Fig. 5.1 Higgs pair production accompanies ETmiss induced by a pair of heavy gauge boson Z′ decay
coupling strength. The couplings between Z′ and SM quarks are generated in the gauge interactions as follows:
L ⊃ g
2 1 + O v2 f2
!!
Z′µ¯uLγµu′L−g
2 1 + O v2 f2
!!
Z′µd¯Lγµd′L+ h.c.. (5.3) In the case that T -odd fermions are heavier than Z′, the only channel allowed for Z′ decay is Z′ → hA′. The LHT provides a framework, the heavy gauge boson Z′ should be pair produced by its couplings to SM fermions and new fermions. And conveniently coupled to the Higgs and dark sectors for its decay.
To simplified our discussion, we rewrite the Lagrangian into the notation
L⊃1
2ghZ′χZµ′Aµh+guu′Z′Zµ′¯uLγµu′L+ gdd′Z′Zµ′d¯Lγµd′L+ h.c. (5.4) where the couplings ghZ′χ, guu′Z′ and gdd′Z′ are free parameters in our discussion.
5.2 Collider Study
The production channel we are interested in LHC is:
pp→Z′Z′→h(→b¯b)χh(→γγ)χ (5.5)
where χ denotes for DM, the process is illustrated in Fig.5.1. The final state in collider is b¯bγγ, and DM as our ETmiss.
54 CHAPTER 5. Z′ SEARCH WITH DARK MATTER IN LHC We will list the dominant background in order of respective production cross section as follow:
(B1) t(→ ℓ+νb)¯t(→ ℓ−¯ν¯b)γ — It may mimic the signal if one of the lepton is missed and the other is misidentified as a photon, or missed photon with both lepton misidentified. However the misidentified rate is small, and can further suppressed by the invariant mass window cut for it is non-resonant decay. The neutrino contributed to ETmiss.
(B2) t(→ ℓ+νb)t(→ ℓ−¯ν¯b)γγ — This is similar to (B1) but with both lepton are missed, or one photon is missed and the lepton is misidentified as a photon, or both photon are missed and both lepton are misidentified. However, this background will suppressed by the same reason as (B1).
(B3) t¯th(→ γγ) — Similar to (B2), except the diphoton come from the resonant Higgs decay, hence it can pass one of the diphoton invariant mass window cut. But this channel is suppressed by the small branching ratio, and the ETmiss cut, since this channel typically carried small ETmiss.
(B4) Z(→ b¯b)h(→ γγ) — Unlike previous three backgrounds, this channel has no neutrino, so the ETmiss can only come from the inefficiencies of detector.
The backgrounds jjγγ, b¯bγγ, jjh and b¯bh have been studied and were found to be negligible after ETmiss cut.
We implemented the effective Lagrangian in eq.5.4, the effective couplings between Higgs with two gluons and between Higgs with two photons[48] by FeynRules_v2.3[49]
to generate the model file. The SM parameters taken from[50]. Next we imported the model into MadGraph5_aMC@NLO package [51] to generate parton level events with default cuts and NNPDF23_lo_as_0130_qed parton distribution function[52]. Then we passed the events to Pythia[53] for parton showering, and followed the detector simulation by Delphes-3[54]. Where the tagging efficiencies and fake rates are using the default values, except the photon angular resolution are set to be 0.3. For the BSM parameters, the new couplings are set to be gqq′Z′ = ghZ′χ= 0.6, the new heavy quarks masses are set to be mu′ = md′ = 2.5 TeV. We calculated the cross section of Z′ pair productions for different mZ′ as showed in Fig.5.2. The Z′→hχ is the sole channel of Z′ decay.
The event selection criteria (cf. Table.5.2) begins with the basic cut (C0) on transverse momenta and rapidities:
pγT >15 GeV, |ηγ| <2.5; pℓT >20 GeV, |ηℓ| <2.5 (5.6)
5.2. COLLIDER STUDY 55
400 800 1200 1600 2000
m Z′ [GeV]
10
−510
−410
−310
−2σ ( pp → Z
′Z
′) [p b]
g A
′Z
′h
=g qq
′Z
′= 0.6Fig. 5.2 Cross section of pp→Z′Z′ as mZ′ varied from 500 GeV to 2 TeV at the 14 TeV LHC.
