid:48) ψ v (cid:48) n m Z m Z (cid:48) . (4)We already know that in order to alleviate the discrepancy between the di ff erent direct detectionexperimental results we need to have m DM ∼ f n / f p = − .
71, and the DM-proton crosssection σ p ∼ × − cm . Thus by fixing these three values we find the following relations for4he unknown parameters of the model (cid:12)(cid:12)(cid:12) f p (cid:12)(cid:12)(cid:12) = (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) v ψ v p + v (cid:48) ψ v (cid:48) p m Z m Z (cid:48) (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) = (cid:115) σ p π G F µ p , (5) f n = v ψ v n + v (cid:48) ψ v (cid:48) n m Z m Z (cid:48) = − . f p . (6)Substituting the numbers and dividing by the known values of the parameters v p = .
055 and v n = − . v ψ + v (cid:48) ψ v (cid:48) p v p m Z m Z (cid:48) = v ψ + v (cid:48) ψ v (cid:48) p (cid:18) m Z (cid:48)
100 GeV (cid:19) − = ± , (7) v ψ + v (cid:48) ψ v (cid:48) n v n m Z m Z (cid:48) = v ψ − . v (cid:48) ψ v (cid:48) n (cid:18) m Z (cid:48)
100 GeV (cid:19) − = ± . . (8)The Z -DM coupling v ψ can be constrained using the measurements of the Z decay width intoinvisible channels. The LEP experiment set strict limits on the number of SM neutrinos, i.e. N ν = . ± .
008 [42]. The error in the measurement can be used to constrain non-SM contributionsto the Z decay width. Using the uncertainty in the LEP result δ LEP = . v ψ β (3 − β ) + a ψ β < δ LEP , (9)where β = (cid:113) − m DM / m Z is the velocity factor. Assuming a DM mass of ∼ a ψ = v ψ can assume its maximal allowed value | v ψ | < . a ψ = v ψ this constraint gives | v ψ | < . Z (cid:48) alone. Thereforeinterference is not relevant for this kind of DM interaction with the SM particles. Similar studieshave been performed recently in [43]. III. Z (cid:48) INTERFERING WITH HIGGS
Before proceeding, let us comment, that the DM signals seen in DAMA / CoGeNT and the nullresults of the other direct DM experiments cannot be explained simultaneously through a Z andHiggs interference. The reason for this is that a light ( ∼ Z -boson such that σ p ∼ × − cm and f n / f p = − .
71, is ruled out by the aforementionedLEP constraints. However, as we will demonstrate below, interference between Z (cid:48) and the Higgsis a viable possibility.The relevant Higgs ( h ) interaction Lagrangian is L h = m DM ¯ ψψ − h ¯ ψ ( d h + a h γ ) ψ − m p v EW f h ( ¯ pp + ¯ nn ) , (10)5here d h and a h are the dimensionless scalar and pseudo-scalar Higgs-DM couplings respectively.The Higgs field h is here the physical field, i.e. the oscillation around the vacuum expectation value v EW . We have specified a mass term for the DM to point out that it doesn’t need to be generatedby the vacuum expectation value of the Higgs field.Combining the scalar interaction from this Lagrangian, with the vector one for the Z (cid:48) as itappears in (2), we get the DM-nucleus spin-independent cross section as in Eq. (3), where now thedimensionless couplings to protons and neutrons are defined as f p = v (cid:48) ψ v (cid:48) p m Z m Z (cid:48) − d h f m p v EW m h , f n = v (cid:48) ψ v (cid:48) n m Z m Z (cid:48) − d h f m p v EW m h . (11)As for the Z - Z (cid:48) case, the pseudo-scalar and pseudo-vector couplings of the DM with the Higgsand the Z (cid:48) respectively lead to negligible contributions to the cross section compared to the scalarand vector ones investigated here. The constraints are | f p | = (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) v (cid:48) ψ v (cid:48) p m Z m Z (cid:48) − d h f m p v EW m h (cid:12)(cid:12)(cid:12)(cid:12)(cid:12)(cid:12) = .
92 (12) f n = v (cid:48) ψ v (cid:48) n m Z m Z (cid:48) − d h f m p v EW m h = − . f p = ± . . (13)These can be rewritten as v (cid:48) ψ v (cid:48) p (cid:18) m Z (cid:48)
100 GeV (cid:19) − − . × − d h (cid:18) m h
100 GeV (cid:19) − = ± . v (cid:48) ψ v (cid:48) n (cid:18) m Z (cid:48)
100 GeV (cid:19) − − . × − d h (cid:18) m h
100 GeV (cid:19) − = ∓ . , (15)where we have used f = . m Z (cid:48) , m h ∼
100 GeV, the Higgs contribution to theinterference is negligible, and the Z (cid:48) has to directly account for the isospin violation needed toget the desired value of f n / f p . A substantially lighter Higgs, around 50 GeV with a coupling d h in the range 5 −
10, can lead to a phenomenologically viable interference. Note that such a lightHiggs-like state is not immediately ruled out by collider experiments since this state has newdecay modes, e.g. to two DM particles which are not accounted for in the SM (see e.g. [45]).
