PDF《ULB-TH/09-03》

arXiv:0903.

4010v1 [hep-ph]

24 Mar

2009 ULB-TH/09-03 FTUAM-09-04 Scalar Multiplet Dark Matter T. Hambyea, F.-S. Linga, L. Lopez Honoreza,b and J. Rochera

1 aService de Physique Th? eorique, Universit? e Libre de Bruxelles,

1050 Brussels, Belgium bDepto de Fisica Teorica, Universidad Autonoma de Madrid, Cantoblanco, Madrid, Spain Abstract We perform a systematic study of the phenomenology associated to models where the dark matter consists in the neutral component of a scalar SU(2)L n-uplet, up to n = 7. If one includes only the pure gauge induced annihilation cross-sections it is known that such particles provide good dark matter candidates, leading to the observed dark matter relic abundance for a particular value of their mass around the TeV scale. We show that these values actually become ranges of values - which we determine - if one takes into account the annihilations induced by the various scalar couplings appearing in these models. This leads to predictions for both direct and indirect detection signatures as a function of the dark matter mass within these ranges. Both can be largely enhanced by the quartic coupling contributions. We also explain how, if one adds right-handed neutrinos to the scalar doublet case, the results of this analysis allow to have altogether a viable dark matter candidate, successful generation of neutrino masses, and leptogenesis in a particularly minimal way with all new physics at the TeV scale.

1 Introduction There are many possible dark matter (DM) candidates and a systematic study of all possi- bilities, and associated phenomenology, is not conceivable. However if one takes as criteria the minimality of the model, in terms of the number of new ?elds and parameters, such a systematic study becomes feasible. Such approach is di?erent and complementary to the ones that led to theories with e.g. Supersymmetry [1C3] or Universal Extra Dimensions [4C6], which were invented as an attempt to address and solve other fundamental questions such as the Hierarchy problem, and where the number of parameters and possibilities can be huge. Another criterion of selection one can consider is the predictivity and the testability of the model in current and future accelerators, and direct or indirect DM detection experiments. Particularly simple possibilities along these lines of thought arise if one adds to the Standard Model only one extra SU(2)L singlet or multiplet, scalar or fermion, containing a neutral DM candidate ?eld. The stability of the DM is usually achieved in this case by introducing a Z2 parity symmetry, under which the extra multiplet is odd and all the SM particles are even. Several possibilities of this kind, such as the scalar singlet [7C14], the fermion singlet [15, 16], the scalar doublet (in the Inert Doublet Model [13, 17C24]), the fermion doublet candidate [25, 26], etc, have already been explored and they o?er a rich phenomenology. A systematic study has been performed in Ref. [25] for any multiplet from the doublet up to the

1 thambye@ulb.ac.be;

?ing@ulb.ac.be;

llopezho@ulb.ac.be;

jrocher@ulb.ac.be

1 7-plet. Multiplets o?er the advantage that they could be potentially produced at colliders through gauge interactions. In this analysis the relic density of such DM candidate has been calculated considering all annihilation processes induced by the known SU(2)L *U(1)Y gauge interactions. This framework is particularly predictive, the only free parameter is the DM mass, mDM , and the observed relic density can be obtained for only one value of this mass. Considering only the gauge induced processes in such a way is fully justi?ed for an extra fermion multiplet because no other renormalizable interaction with the SM particles can be written. However, for a scalar multiplet this assumption is not at all automatic as quartic scalar interactions involving both the scalar multiplet and the Brout-Englert-Higgs doublet are perfectly allowed. Therefore, the analysis of Ref. [25] for scalar multiplets does not hold if these scalar couplings are not suppressed. In this paper, we study in a systematic way the rich phenomenology which arise if one includes the e?ects of the quartic couplings for all scalar multiplets up to the 7-plet. This we do in the high mass regime, that is to say for mDM >

mW , where the observed relic density is obtained for annihilation cross-sections ∝ 1/m2 DM (which is typical of the large DM mass asymptotic regime). We show in particular that, due to a large enhancement of the (co)annihilation of DM into gauge bosons driven by the scalar couplings, the latter cannot be ignored unless they are much smaller than the gauge couplings. Moreover, due to these quartic couplings, and without ?ne-tuning, a large range of values of mDM is compatible with the observed DM relic abundance. These contributions also enhances the predicted ?uxes for direct and indirect detection searches. The case where the multiplet is a doublet, known as the Inert Doublet Model (IDM) has already been extensively studied in the literature. A detailed analysis of the high mass regime was however missing and we provide it here. The phenomenology of this model is particularly rich because it depends on the interplay of three di?erent scalar quartic couplings. The phenomenology of the higher multiplet case on the other hand in ?ne depends on only one quartic coupling, λ3, which renders these cases particularly constrained and predictive. In this work, only higher multiplet models allowed by current direct detection constraints will be considered. This limits us to odd dimension n-uplets with zero hypercharge and n = 3,

