Search for HZZ' couplings at the LHC

Experimental opportunities can be exploited to search for hints beyond the standard model (BSM) physics after the recent discovery of the Higgs boson with a mass of 125 GeV by the ATLAS and CMS experiments [1,2] at the LHC. Due to its gauge charges the Higgs boson may interact with the BSM fields. This new interaction can also modify the couplings between the Higgs and SM fields at tree level or loop level. Within some extensions of the standard model (SM) a new neutral gauge boson Z' can be included [3–6].

The phenomenological studies on the Z' boson signatures can be found in [7–14]. The present constraints on the Z' mass and couplings from both electron-positron and hadron-hadron colliders have been presented in [15]. Since the existing constraints on the Z' boson mass are stringent we take into account two benchmark Z' models, such as the leptophobic $Z'_{LP}$ which has no leptonic couplings and the eta $Z'_{\eta}$ which has small leptonic couplings [16]. The precision measurements at the Z boson resonance lead to the limit on $Z\text{-}Z'$ mixing [17–20]. The ATLAS and CMS experiments at the LHC, running at higher center-of-mass energy and luminosity, have updated the Tevatron limits on the Z' boson mass [21,22]. The ATLAS Collaboration searches for a massive resonance decaying to top quark pairs in the hadronic channels, and excludes the leptophobic Z' boson with mass smaller than 1.32 TeV [23]. The CMS Collaboration excludes leptophobic Z' boson resonance with a mass of $m_{Z'}<1.3\ \text{TeV}$ for its width $\Gamma_{Z'}=0.012m_{Z'}$ in the search of heavy resonance decaying into $t\bar{t}$ pair with subsequent leptonic decays [24].

In this work, we investigate the $HZZ'$ couplings via the processes $pp\rightarrow HZX$ and $pp\rightarrow HHZX$ at the LHC with $\sqrt{s}=14\ \text{TeV}$. The couplings of the Z' boson to quarks can also be investigated via $Z'q\bar{q}$ interactions. For the signal process $pp\to HZX$, the Z' boson contributes in the s-channel resonance diagrams through family diagonal neutral current couplings. However, the signal process $pp\to HHZX$ has contributions from both the Z'-boson resonance and the Z-exchange diagrams. We calculate the signal and background cross-sections and obtain the accessible ranges of the mass for two different Z' models (such as $Z'_{LP}$ and $Z'_{\eta}$) at the four-fermion and six-fermion final states resulting from $H\to b\bar{b}$ and $Z\to l^{+}l^{-}$ decays. These modes exist even if the Z' boson decouples from the leptons. The ratio of the cross-sections for the HZ and HHZ production can help to understand the $HZZ'$ interaction and distinguish between different Z' models.

The interaction of the Higgs boson (H) with the Z boson and the new Z' boson can be written through the kinetic term of the scalar field. The relevant interaction term can be written as $L_{HZZ'}=-g_{Z}g_{Z'}z[H]\upsilon HZ_{\mu}Z'^{\mu}$. The new boson Z' couples to the fermion field (f) with the interaction term $L_{f\bar{f}Z'}=(g_{Z'}/2)\bar{f}\gamma^{\mu}(C_{V}^{f}-C_{A}^{f}\gamma^{5})f$. Here, the vector $(C_{V}^{f})$ and axial-vector $(C_{A}^{f})$ couplings are model dependent. We use a linear change of variable $g_{Z'}=\gamma_{Z'}g_{e}/\cos\theta_{W}\sin\theta_{W}$ for the coupling constant. The triple coupling $HZZ'$ depends on the $U(1)'$ charge. In the model the triple coupling parameter $z[H]=-1$. The $U(1)'$ couplings to the fermions for two different Z' models are given in table 1. Since the extensively studied Drell-Yan process even constrained the possible $Z'l^{+}l^{-}$ couplings, we consider two candidate models in which the Z' bosons have small or no couplings to leptons. We implement tree-level interaction vertices of $HZZ'$ and $Z'f\bar{f}$ into CalcHEP [25] and we use the proton parton distribution function CTEQ6L [26].

Table 1:.  Vector and axial-vector couplings of Z' boson predicted by the leptophobic (LP) model and the η (ETA) one.