IV. INTERFERENCE WITHIN THE TWO HIGGS DOUBLET MODEL
We will now consider a two Higgs doublet model where one of the Higgs fields couples toup-type quarks and the other to down-type quarks. This kind of scenario albeit more general,6s similar to the Minimal Supersymmetric Standard Model Higgs sector. We consider Yukawa-type interactions between the two Higgs fields and the fermionic DM ψ . We write also e ff ectiveinteractions with the SM proton p and neutron n . The interaction Lagrangian is L H = λ DM h ¯ ψψ + λ p h ¯ pp + λ n h ¯ nn + λ DM h ¯ ψψ + λ p h ¯ pp + λ n h ¯ nn . (16) h and h are here the physical scalars, i.e. the mass eigenstates after diagonalization, where theoriginal Higgs fields coupled one to the up-type quarks and the other to the down-type. Thenucleon couplings are then λ p = cos θ v (cid:88) q u (cid:104) p | m q u ¯ q u q u | p (cid:105) − sin θ v (cid:88) q d (cid:104) p | m q d ¯ q d q d | p (cid:105) , (17a) λ n = cos θ v (cid:88) q u (cid:104) n | m q u ¯ q u q u | n (cid:105) − sin θ v (cid:88) q d (cid:104) n | m q d ¯ q d q d | n (cid:105) , (17b) λ p = sin θ v (cid:88) q u (cid:104) p | m q u ¯ q u q u | p (cid:105) + cos θ v (cid:88) q d (cid:104) p | m q d ¯ q d q d | p (cid:105) , (17c) λ n = sin θ v (cid:88) q u (cid:104) n | m q u ¯ q u q u | n (cid:105) + cos θ v (cid:88) q d (cid:104) n | m q d ¯ q d q d | n (cid:105) , (17d)where the sums over up-type ( q u ) and down-type ( q d ) quarks account for the scalar quark currentswithin the nucleons. v and v are the vacuum expectation values of the two Higgs fields, whichobey the relation v EW / = v + v ( v EW (cid:39)
246 GeV). θ is the mixing angle needed to diagonalizethe Higgs system, and here is a free parameter. We also assume that the DM particle massis not generated by the vacuum expectation values of the Higgs fields. The matrix elements (cid:104) p , n | m q u , d ¯ q u , d q u , d | p , n (cid:105) in (17) are obtained in chiral perturbation theory, when dealing with lightquarks, using the measurements of the pion-nucleon sigma term [46], and in the case of heavyquarks, from the mass of the nucleon via trace anomaly [44, 47]. The experimental uncertainties,especially in the pion-nucleon sigma term, give rise to di ff erences in the values of these matrixelements. As long as λ pi and λ ni are not identical, isospin violation can always be guaranteed. Toevaluate the matrix elements we follow Ref. [41] which makes use of the results found in [44, 46, 47]. (cid:88) q u (cid:104) p | m q u ¯ q u q u | p (cid:105) ≈
105 MeV , (cid:88) q d (cid:104) p | m q d ¯ q d q d | p (cid:105) ≈
417 MeV , (18a) (cid:88) q u (cid:104) n | m q u ¯ q u q u | n (cid:105) ≈
100 MeV , (cid:88) q d (cid:104) n | m q d ¯ q d q d | n (cid:105) ≈
426 MeV . (18b)The spin-independent DM-nucleus cross section can now be calculated using the interaction7erms from Eq. (16) σ = µ A π (cid:12)(cid:12)(cid:12) f p Z + f n ( A − Z ) (cid:12)(cid:12)(cid:12) , (19)where the couplings to protons and neutrons are f p = λ DM λ p m h + λ DM λ p m h , f n = λ DM λ n m h + λ DM λ n m h . (20)Eqs. (19) and (20) can be used to study the e ff ects of the interference in a generic two Higgs doubletmodel. Substituting the couplings from (17), (18) into (20), and imposing the fitting values for m DM , f n / f p and σ p , we get the following constraint equations for the unknown parameters: λ DM (cid:18) v v EW (cid:19) − (cid:18) cos θ − . θ v v (cid:19) (cid:18) m h
