Dark Matter after LHC Run I: Clues to Unification

After the results of Run I, can we still ‘guarantee’ the discovery of supersymmetry at the LHC? It is shown that viable dark matter models in CMSSM-like models tend to lie in strips (co-annihilation, funnel, focus point). The role of grand unification in constructing supersymmetric models is discussed and it is argued that non-supersymmetric GUTs such as SO(10) may provide solutions to many of the standard problems addressed by supersymmetry.

Long list of observables to constrain CMSSM parameter space nificant tension with the others.

Description of the Frequentist Stat Method Employed
We define a global χ 2 likelihood function, whic all theoretical predictions with experimental c Here N is the number of observables studied sents an experimentally measured value (cons each P i defines a prediction for the correspo straint that depends on the supersymmetric p The experimental uncertainty, σ(C i ), of eac ment is taken to be both statistically and sys independent of the corresponding theoretical u σ(P i ), in its prediction. We denote by χ 2 χ 2 (BR(B s → µµ)) the χ 2 contributions from th surements for which only one-sided bounds ar

Multinest
Δχ 2 map of m 0 -m 1/2 plane ltiplets that break SO(10) and G int are labeled by R 1 and R 2 , respectively. n the introduction, this Z 2 symmetry is a remnant of an extra U(1) symmetry 8] and is used to stabilize DM candidates [9, 10]. A brief introduction to ate subgroups and Z 2 symmetry will be given in Sec. overview of the basic SO(10) model needed to accommodate a DM tioned above, in this work, we consider SO(10) GUT models and a two step simultaneous symmetry breaking chain, 1 in which the p is broken to an intermediate gauge group G int at the GUT scale ently broken to the SM gauge group ts that break SO(10) and G int are labeled by R 1 and R 2 , respectively. ntroduction, this Z 2 symmetry is a remnant of an extra U(1) symmetry is used to stabilize DM candidates [9, 10]. A brief introduction to bgroups and Z 2 symmetry will be given in Sec.
where h i = v R T with T ⌘ ( 1 i 2 )/2. As is w known, these threshold e↵ects always go in the directio of benefiting vacuum stability [7]. The evolution of t quartic couplings, c , c , and c above the intermedia scale are also shown in Fig. 1 using the matching cond tions in (4). We use the one-loop RGEs for these quart couplings. Although we do not explicitly display the ru ning of all quartic terms above the intermediate scale, w have checked that although some run negative (notab c 0 ), we have verified that the couplings satisfy su cie conditions which guarantee stability of the vacuum up the GUT scale.
The quadratic and cubic parts (which can lead to ma Example based on scalar! singlet DM (SA 3221 ) with cation occurs, ii) that the intermediate scale is found to be below the GUT scale, and iii) that the GUT scale is high enough so that the proton lifetime exceeds current experimental bounds, only a handful of possible models survive [14,15]. Furthermore, since any dark matter candidate must be part of a larger SO(10) representation, that multiplet must be split, putting further constraints on the possible choice of field content.
In this letter, we choose one example of a scalar dark matter model with an intermediate scale gauge group given by We will examine the model labeled SA 3221 in [15] for which the dark matter is a scalar singlet originating in a 16 of SO(10). In addition to SM fields, the model employs a 45 (or 210) to break SO(10) to G int when the (15, 1, 1) component (under SU(4) C ⌦SU(2) L ⌦SU(2) R ) acquires a vacuum expectation value (vev). The intermediate scale gauge group is subsequently broken when the color singlet, right-handed triplet sitting in the 126 acquires a vev. All other components of the 126 are expected to have GUT scale masses. In addition to an explicit (GUT scale) mass term for the 16, the scalar multiplet can have mass contributions from its couplings to the Higgs 45 and 126. An explicit calculation of the fine-tuning needed to obtain a TeV scale mass for the presence of the singlet scalar DM at low deflects the running of the Higgs quartic reover, we show that the negative massd for electroweak symmetry breaking runs he coupling of the Higgs field with the DM ment for the radiative electroweak symng imposes a lower bound on the DMg. This then leads to a lower limit on the ne assumes that the thermal relic abun-DM agrees with the observed DM density 2 [21]. On the other hand, perturbativity gs in the model gives an upper limit on the upling, and thus on the DM mass. As a DM mass region is allowed by these two e find that this mass range can be probed 1T experiment [22].
In many ways, this resembles the minimal dark m ter model often referred to as the Higgs portal [23, The mass of our dark matter candidate is given m 2 DM = sH v 2 /2+µ 2 s . Furthermore, fixing the dark m ter mass will also fix sH at the weak scale (taken to be m t ) through the relic density (assuming stand thermal freeze-out): m DM ' 3.3 sH TeV. In this pa we compute the DM relic density using micrOMEGAS The evolution of the Higgs quartic coupling in the with scalar potential Additional fields appear at ! the intermediate scale.
perturbatitivity implies m DM < 2 TeṼ Mambrini, Nagata, Olive, Zheng Vacuum stability and radiative EWSB Higgs mass term runs ! negative and depends on λ sH When one imposes the constraint from the relic density, we obtain somewhat stronger bounds on sH . In Fig. 2, we show the value of sgn(µ 2 )|µ| for Q = M int and 1 TeV as a function of sH (m t ). Here again, we set s (m t ) = 0. As one can see that when Q = M int , we have sH (m t ) > 0.2 corresponding to m DM > 670 TeV and when Q = 1 TeV, we have sH (m t ) > 0.41 corresponding to m DM > 1.35 TeV.  Summary.-We have presented an SO(10) model w gauge coupling unification made possible through an termediate scale at ' 10 9 GeV. SO(10) is broken G int = SU(3) C ⌦ SU(2) L ⌦ SU(2) R ⌦ U(1) B L when t right-handed triplet in the 126 obtains a vev. In t model, the lightest member of a complex scalar 16 stable and plays the role of our dark matter candida s. The specific example discussed here can be view as a UV completion of the minimal (scalar) dark mat model. We have shown that in addition to gauge co pling unification, and a dark matter candidate, unlike t case in the SM, vacuum stability is achieved up to t GUT scale, and radiative electroweak symmetry brea ing is triggered by the interactions of the dark mat and the SM Higgs. The latter result taken together w the requirement of perturbative couplings to the GU scale limit the DM mass to lie between 1.35-2 TeV. T mass range should be probed in future direct detecti experiments.

SM Fermion Singlets: Produced thermally out of equilibrium!
Fermionic candidates (NETDM)       The mass scales and proton decay lifetime are in units of GeV and years, respectively. We find that there is only one promising model with G int = SU(4) C ⌦ SU(2) L ⌦ SU(2) R , which is highlighted can be probed in future LHC experiments; for instance, dilepton resonance searches [64] are powerful probes for such a Z 0 . The leptoquarks are pair produced at the LHC, and their signature is observed in dijet plus dilepton channels [65]. Since they are produced via the strong interaction, their production cross section is quite large. Thanks to the distinct final states and large production cross section, the LHC experiments can probe TeV-scale leptoquarks at the next stage of the LHC running.  (1, 2, 2) W (1, 3, 1) W (15, 1, 1 To conclude this section, we perform a scan for more general models where the addi-Nagata, Olive, Zheng