# Exclusion of heavy, broad resonances from precise measurements of *WZ* and *VH* final states at the LHC

## Abstract

A novel search for heavy vector resonances in the \(H\rightarrow b{\bar{b}}\) and \(Z\rightarrow b{\bar{b}}\) final states in association with a leptonically decaying *V* (*Z* or *W*) and *W*-only respectively, is proposed. It is argued that excesses with respect to the Standard Model prediction should be observed in all final states (0, 1 or 2 leptons), with the 1-lepton final state being the strongest. Since the relative strengths of these excesses depend on branching ratios and efficiencies, this is a clear signal for the presence of heavy resonances or their low mass tails. A general vector-triplet model is used to explore the discovery potential as a function of the resonance mass and width. Recent Higgs to \(b{\bar{b}}\) observation data reported by the experiments ATLAS and CMS are used to test the model. Current limits are extended to resonance widths over mass as large as 9%.

## 1 Introduction

Heavy vector resonances naturally appear in several extensions of the Standard Model (SM), such as GUT theories [1, 2, 3], composite Higgs [4, 5], little Higgs [6, 7, 8], and models with vector \(Z^\prime \) [9, 10], and \(W^\prime \) models [11]. The LHC experiments, in most cases, have performed direct searches for heavy narrow resonances decaying to dibosons and *VH* final states and have put limits to masses up to about 5.5 TeV [12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23].

Broader resonances (\(\varGamma /m > 4\%\)) appear for larger values of the resonance coupling strength to weak bosons and the Higgs, \(g_V\), and depending on their mass, width, and production cross section, the LHC experiments can be sensitive to a large part of the resonance distribution. It is interesting to study to what extent the experiments can be sensitive to the full distribution or tails of such resonances and what the best observables are. In this work, we start addressing this question with a specific final state: a pair of *b* quarks produced in association with a weak gauge boson (*Z* or *W*) that subsequently decays leptonically (where leptons \(\ell \) are electrons and muons). The interest in this final state is because in the large coupling regime, \(g_V>3\), the heavy boson branching fraction is dominated by decays to *WZ* and *VH*, while the decays to fermions are suppressed [24]. At the same time, both the Drell–Yan \(q{\bar{q}}\) and the VBF production modes contribute, providing non-negligible cross sections. Here, we propose as an early indirect signal of the presence of vector resonances, the simultaneous excess in the 0, 1, and 2-lepton final states, for both \(WZ\rightarrow \ell \nu b{\bar{b}}\) and \(VH\rightarrow \ell \ell (\nu ) b{\bar{b}}\), in a measurement of the \(b{\bar{b}}\) quark invariant mass \(M_{bb}\). The strength of these excesses in the different final states can be predicted by branching ratios and experimental efficiencies. We argue that the 0, 1, and 2-lepton final states should all be sensitive, albeit with very different sensitivity, to exotic \(V^\prime \rightarrow VH\) decays. In particular, the 1-lepton state will be the most sensitive in Higgs excesses and in addition, it should also show a smaller level of excess in the *Z*-boson \(b{\bar{b}}\) peak. The pattern of these excesses should be a clear sign of a heavy vector triplet (HVT), even before its observation as a (broad) mass resonance at the TeV scale. Using a general HVT framework that is also used by the experiments to model such heavy vector triplets [25], we derive the sensitivity of a single LHC experiment as a function of the resonance width.

In this paper, we first introduce the HVT framework and summarize the recent LHC results. In Sect. 3 we present an analysis used to search for heavy vector triplets at the LHC, and we report on the search potential for the \(b{\bar{b}}+0\), 1, and 2-lepton final states, for a range of masses and widths. Finally, the compatibility of our predictions with the recently published 13 TeV \(H\rightarrow b{\bar{b}}\) data from ATLAS and CMS in terms of expected and observed limits, is discussed.

## 2 BSM heavy vector resonances

*H*is the Higgs doublet and \(\sigma ^a\) the three Pauli matrices. In this Lagrangian, the HVT triplet \(V^{a \prime }=(W^{+\prime },W^{-\prime },Z^{\prime })\) interacts with the Higgs doublet, i.e. the longitudinal degrees of freedom of the SM

*W*and

*Z*bosons and the SM Higgs, with a coupling strength \(g_V\). In order to allow for a broader class of models, this coupling strength can be varied by the parameter \(c_H\), so in the Lagrangian the full coupling to the SM weak and Higgs bosons is \(g_Vc_H\). The HVT resonances also couple to the SM fermions, again through their coupling to the SM weak and Higgs bosons, \(g^2/g_V\), where