Due to the triggering efficiency of detector. We need to more than 2 photons(Nγ≥2) to reconstruct one of the Higgs in our signal.
We need at least a pair of photon(Nγ≥2) to reconstruct one of the Higgs. We will focus on the boosted regime for another Higgs that decay to b-quark pair and employed jet substructure technique since it decay from much heavier Z′ boson. When clustering jets for jet substructure study, using the Cambridge/Aachen(C/A)[40, 41] algorithm would be the best option[55]. Next we are investigating angular distance between 2b versus the transverse momentum of the mother Higgs in the parton level simulation of the signals events and plot in Fig.5.3, and found the correlation agree with:
∆Rb¯b ∼ 2mh
phT (5.7)
In the boost regime of pT >200 GeV corresponds ∆R ≲ 1.25, this motivated to setting the cone radius to R = 1.2 when clusting jets by C/A algorithm, and (C9) cut. We only took those jets with transverse momentum larger than 50 GeV to reject the backgrounds. Then we followed by the BDRS algorithm to reclusting for tagging the Higgs-candidate fatjet, which is available in fastjet[56]. The BDRS algorithm
56 CHAPTER 5. Z′ SEARCH WITH DARK MATTER IN LHC
Fig. 5.3 The correlation of transverse momentum of Higgs and ∆R between its two daughter b-quark. The green line represent the relation5.7.
reverses clustering a jet to its components j1 and j2, where we label the subjets by their mass mj1 > mj2. Then passed to next step if there was a significant mass drop(MD) µmj > mj1 without the splitting y being too large. Otherwise, redefine j1 as j, and redo the process. The MD and splitting parameters are chosen to be:
µ= mj1
mj <0.667; y= min(p2Tj1, p2T
j2)
m2j2 ∆Rj21,j2 >0.09 (5.8) Then we take Rf ilt = min(0.3, Rj1j2/2) for reclusting to filter the Higgs neighborhood, and take the three hardest of subjets to filer away the underlying event contamination.
And we defined the two hardest of the subjets as our b-jets. For the b-tagging, if a parton level b-quark∗within the cone radius 0.9Rf iltof subjets, we tag the subjet as b-jet with 70% efficiency, and 1% mistag rate. We required only one b-tag in Higgs candidate fatjet to keep as much as possible for the signal when reducing the background.
∗(pbT > 20 GeV, |ηb| < 2.5)
5.2. COLLIDER STUDY 57
Fig. 5.4 The symmetric distribution of two Higgs pT are indicate they are both daughter of heavy particles decay.
Fig.5.4 shows the symmetric correlation of candidate transverse momentum of two Higgs indicate of both Higgs are decay product of same channel Z′→hχ.
The production of neutrinos are from charged weak current, hence they were accompanied by charged lepton, which is absence in signal, and motivated the (C3) cut.
Fig.5.5shows the distributions of ETmiss for signal as well as the main backgrounds.
The undetectable DM χ contributed most of the ETmiss, and it gets more energetic as mZ′ increasing. In the SM background, the ETmiss is comes from the inefficiencies of detector and mostly from neutrinos, but both of them are much softer than our signal events, hence the (C4) cut are suppressed more than one orders for the backgrounds.
(C5) (C6) are the invariant Higgs mass window cut at around 125 GeV for diphoton and fatjet. As showed in Fig.5.6, (C5) cut is very effective for those no-resonance diphoton decay; mf atjet cut seems not so effective is that we choose wider window for fatjet to retain the signal strength.
58 CHAPTER 5. Z′ SEARCH WITH DARK MATTER IN LHC
0 500 1000 1500 2000
E
Tmiss [GeV]0 500 1000 1500 2000
E
Tmiss [GeV]Fig. 5.5 The ETmiss of signals for various masses of Z′ boson (left) and signal versus various backgrounds. (right)
100 110 120 130 140 150
m
γγ [GeV]100 110 120 130 140 150
m
fatjet [GeV]Fig. 5.6 The reconstructed invariant mass of Higgs from γγ (left) and fatjet (right) before the (C4) cut.