	$C_{V}^{u}$	$C_{A}^{u}$	$C_{V}^{d}$	$C_{A}^{d}$	$C_{V}^{l}$	$C_{A}^{l}$	$C_{V}^{\nu}$	$C_{A}^{\nu}$
Z'(LP)	$-7/9$	1	$2/9$	0	0	0	0	0
Z'(ETA)	0	$4/6$	$1/2$	$1/6$	$-1/2$	$1/6$	$-1/6$	$-1/6$

The production processes have contribution from the resonance production of the Z' boson. Therefore, we have included the decay width $(\Gamma)$ of the Z' boson in the calculation for different Z' models, as shown in fig. 1 for leptophobic (LP) and η (ETA) models. The branching ratios (BR) vs. Z' mass are given in fig. 2 and fig. 3 for the LP and ETA models, respectively.

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At the LHC with $\sqrt{s}=14\ \text{TeV}$, the cross-section of the HZ production through the signal process is about 0.20 pb and 0.15 pb with Z' boson mass $m_{Z'}=1.5\ \text{TeV}$ for the LP and the ETA models, respectively. The cross-section of the HHZ production is around 3.85 fb and 2.78 fb with Z' boson mass $m_{Z'}=1.5\ \text{TeV}$ for the LP and the ETA model, respectively. As shown in figs. 4, 5 and 6, 7, the background cross-sections result in 0.7 pb and 0.29 fb for the HZ and the HHZ production at $\sqrt{s}=14\ \text{TeV}$, respectively. The ratios of the cross-sections for $pp\to HZX$ and $pp\to HHZX$ processes depending on the mass of the Z' boson for the two different Z' models ETA and LP are presented in fig. 8. This figure also includes the ratio of the SM cross-sections for the given processes. The curves shown in fig. 8 represent large deviations from the SM line depending on the Z' boson mass. While the mass of the Z' boson is increasing, the model difference becomes more apparent. The final states of $2l+2b_{\textit{jet}}$ and $2l+4b_{\textit{jet}}$ are the main backgrounds for the HZ and the HHZ productions. In order to suppress the relevant background, we can apply the invariant mass cuts, on dileptons to be around the Z boson mass, on dijets with each jet as b-tagged to be around the Higgs mass.

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In the analysis, we use the cross-section of the signal and background for the final states explained in the previous section. A pair of b-jets gives an invariant mass distributions peak around the Higgs mass and the dilepton invariant mass distribution give peak around the Z mass. It is also helpful to use angular seperations of the leptons, b-jets and between leptons and jets. The massive Z' boson can be reconstructed from the resonance peak in the invariant mass spectrum of the final states $2l+2b_{\textit{jet}}$ and $2l+4b_{\textit{jet}}$ originating from the HZ and the HHZ productions, respectively. The luminosity needs for $3\sigma$ signal observability for the final state $2l+2b_{\textit{jet}}$ depending on the mass of Z' boson for the two different Z' models ETA and LP are given in fig. 9. Having an integrated luminosity of $L_{\textit{int}}=100\ \text{fb}^{-1}$ at the LHC with $\sqrt{s}=14\ \text{TeV}$, it is possible to search for the Z' boson up to a mass value of $M_{Z'}=1.50\ \text{TeV}$ and 1.80 TeV for the ETA and the LP models as seen from fig. 9. The search range for the Z' boson mass can be found as $M_{Z'}=1.80\ \text{TeV}$ and 1.95 TeV for the ETA and the LP models for $2l+4b_{\textit{jet}}$ as given in fig. 10.

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We present the attainable parameter space for two different $U(1)'$ models by studying the processes $pp\to HZX$ and $pp\to HHZX$ at the LHC with $\sqrt{s}=14\ \text{TeV}$. The HZ production has large cross-section and it has the advantage of two b-jets and two charged leptons in the final state. The background for the HHZ production has lower cross-section than the HZ production, however it has the advantage of four b-jets and two charged leptons in the final state. The Higgs boson mostly decays into two b-jet channel and we use the advantage of efficient identification of dileptons from the Z boson. The couplings of the Z' boson to the SM quarks play a role in the production, and the $U(1)'$ charge of the Higgs boson scales the $HZZ'$ coupling. The searches for HVV couplings will also extend our perspectives for new physics at the LHC with $\sqrt{s}=14\ \text{TeV}$ and $L_{\textit{int}}=100\ \text{fb}^{-1}$.

The work of OC and SK was supported in part by the Turkish Atomic Energy Authority under the project Grant No. 2011TAEKCERN-A5.H2.P1.01-19.