*g*is the SM \(SU(2)_L\) weak gauge coupling. This coupling between HVT resonances and fermions is also controlled by an additional parameter \(c_F\) to allow for a broader range of models to be included, as follows: \(g^2c_F/g_V\). As discussed in [23], the experiments consider two Drell–Yan (DY) production scenarios: model A is a scenario that reproduces the phenomenology of weakly coupled models based on an extended gauge symmetry [9]. In this case, the couplings are \(\frac{g^2c_F}{g_V}=-0.55\) and \(g_Vc_H=-0.56\), with the fermion coupling being universal. The second DY scenario, referred to as model B, implements a strongly coupled scenario as in composite Higgs models with \(\frac{g^2c_F}{g_V}=0.14\) and \(g_Vc_H=-2.9\). In model B, the \(V^{\prime }\) resonances are broader than in the weakly coupled scenario, model A, but for \(|g_Vc_H|\le 3\) they remain narrow relative to the experimental resolution. For \(|g_Vc_H|>3\), the resonance intrinsic width becomes significant and cannot be neglected. In summary, the ATLAS and CMS benchmarks correspond for Model A to \(c_H=-\frac{g^2}{g_{V}^2}\), \(c_F=-\frac{1}{3}\) and \(g_V=1\), and for model B to \(c_H=-1\), \(c_F=1\) and \(g_V=3\). ATLAS and CMS experimental data from direct \(m_{VH}\) and \(m_{VV}\) searches, exclude part of the parameter phase space \((g_V, c_H, c_F)\), for which the intrinsic width \(\varGamma \) of the new bosons is dominated by the experimental resolution (\(\sim 4\%\) of the mass). This is also the case, for example, for \(|g_Vc_H|\le 3\), where negligible natural width is assumed (narrow width assumption). The goal of this work is to explore the part of the HVT parameter space with \(|g_Vc_H|>3\), where the heavy resonances have a significant natural width. Following the model B benchmark, we fix the two constant factors to \(c_H=-1\), \(c_F=1\) and allow \(g_V\) to vary.

In this work we argue that the presence of non-zero width resonances, could be observed as an excess of events in the \(VH\rightarrow \ell \ell (\nu )b{\bar{b}}\) and \(WZ\rightarrow \ell \nu b{\bar{b}}\) decays with 0, 1, or 2 leptons in the final state. Independent of the fact that due to the experimental resolution the close-by \(Z\rightarrow b{\bar{b}}\) and \(H\rightarrow b{\bar{b}}\) peaks have a partial overlap, in the 1-lepton case the excess must be present in both peaks, while in the 0 and 2-lepton final states it should appear only in the Higgs peak (\(Z^{\prime }\) does not couple to *ZZ*). In addition, the excess in the 1-lepton category should be more significant, since in this case both \(W^+\) and \(W^-\) contribute. A combined analysis of the three final states can quantify the excess and correlate it to events with \(b{\bar{b}}\) pairs of higher \(p_T\) than in the SM Higgs production, since these pairs originate from heavy TeV-scale objects.

*VH*,

*VV*) is dominant. Direct searches for resonances in the

*VV*and

*VH*channels assume narrow resonance width that corresponds to \(g_V\le 3\), leaving unexcluded a large part of the HVT model parameter space.

*O*(1) to \(O(100)~\hbox {fb}\), leading to non-vanishing contributions at present and future measurements. For parts of the parameter space corresponding to low resonance masses and high \(g_V\) that are theoretically excluded (parts for which the input electroweak parameters \(\alpha _{EW}\), \(G_F\) and \(M_{Z}\), are not reproduced by the HVT model), the cross section is not provided in Fig. 6.

## 3 Resonance search potential at colliders

*VH*with \(H\rightarrow b{\bar{b}}\) results from ATLAS and CMS [26, 27]. As discussed later, the efficiencies were normalized to the experimental ones. The selected events were split in three categories according to the final state: two

*b*jets with 0, 1 or 2 leptons. We follow more closely the ATLAS selection including the requirement of 2 or more jets out of which exactly two must be

*b*jets. We will call this SM selection, the baseline selection, in order to differentiate from additional discriminants which enhance the BSM Higgs signal. The BSM Higgs signal decays to a \(b{\bar{b}}\) pair with a transverse momentum, \(p_{\perp }\), significantly larger than the SM Higgs. For this reason, an additional requirement applied to the baseline analysis, is a cut on the transverse momentum of the \(b{\bar{b}}\) system. As in the LHC analyses, we only consider resolved \(b{\bar{b}}\) pairs although the search can be extended to a single, fat \(b{\bar{b}}\) jet analysis. As a discriminant, the \(b{\bar{b}}\) invariant mass \(M_{bb}\) is used, which after full selection and subtraction of the \(b{\bar{b}}\) continuum shows two peaks due to the presence of \(Z\rightarrow b{\bar{b}}\) and \(H\rightarrow b{\bar{b}}\).

