Summary

In this chapter, we introduced a sophisticated model of BSM, that extended the SM gauge group to SU(3)C × SU(2)L× U(1)Y × SU(2)H × U(1)X. This model provided varies DM candidate, and we choose scalar DM candidate in our study. We categorized the DM in the doublet-like, triplet-like, and Goldstone-like by their compositions. Then we scanned the parameters in chosen ranges, and collected those points that satisfied the SGSC to calculate the relic density and cross section of direct detection. In these calculation, the mixing matrices from scalar sector and gauge sector play important role for the couplings. We also involved the coannihilation for the calculation of relic density. The DM candidates are complex scalar, the cross section of DM are different with antiDM for the direct detection. In addition, the ISV effect are evident for the direct detection. Due to the coupling to SM Z gauge boson, those interactions mediated by Z1 will make doublet-like DM ruled out by current direct detection search. Unless we have another scenario that SM Z are not the lightest neutral gauge boson, then the mixing O₁₁^G will be suppressed, and maybe doublet-like DM can have smaller scattering cross section of direct detection. The parameter space that can make Goldstone-like DM candidate survived RD+DD constraints are located in a fine-tuning range to have ISV cancellation, which is unpleasant for some taste. The most promising scalar DM candidate is the triplet-like DM, which have wide range of parameter space that can satisfied SGSC+RD+DD constraints as showed in the Fig.4.6 and Fig.4.7.

4.3. RESULTS 49

Fig. 4.6 A summary plot for the scalar potential parameter space allowed by the SGSC constraints (green region) and SGSC+RD+DD constraints (red scatter points) for the triplet-like DM. The numbers written in the first block of each column are the 1D allowed range of the parameter denoted in horizontal axis after the SGSC+RD+DD cut.

50 CHAPTER 4. DARK MATTER IN G2HDM the SGSC constraints (green region) and SGSC+RD+DD constraints (red points) for the triplet-like DM.

Chapter 5

Z ^′ Search with Dark Matter in LHC

Instead of going through the scrutiny of a model like we do in the previous chapter, we will demonstrate a collider search for a specific process of an effective model. The details of the model is not what we interest. We focus on the phenomenology of the process in the collider.

As we discussed in Ch.1, the experiments in LHC proved the existence of Higgs boson. The single Higgs production can be used to measure the gauge and fermionic couplings to the Higgs[35, 36]. Whereas the Higgs self couplings are essential to reconstruct the shape of Higgs potential, which can be measured by the production of Higgs pair in collider.

In the SM, there are two channels that produced a pair of Higgs, one is triangle loop diagram with Higgs boson as the mediator, another is box loop diagram. Any deviation will be indicated the discovery of new physics[37]. For instance, the new scalar as mediator, new color particles running inside the loops, modified Yukawa couplings, etc.[38].

Higgs pair can also be produced in association with other particles from decay of heavier particles. For example, in some BSM with extended gauge group that contained new parity symmetry, under which all the SM particles are even while the new heavy gauge boson Z^′ and DM candidate are odd. Thus, the Z^′ can only produce in pair. In the scenario where Z^′ is much heavier than DM and Higgs, and Z^′ predominantly decay into DM and Higgs, then the collider signature to search this kind of Z^′ would be a pair of highly boosted decay products of Higgs plus large MET by the undetectable DM. In other words, the DM signature in collider can combine with Higgs pair production for searching the new gauge boson Z^′.

52 CHAPTER 5. Z^′ SEARCH WITH DARK MATTER IN LHC To study the phenomenology in LHC, we need to employ jet algorithms[39–42] for the reconstruction of jets, where the jets are the observed colorless particles by the hadronization of quark or gluon from the proton collision. Furthermore, for the better resolution of highly boosted Higgs topology, jet substructure analysis[43] is essential;

for our studies, we will use BDRS algorithm[44] to get the better signal/background ratio. The reason we employed BDRS is that the traditional clustering algorithm are not efficient for the small separation of b¯b from the decay of fast moving Higgs, and will mis-clusting as only one jet, whereas BDRS algorithm is optimal for boosted Higgs decay.

5.1 Benchmark model

We will discuss the Little Higgs Model with T-parity (LHT) as a benchmark model. Due to the additional symmetry, the heavy gauge boson Z^′ must be paired-produced. Then, the Z^′ decays exclusively into a Higgs boson and a DM candidate. The gague symmetry in prototype Little Higgs(LH)[45] is [SU(2) × U(1)]1×[SU(2) × U(1)]2 ⊂ SU(5), which broken down to a diagonal SU(2) × U(1) ⊂ SO(5), which is identified as the SM SU(2)L× U(1)Y. The T -parity act as a Z2 symmetry between the two SU(2) × U(1) copies, which demanding g1 = g2 =√

2g and g^′1 = g^′2 =√

2g^′. Where g1,2(g^′1,2) and g(g^′) are the gauge couplings of SU(2)1,2(U(1)1,2) and the SM SU(2)L(U(1)Y), respectively.

In LHT, the SM fields are T -even under T -parity transformation, while the new heavy gauge bosons are T -odd. Furthermore, the T -odd partner of SM photon is suitable for DM candidate[46, 47]. After the electroweak symmetry is broken, the masses of T -odd heavy gauge bosons are

where f is the energy scale that SU(5) broken to SO(5).

Due to T -parity exchanging SU(2)1 and SU(2)2, it is necessary to introduce two fermion doublets ψ1,2 that transform linearly under the respective groups. In the end, we have heavy fermions with masses given by

m_u^′ =√ neutrinos and charged leptons, respectively. The κq and κℓ denote the Yukawa-type