5 and 7. For these models the high mass regime, mDM >

mW , which we study is the only possible one. We also present in this paper an intriguing possible consequence of our results for the doublet model: in agreement with the DM constraints, if, in order to explain the neutrino masses, one adds to this model right-handed neutrinos, it is possible to induce in a particularly simple way baryogenesis through leptogenesis with all new physics around the TeV scale. The paper is organized as follows. We ?rst present the inert doublet and the higher mul- tiplet models in Section 2. Aside from ?xing notations and de?nitions, a discussion on the number of relevant quartic couplings for the higher multiplets is made. Predictions for the relic density are made in Section 3, both numerically and (in the instantaneous freeze-out approximation) analytically. The latter method allows to show the enhancement of the scalar coupling contribution in the various cross-sections, in particular the important coannihilation ones. For the doublet case, maximal mass splittings between the DM doublet components compatible with the WMAP constraint are given as a function of the DM mass. For higher multiplets, this constraint ?xes the value of λ3 as a function of the DM mass. A discussion is also made about the consequences of having, for very heavy DM candidates, freeze-out before the electroweak phase transition. In Section 4, predictions on the DM-nucleon elastic scat- tering cross-section relevant for direct detection searches are made, and compared to current

2 experimental limits and projected reaches of future experiments. In Section 5, predictions for various indirect detection signals are discussed. The possibility of resonances [27,28] is reex- amined in light of the enlarged mass range of the DM candidate. Photon and neutrino ?uxes from the galactic center are compared with the sensitivity of current telescopes (FERMI and KM3net). The ?uxes of charged antimatter cosmic rays (positrons and antiprotons) are cal- culated with DarkSUSY and confronted with data. Finally, the extension of the doublet by right-handed neutrinos and consequences for neutrino masses and leptogenesis, are discussed in Section 6. Conclusions are drawn in Section 7. Appendix A contains precise discussions, for the higher multiplet cases, on the most general scalar potential and the di?erences and the similarities between complex and real multiplets. Appendix B gives the complete set of (co)annihilation Feynman diagrams for all the models studied in this paper.

2 Models 2.1 Inert Doublet Model The Inert Doublet Model (IDM) is a two Higgs doublet model with a Z2 symmetry. They are denoted by H1 and H2, H1 being the usual Brout-Englert-Higgs doublet. All SM particles are even under the Z2 symmetry, while H2 is odd. This ensures the stability of the lightest member of H2, which will be the DM candidate, and prevents from ?avor changing neutral currents (FCNC) [17]. We will assume that Z2 is not spontaneously broken, in particular, H2 does not develop a vacuum expectation value. In order to have a neutral component, the hypercharge of a scalar doublet is necessarily Y = ±1 (we choose to write the electric charge Q = T3 + Y/2). We conventionally assign +1 to the hypercharge of H2: one can write H2 = (H+ (H0 + iA0)/ √ 2)T , similarly to the ordinary Higgs doublet, where H1 = (h+ (v0 + h + iG0)/ √ 2)T . The most general renormalizable scalar potential with two doublets is given by1 V (H1, H2) = ?2 1|H1|2 + ?2 2|H2|2 + λ1|H1|4 + λ2|H2|4 + λ3|H1|2 |H2|2 + λ4|H? 1H2|2 + λ5

2 (H? 1H2)2 + h.c. . (1) After the electroweak symmetry breaking, H1 develops its vev, v0 = ??2 1/λ1 ?

246 GeV, and the scalar potential in the unitary gauge then becomes, V =

1 2 m2 hh2 + λ1v0h3 +

1 4 λ1h4 +

1 2 m2 H0 H2

0 +

1 2 m2 A0 A2

0 + m2 Hc H+ H? +

1 2 λH0 H2

0 + λA0 A2

0 + 2λHc ........