100 GeV (cid:19) − + . λ DM (cid:18) v v EW (cid:19) − (cid:18) cos θ + .
25 sin θ v v (cid:19) (cid:18) m h
100 GeV (cid:19) − = ± . × , (21) λ DM (cid:18) v v EW (cid:19) − (cid:18) cos θ − . θ v v (cid:19) (cid:18) m h
100 GeV (cid:19) − + . λ DM (cid:18) v v EW (cid:19) − (cid:18) cos θ + .
23 sin θ v v (cid:19) (cid:18) m h
100 GeV (cid:19) − = ∓ . × . (22)For natural values of v and v , i.e. of the order of v EW , and for m h and m h of the order of 100-1000GeV, the DM couplings to the Higgs fields need to be of O (10 ) to fit the data. This large couplingsare of course unnatural as such. Thus the original DM-Higgs interactions and related couplings,introduced in Eq. (16), need to be considered as a simple e ff ective description.We will introduce now a model that will accommodate such large values for the e ff ectivecouplings, and link it also to Electroweak Baryogenesis [36, 37, 48–50]. We start by recallingthe three Sakharov conditions needed for successful production of a baryon asymmetry for themodel considered here [36]: the baryon number violation originates from SM sphalerons; out-of-equilibrium conditions are generated by bubble nucleation in a strong first order electroweak (EW)phase transition; a new CP violating phase which we take it to be generated within the two Higgsdoublet model. Thus we will now investigate whether both baryogenesis and the explanationof the direct detection data via interference can be achieved simultaneously using a two Higgsdoublet model.We start by introducing a DM-Higgs e ff ective Lagrangian, which avoids the large DM-Higgscouplings discussed in the end of the last section. The Lagrangian reads L DM = ( m DM − λ DM v Λ − λ DM v Λ ) ¯ ψψ + λ DM Λ φ † φ ¯ ψψ + λ DM Λ φ † φ ¯ ψψ , (23) The normalization for f p and f n here is di ff erent than the one used in Eq. (3). ff Λ is assumed to be of the order of 1-10 GeV. We will show that for such a rangeof Λ the required couplings to DM will turn to be between 1-10. Here we indicated the Higgsdoublets before EW symmetry breaking by φ . In principle it is not hard to construct a UV completetheory for such a generic e ff ective Lagrangian. We give one such a model in the Appendix A. Asan underlying two Higgs model we will use the one studied in [36–38]. After implementing theDM part, the full two Higgs model Lagrangian is L H = (cid:88) i = | D µ φ i | − V ( φ , φ ) + L DM + L fermions + L Yuk + L gauge , (24)where the two Higgs doublets scalar potential is V ( φ , φ ) = λ ( φ † φ − v ) + λ ( φ † φ − v ) + λ [( φ † φ − v ) + ( φ † φ − v )] + λ [( φ † φ )( φ † φ ) − ( φ † φ )( φ † φ )] + λ [Re( φ † φ ) − v v cos ξ ] + λ [Im( φ † φ ) − v v sin ξ ] , (25) ξ being the relative CP violating phase between the two Higgs fields, which cannot be entirelyrotated away by field redefinitions [51]. L fermions and L gauge account for the fermion covariantderivative terms and the gauge field kinetic terms respectively. Yukawa interactions in L Yuk couple the up-type quarks to φ and the down-type quarks to φ , resulting in identical Higgs-proton and Higgs-neutron couplings as presented in Eqs. (16) and (17). The only relevant SMYukawa coupling for baryogenesis is the top quark one [36]. Due to the specific choice of theinteraction between DM and the Higgs fields, baryogenesis is not a ff ected by the presence of theDM sector. Fitting now the DM direct detection data using the model (23), we get the followingconstraints ˜ λ DM (cid:18) Λ v EW (cid:19) − (cid:18) cos θ − . θ v v (cid:19) (cid:18) m h