5.2.COLLIDERSTUDY59
Cuts
σ [10−4 fb]
pp → Z′Z′ pp → t¯tγ pp → t¯tγγ pp → jjh(→ γγ) pp → t¯th(→ γγ) pp → Z(→ bb)h(→ γγ) (C0) Basic cut 9.70 × 103 2.44 ×107 1.18 ×105 5.74 ×104 7.55 ×103 1.41 ×103 (C1) Nγ ≥ 2 6.10 × 103 5.40 ×105 4.61 ×104 3.23 ×104 4.18 ×103 6.80 ×102
(C2) Nfatjet≥ 1 6.01 × 103 5.37 ×105 4.60 ×104 2.95 ×104 4.17 ×103 6.33 ×102
(C3) Nℓ= 0 6.00 × 103 4.46 ×105 3.54 ×104 2.95 ×104 3.22 ×103 6.32 ×102 (C4) ETmiss≥ 150 GeV 4.91 × 103 3.89 ×104 3.12 ×103 4.12 ×101 2.40 ×102 1.77 (C5) |mγγ− 125 GeV| < 10 GeV 4.84 × 103 2.81 ×103 2.29 ×102 4.06 ×101 2.27 ×102 1.77 (C6) |mfatjet− 125 GeV| < 30 GeV 3.23 × 103 8.55 ×102 7.97 ×101 2.51 ×101 8.90 ×101 1.23 (C7) (1+)b in fatjet 1.24 × 103 1.83 ×102 3.47 ×101 - 2.42 ×101 4.23 ×10−2
(C8) mhh> 252 GeV 1.22 × 103 1.83 ×102 3.41 ×101 - 2.31 ×101 3.53 ×10−2
(C9) pfatjetT > 200 GeV 1.20 × 103 1.83 ×102 3.27 ×101 - 2.07 ×101 3.17 ×10−2
Table 5.1 Select cuts and resulting cross sections for the signal and backgrounds of 14 TeV LHC. Here, we set mZ′ = 500 GeV, mχ= 100 GeV, and ghZ′χ= gqq′Z′ = 0.6.
60 CHAPTER 5. Z′ SEARCH WITH DARK MATTER IN LHC
By the cut efficiency in the Table.5.2, we calculated the discovery sensitivity of mZ′ = 500, 1000 GeV, mχ = 100 GeV, and gqq′Z′ = 0.6 at 14 TeV HL-LHC[57] in Fig.5.7 by using the approximate median significance (AMS)[58]:
S :=
which represents the statistic significance for the discovery of BSM. With luminosity of 100fb−1, we expected 11 events at 14 TeV LHC with mZ′ = 500GeV and new couplings set to be 0.6. We also investigated in the case of fixed Z′ mass with varies couplings in Fig.5.7. The couplings have to be at least 4.2 to claim discovery for 500GeV Z′
5.3 Summary
As discussed in Ch.3, the mono-jet process is simplest case for DM search in collider.
In this chapter, we propsed a sophisticate method for searching Z′ and DM, where the new particles are being odd under a Z2 symmetry whereas the SM are even under same symmetry. One of the common method to search new heavy gauge boson is looking for dilepton resonances in collider[59, 60], where the heavy gauge bosons are singly produced, and those experiments are set stringent constraints on the lower bound of the messes for the heavy gauge bosons in given model. In contrast, the Z2-odd Z′ has to be pair-produced in colliders, which limit are much loose compared to the resonance search.
We took the LHT as benchmark model, and focus on the process of pp→Z′Z′→h(→b¯b)χh(→γγ)χ.
