Two natural scenarios for dark matter particles coexisting with supersymmetry
Maxwell Throm, Reagan Thornberry, John Killough, Brian Sun, Gentill Abdulla, Roland E. Allen
aa r X i v : . [ h e p - ph ] J a n January 10, 2019 1:30 WSPC/INSTRUCTION FILE Allen-DM-Dec20
Two natural scenarios for dark matter particles coexisting withsupersymmetry
Maxwell Throm, Reagan Thornberry, John Killough, Brian Sun, Gentill Abdulla,Roland E. Allen
Department of Physics and Astronomy, Texas A&M UniversityCollege Station, Texas 77843, [email protected]
We describe two natural scenarios in which both dark matter WIMPs (weakly interact-ing massive particles) and a variety of supersymmetric partners should be discoveredin the foreseeable future. In the first scenario, the WIMPs are neutralinos, but theyare only one component of the dark matter, which is dominantly composed of otherrelic particles such as axions. (This is the multicomponent model of Baer, Barger, Sen-gupta, and Tata.) In the second scenario, the WIMPs result from an extended Higgssector and may be the only dark matter component. In either scenario, both the darkmatter WIMP and a plethora of other neutral and charged particles await discovery atmany experimental facilities. The new particles in the second scenario have far weakercross-sections for direct and indirect detection via their gauge interactions, which are ei-ther momentum-dependent or second-order. However, as we point out here, they shouldhave much stronger interactions via the Higgs. We estimate that their interactions withfermions will then be comparable to (although not equal to) those of neutralinos with acorresponding Higgs interaction. It follows that these newly proposed dark matter par-ticles should be within reach of emerging and proposed facilities for direct, indirect, andcollider-based detection.
Keywords : dark matter; supersymmetry; Higgs
1. Introduction
After decades of intense efforts, neither supersymmetry nor dark matter parti-cles have been detected. One should recall, however, that historically importantdiscoveries typically require patient waits – 48 years for the Higgs boson, a cen-tury for gravitational waves, and almost two centuries for black holes. There arestill compelling motivations for seeking both of these proposed central features ofnature: Alternatives to dark matter have been rendered increasingly implausible byastronomical observations; and without supersymmetry (susy) it is hard to under-stand the unification of coupling constants at high energy or why the Higgs bosonmass is not enormously increased by radiative corrections.The pessimism regarding susy is in part due to experimental limits that now ruleout the simplest models (minimal supergravity and the minimal supersymmetricstandard model). But there was never any reason to believe that simplistic modelslike these would be quantitatively valid. They have primarily served to providevaluable guidance for the qualitative role of susy in various physical phenomena. anuary 10, 2019 1:30 WSPC/INSTRUCTION FILE Allen-DM-Dec20 Another discouraging development was the finding that natural supersymmetricmodels (which are consistent with experiment) have difficulty in predicting theobserved relic abundance of dark matter, if it is assumed that the dark matterconsists entirely of supersymmetric partners . But if this assumption is dropped, asin the scenarios of the next section, the tension between theory and observation isameliorated. Regarding dark matter searches, the cross-sections were always known to besmall, since observations demonstrate that these particles cannot interact throughthe electromagnetic or strong force. The limits that have been established are con-sistent with either of the two scenarios in the next section. On the other hand, bothneutralinos and the new particles discussed here can still lie within reach of thedirect-detection experiments planned for the next few years, as well as an upgradedLHC, and possibly the AMS and Fermi satellite experiments.
2. Two testable scenarios: neutralinos plus axions, and a newWIMP candidate with mass ≤
125 GeV
Recently it has been pointed out that a multicomponent dark matter scenario,dominated by e.g. axions, but with a significant admixture of neutralinos, relievesthe tension between susy dark matter and the observed dark matter abundance. This suggestion provides motivation for both the many WIMP searches – includingXenon, LZ, and SuperCDMS – and the very different searches for axions.An alternative scenario is that the (only or principal) dark matter particle isthe one recently proposed in an extension of the Higgs sector.