100 GeV (cid:19) − + . λ DM (cid:18) Λ v EW (cid:19) − (cid:18) cos θ + .
25 sin θ v v (cid:19) (cid:18) m h
100 GeV (cid:19) − = ± . × , (26)˜ λ DM (cid:18) Λ v EW (cid:19) − (cid:18) cos θ − . θ v v (cid:19) (cid:18) m h
100 GeV (cid:19) − + . λ DM (cid:18) Λ v EW (cid:19) − (cid:18) cos θ + .
23 sin θ v v (cid:19) (cid:18) m h
100 GeV (cid:19) − = ∓ . × . (27)˜ λ DM and ˜ λ DM are here defined so that 2 ˜ λ DM v / Λ and 2 ˜ λ DM v / Λ are the actual couplings of theDM to the physical Higgs fields h and h , respectively,˜ λ DM = λ DM (cos θ − sin θ λ DM λ DM v v ) , ˜ λ DM = λ DM (cos θ + sin θ λ DM λ DM v v ) . (28)9iven the potential in Eq. (25), the mixing angle θ is now given bytan 2 θ = v v (4 λ + g )4 v ( λ + λ ) − v ( λ + λ ) + g ( v − v ) , (29)where g = λ cos ξ + λ sin ξ . If we assume that Λ ∼ O (100) GeV, we find that the DM couplings to the Higgs doublets λ DM and λ DM (or at least one ofthem) need to be of the order O (10) to be able to fulfill the above constraint equations. The size ofthese couplings is now substantially reduced with respect to the previous model.Summarizing, since the CP violating phase can be rotated away in the light quark sector [51]there are no direct implications for the direct detection experiments. A welcome feature is that byincluding the interaction of the Higgs fields to DM using higher order operators, the energy scale Λ can be traded for a more natural value of the dimensionless couplings when fitting their valuesto direct detection data. V. CONCLUSIONS
We have investigated several quantum mechanical interfering patterns for DM scattering o ff nuclei that can explain the DAMA and CoGeNT results. In particular we considered the case inwhich DM interacts via Z and Z (cid:48) , Z (cid:48) and Higgs, and two Higgs fields with or without CP violation.We found that in the first case due to the constraints from the invisible decay width of the Z , thedominant contribution should come from the Z (cid:48) exchange. In the second case, Z (cid:48) dominates againupon assuming natural values of the Higgs coupling and masses. In the last case we found thatan explanation of the DAMA / CoGeNT results based on interference of two Higgs fields besidesbeing phenomenologically viable, is also consistent with the Electroweak Baryogenesis scenariosbased on two Higgs doublet models.
Appendix A: An ultraviolet completion
In the Lagrangian below we introduce a simple renormalizable ultraviolet complete model forthe e ff ective theory presented in (23): L S =
12 ( ∂ µ S )( ∂ µ S ) − λ s ( S − v s ) + y DM S ¯ ψψ − y [( φ † φ − v ) + ( S − v s )] − y [( φ † φ − v ) + ( S − v s )] , (A1)where S is a new real, EW singlet, scalar field and y DM , y , y and λ s are the dimensionless scalar-DM, scalar-Higgs 1, scalar-Higgs 2 and scalar self-couplings respectively. The scalar potential,10ncluding the terms with couplings λ s , y and y , is minimized together with the two Higgspotential (25). We define with s the physical fluctuation of S around its vev v s . As long as the φ i − s mixings in the Higgs-scalar mass matrix are tiny, the singlet field s will couple mostly to the DMwhereas the SM particles will couple mostly to the two Higgs fields.After integrating out the massive degrees of freedom, i.e. the Higgses and the scalar S , from thefull model, the low energy e ff ective theory describes also the four fermion interactions betweenthe DM and the quarks, with e ff ective couplings8 y DM y y q , v v s m s m h (cos θ − sin θ y v y v )(cos θ − sin θ y q , y q , ) + y DM y y q , v v s m s m h (cos θ + sin θ y v y v )(cos θ + sin θ y q , y q , ) , (A2)where y q , i is the quark-Higgs i Yukawa coupling, before the diagonalization of the Higgs system,and m s and m h i are the physical masses of the singlet and the Higgs fields respectively. Matchingthe Lagrangian (A1) with (23) implies 4 y DM y i v s / m s = λ DM i / Λ . As long as the fundamental energyscale for S is less than EW, i.e. m s ∼ Λ ≤ v EW , the e ff ective four fermion couplings can be muchlarger than the underlying couplings y DM , y i taken to be of the order of unity. [1] A. Belyaev, M. T. Frandsen, S. Sarkar and F. Sannino, “Mixed dark matter from technicolor,” Phys.Rev. D , 015007 (2011) [arXiv:1007.4839 [hep-ph]].[2] S. Nussinov, “TECHNOCOSMOLOGY: COULD A TECHNIBARYON EXCESS PROVIDE A ’NATU-RAL’ MISSING MASS CANDIDATE?,” Phys. Lett. B , 55 (1985).[3] S. M. Barr, R. S. Chivukula and E. Farhi, “ELECTROWEAK FERMION NUMBER VIOLATION ANDTHE PRODUCTION OF STABLE PARTICLES IN THE EARLY UNIVERSE,” Phys. Lett. B , 387(1990).[4] S. B. Gudnason, C. Kouvaris and F. Sannino, “Towards working technicolor: E ff ective theories anddark matter,” Phys. Rev. D , 115003 (2006) [arXiv:hep-ph / , 095008 (2006) [arXiv:hep-ph / , 037702 (2009)[arXiv:0812.3406 [hep-ph]].[7] M. Y. Khlopov and C. Kouvaris, “Composite dark matter from a model with composite Higgs boson,”Phys. Rev. D , 065040 (2008) [arXiv:0806.1191 [astro-ph]].[8] D. D. Dietrich and F. Sannino, “Conformal window of SU(N) gauge theories with fermions in higherdimensional representations,” Phys. Rev. D , 085018 (2007) [arXiv:hep-ph /
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