However, our result can applied to other model with similiar process. The large mass
5.3. SUMMARY 61 gap mZ′≫mh+ mχ gave the advantage to distinguish the signal from SM background by contributed to large EmissT and boosted topology of Higgs. Thus, we employed the jet substructure technic in order to have better reconstruction for the boosted b¯b of Higgs decay. The missing transverse momentum in the signal not only indicate the existence of DM, but also a leverage for discovering new gauge boson. We simulated whole process of signal and varies of background to the collider level. Then the data went through a sequance of cuts. The result of our analysis shows the signal will have 11 events for 14 TeV HL-LHC at 100−1f b with m′Z = 500 GeV and couplings set to be 0.6. We also examined for different mass of Z′ as in Table.5.3.
62CHAPTER5.Z ′SEARCHWITHDARKMATTERINLHC
Cuts σ(pp → Z′Z′) [10−4 fb] (mZh= 5 mAh) mZh = 500 GeV 1000 GeV 1500 GeV 2000 GeV (C0) Basic cut 9.70 ×103 2.73 ×102 2.19 ×101 2.45
(C1) Nγ≥ 2 6.10 ×103 1.64 ×102 1.22 ×101 1.17
(C2) Nfatjet≥ 1 6.01 ×103 1.63 ×102 1.21 ×101 1.16
(C3) Nℓ= 0 6.00 ×103 1.62 ×102 1.21 ×101 1.16
(C4) ETmiss≥ 150 GeV 4.91 ×103 1.50 ×102 1.16 ×101 1.13 (C5) |mγγ− 125 GeV| < 10 GeV 4.84 ×103 1.48 ×102 1.14 ×101 1.11 (C6) |mfatjet− 125 GeV| < 30 GeV 3.23 ×103 9.55 ×101 7.27 6.75 ×10−1 (C7) (1+)b in fatjet 1.24 ×103 3.66 ×101 2.85 2.91 ×10−1 (C8) mhh> 252 GeV 1.22 ×103 3.59 ×101 2.80 2.873 ×10−1
(C9) pfatjetT > 200 GeV 1.20 ×103 3.56 ×101 2.79 2.867 ×10−1
Table 5.2 Select cuts and resulting cross sections for the signals of 14 TeV LHC. Here, we set mχ = 100 GeV, and gZ′χh = guu′Z′ = 0.6.
Chapter 6 Summary
In this thesis, we demonstrate two different approaches to study Dark Matter physics.
One by going through the details of a fully established model. Another is to apply an effective model that only contains a specific process into collider studies. Both approaches have their proponents, and have their pros and cons for DM search.
In the studies of DM in G2HDM, we brifely described the particle content and the spontaneous breaking of SU(2)L× U(1)L symmetry which left with a Z2 symmetry.
The accidental Z2 will protect the stability of DM, hence the Z2-odd particles can be DM candidate except charged Higgs. We choose Z2-odd scalar as our DM candidate and categorized into Goldstone-like (GL), doublet-like (DL), and triplet-like (TL) DM by their compositions. We then scan the free parameters in reasonable ranges. Before going to the DM calculation, we need to consider the scalar and gauge constraint (SGSC). We assume the DM are in thermal equilibrium before decoupling, then we calculated the relic density (RD) and scattering cross section of direct detection (DD).
The coupling to the Zi gauge bosons of each type DM leads to the isospin violation (ISV), and play an important role in RD and DD. In addition, the cross section of DM-nucleon is different with antiDM-nucleon, because the DM candidate is complex scalar. After the analysis, we found the doublet-like DM is ruled out by RD+DD, due to its main composition SU(2)H-doublet that has large coupling with the Z1 gauge boson. There are paremeter spaces that can satisfy both PLANK and XENON1T constrains for TL and GL DM, mostly due to the gauge boson couplings are suppressed by the mixing. However, the GL DM can only be found in a more fine-tuned region.
Next, we studied a process where Z′ are pair produced, and exclusively decay into Higgs and DM, resulting in the Higgs pair accompany with missing transverse energy (MET) in the final state. And we execute thorough collider simulations of signal and potential background. We then applied a series cuts including jet substructure
64 CHAPTER 6. SUMMARY technique to increase the signal to background ratio. The DM in the final state contributed to the large MET, which is absences in the back ground. And the mass gap between Z′ and its daughter particles resulting the boosted topology of Higgs, which is suited for the jet substructure technique.
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