19, 20
To facilitate thediscussion below, in which this particle is compared with the neutralino, we will callparticles of this kind (neutral or charged) “Higgsons”, and will represent them by H . (They are then to be distinguished from Higgs bosons h and their superpartners,the Higgsinos e h .)In Figs. 1-5 we show a few of the most basic interactions of Higgsons in directdetection experiments (Figs. 1-3), indirect detection following annihilation (Fig. 4),and collider detection after creation by proton-proton collisions (Fig. 5). The firstthree processes follow from the action in Eq. (40) of Ref. : S H = X i Z d x (cid:18) H i † ( x ) D µ D µ H i ( x ) − (cid:18) H i † ( x ) S µν F µν H i ( x ) + h.c. (cid:19)(cid:19) where i labels the various species of neutral plus charged Higgson fields.Here we point out that there should also be an interaction with the recentlyobserved Higgs boson h . This is consistent with the quartic self-interaction of theHiggs field φ : L φ = λ h (cid:0) φ † ( x ) φ ( x ) (cid:1) (1)with φ = (cid:18) φ + φ (cid:19) . (2)anuary 10, 2019 1:30 WSPC/INSTRUCTION FILE Allen-DM-Dec20 Z exchange with first-order momentum-dependent vertex.Fig. 2. Left: Direct detection via double Z exchange with second-order vertex. Right: Directdetection via double W exchange with second-order vertexFig. 3. Left: Direct detection via h exchange with, e.g., strange quark. Right: Direct detectionvia h exchange with top quark triangle coupled to gluons anuary 10, 2019 1:30 WSPC/INSTRUCTION FILE Allen-DM-Dec20 Z . Right: Indirect detection via h .Fig. 5. Left: Collider production via Z . Right: Collider production via h . In the present theory, a scalar field φ r represents the amplitude of a 4-component field Φ r : Φ r = φ r χ r [no sum on r ] (3)with χ r † χ r = 1 [no sum on r ] . (4)Let us focus on the neutral field Φ , with condensation of the Higgs field φ plusexcitation of a Higgs boson h and a Higgson H . The simplest generalization whichyields (1) (and which has the correct symmetries) is L int = λ h (cid:0) φ ∗ φ + H † H (cid:1) (5)with φ = v + h , where v is the vacuum expectation value of the Higgs field. (Both φ and H are dimension 1 bosonic fields.) It follows that there is a lowest-orderinteraction of the Higgson with the Higgs, given by L Hh = 4 λ h vH † h H . (6)anuary 10, 2019 1:30 WSPC/INSTRUCTION FILE Allen-DM-Dec20 The Higgson H then interacts with quarks and other fermions through an exchangeof Higgs bosons h as well as vector bosons ( W ± and Z ).The neutralino χ also has an interaction through the Higgs, if χ has an ap-preciable admixture of both a Higgsino e h and a zino e Z , resulting from a term L χh = λ χ e h † h e Z . (Both e h and e Z are dimension 3/2 fermionic fields.)
3. Relative cross-sections for the two varieties of WIMPs
We can now estimate the ratio of each cross-section for a Higgson H to the cor-responding one for a neutralino χ , by comparing the order of magnitude of thecontributions from external lines and vertices in the Feynman diagrams of Figs. 1-5and their neutralino counterparts.The external lines for a H pair contribute (in order of magnitude) 1, sincethe normalization for this particle is the same as for a scalar boson. The externallines for a χ pair (again in order of magnitude) contribute the neutralino mass M χ , since these are Majorana fermions. The H , Z vertex of Fig. 1 is momentum-dependent, and therefore makes a contribution that can be represented as p W g w ,where g w ∼ . p W is the WIMP momentum loss,which is of order 10 − M H at very best, in natural units. For M H ∼ M χ , we concludethat the amplitude represented by Fig. 1 is typically lower by a factor of . − compared to its neutralino counterpart, and the cross-section is consequently lowerby . − . The reason for this enormous decrease is that the coupling of H to Z is first-order but momentum-dependent. H also has second-order couplings (which are momentum-independent), as re-flected in Fig. 2. But these contributions are even smaller, because they involve two Z or W propagators in addition to two factors of g w . An extra factor of g w /M Z or g w /M W will reduce the cross-section by many orders of magnitude..Furthermore, these gauge interactions are most relevant for spin-dependent scat-tering, which is weak even for the neutralino. The final conclusion, then, is that thegauge interactions lead to cross-sections that are hopelessly small for direct detec-tion.On the other hand, the interactions via the Higgs in Fig. 3 are comparable towhat they are for the neutralino: In the processes involving h exchange, thereare factors of roughly 1 from the external lines and λ H v from the vertex. For theneutralino, the external lines and vertex respectively contribute roughly M χ and λ χ .The product is then roughly the same if M χ ∼ v ≈
250 GeV and λ χ ∼ λ H ∼ . mass of the top, with an enormous Yukawa coupling that compensates for the needto go to higher order, using the coupling of the gluons g to a nucleus in the detector.We conclude that the Higgson H and the neutralino χ should have comparablecross-sections for Higgs exchange. Since this is the dominant process for direct detec-tion via spin-independent scattering, H is in the same basic range of detectabilityas the neutralino.The amplitudes can easily differ by an order of magnitude, however, and thecross-sections by two orders of magnitude, so quantitative calculations are needed.The mass of the H is ≤
125 GeV and its coupling constant λ H is related to thequartic coupling constant of the Higgs (about 1/6), so better estimates are feasible.Fig. 4 shows the simplest processes resulting from the annihilation of H withits antiparticle H , producing a fermion-antifermion pair. Again, for slowly movingdark matter particles the momentum dependence of the first vertex leads to a tinycross-section in the left panel of Fig. 4, but the process in the right panel occurswith comparable amplitudes for H and χ .Finally, in Fig. 5, two of a vast number of possible processes are shown for pro-duction at the LHC. The momenta can now be large, and the momentum-dependentvertex can therefore be comparable to the corresponding vertex for neutralino pro-duction. The present theory also predicts production of H ± particles, which will bemore readily detectable but which presumably have much higher masses.
4. Conclusion
Supersymmetry predicts a doubling of particles and thus a doubling of the range ofphysics. The theory of Refs. retains this prediction, and also predicts anotherclass of new particles, resulting from an extended Higgs sector. The lowest in massof these new particles will be stable (with an R-parity of −
1) if its mass m H is lowerthan that of the lowest mass superpartner. This is likely, since m H ≤ m h , where m h = 125 GeV/c is the mass of the observed Higgs boson. With a well-definedmass, which is in an optimal range for direct detection, and a substantial estimatedcross-section via Higgs exchange for many relevant processes, it appears to be ideallysuited for direct, indirect, and collider-based detection within the foreseeable future. Acknowledgement
REA benefitted greatly from discussions with Howard Baer and Keith Olive.
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