Signal yield and resonant SM background yields for a 1.5 TeV resonance, \(g_V=5\) and an integrated luminosity of \(100~\hbox {fb}^{-1}\), after baseline selection, and after an additional \(p_{\perp }>200~\hbox {GeV}\) cut (last column). The resonance width over its mass is \(\varGamma /m\simeq ~10\%\)

Process \(qq\rightarrow V^\prime \) | \(\sigma \times BR\) (fb) | \(\hbox {A}\times \epsilon \) (%) | Yield (\(100~\hbox {fb}^{-1}\)) | Yield \(p_{\perp }> 200~\hbox {GeV}\) |
---|---|---|---|---|

\(Z^{\prime }\rightarrow ZH\rightarrow \nu \nu b{\bar{b}} \) | 1.58 | 2.45 | 3.78 | 3.51 |

\(Z\rightarrow ZH\rightarrow \nu \nu b{\bar{b}} \) | 97.2 | 5.01 | 486 | 224 |

\(ZZ \rightarrow \nu \nu jj \) | 2580 | 0.27 | 697 | 248 |

\(W^{\prime }\rightarrow WH\rightarrow \ell \nu b{\bar{b}} \) | 3.87 | 5.5 | 21.3 | 19.4 |

\(W^{\prime }\rightarrow WZ\rightarrow \ell \nu jj \) | 3.79 | 0.23 | 0.81 | 0.59 |

\(W\rightarrow WH\rightarrow \ell \nu b{\bar{b}} \) | 225 | 1.44 | 324 | 148 |

\(WZ\rightarrow \ell \nu jj \) | 4148 | 0.13 | 529 | 173 |

\(Z^{\prime }\rightarrow ZH\rightarrow \ell \ell b{\bar{b}} \) | 0.553 | 4.76 | 2.6 | 2.2 |

\(Z\rightarrow ZH\rightarrow \ell \ell b{\bar{b}} \) | 34.2 | 13.7 | 467 | 68.6 |

\(ZZ\rightarrow \ell \ell jj \) | 910 | 0.96 | 875 | 72.6 |

*VH*and

*WZ*final states. As we have already seen from Table 1, most of the Higgs excess comes from the 1-lepton category, while all of the

*ZW*excess comes from the 1-lepton category but it is rather small.

*b*quark pairs fall in the same jet. More precisely, for resonance masses of 2 TeV or higher, the fraction of resolved \(b{\bar{b}}\) pairs is 5% or less, respectively. Here it should be stressed that an extension of the proposed search to include fat jets could push these limits at higher values.

## 4 Summary and conclusions

In this work we explored the potential of a novel search of heavy vector resonances of non-zero natural width, decaying almost exclusively in the \(H\rightarrow b{\bar{b}}\) and \(Z\rightarrow b{\bar{b}}\) final states in association with a leptonically decaying *V* (*Z* or *W*) and *W*-only, respectively. For large \(g_V\) coupling of the exotic resonance to the *W* and *Z* bosons and the SM Higgs, the branching ratio to *VH* and to two gauge bosons *VV* dominates, leading to a simultaneous excess to both Higgs \(WH\rightarrow \ell \nu b{\bar{b}}\), \(ZH\rightarrow \ell \ell b{\bar{b}}\) and non-Higgs \(WZ\rightarrow \ell \nu b{\bar{b}}\) final states.

We showed that excesses of varying strengths should be observed in all final states (0, 1 or 2 leptons). The fact that the relative strengths of these excesses depend on branching ratios and efficiencies, provides a clear signature of the presence of heavy resonances or even their low mass tails. For a luminosity accessible by the LHC experiments of \(200~\hbox {fb}^{-1}\), the search is sensitive up to resonance masses of 2 TeV and widths \(\varGamma /m\) of 10%. A first test of a heavy vector triplet model against ATLAS and CMS data in terms of expected and observed limits was presented. Although experimental uncertainties on the \(VH\rightarrow b{\bar{b}}\) signal strength \(\mu _{VH}\) are still large, the LHC experiments are expected to accumulate significant amounts of data in 2018 and beyond, making the search proposed here a very useful tool in evaluating potential excesses in Higgs yield measurements when the Higgs is produced in association with a weak vector boson.

## Notes

### Acknowledgements

This work was supported by the Taiwanese Ministry of Science and Technology under Grant number 106-2112-M-002-011-MY3.

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