Improved Constraints on the Heavy Gauge Bosons Decaying into a Vector Boson and a Higgs Boson at the LHC

Nonlinear Phenomena in Complex Systems, vol. 28, no. 3 (2025), pp. 269 - 279 Improved Constraints on the Heavy Gauge Bosons Decaying into a Vector Boson and a Higgs Boson at the LHC I. A. Serenkova∗ Abdus Salam ICTP Affiliated Centre at Pavel Sukhoi Gomel State Technical University, Gomel 246746, BELARUS (Received 6 November, 2024) The full CMS and ATLAS Run 2 datasets with time-integrated luminosity of 137 and 139 fb−1in the diboson channels are used to probe benchmark models with extended gauge sectors such as left-right symmetric (LR) and the sequential standard model (extended gauge model, EGM), that predict the existence of neutral Z0and charged W0bosons decaying to a pair of bosons ZH and WH in the semileptonic final state. These benchmark models are used to interpret the results. Exclusion limits at the 95% C.L. on the Z0and W0 resonance production cross section times branching ratio to electroweak gauge boson pairs in the resonance mass range between 1.0 and 5 TeV are here converted to constraints on Z-Z0 and W-W0mixing parameters and masses. We present exclusion regions on the parameter spaces of the Z0and W0and show that the obtained exclusion regions are significantly extended compared to those derived from the previous analysis performed with Tevatron data as well as with the CMS and ATLAS data collected at 7 and 8 TeV in Run 1. The reported limits are the most restrictive to date. PACS numbers: 12.60.-i Keywords: new gauge Z0and W0bosons, mixing angle, ATLAS experiment, Large Hadron Collider (LHC) DOI: https://doi.org/10.5281/zenodo.17236521 1. Introduction The search for physics beyond the Standard Model (SM) is a major focus of the physics program at the Large Hadron Collider (LHC). Since its discovery, the Higgs boson has become a tool in this search. In particular, one may expect new heavy resonances to couple to Higgs bosons and weak vector bosons (V=Wor Z). Such resonances are expected to occur in a number of theories beyond the Standard Model. Theories that aim to solve the naturalness problem predict the existence of vector resonances as expected in composite Higgs models [1], Little Higgs models [2], or models with extra dimensions [3, 4]. The extended gauge models are among the best motivated theoretical scenarios beyond the SM ∗E-mail: [email protected] that predict the existence of new heavy neutral and charged vector bosons (Z0and W0) [5, 6] with their diboson decay modes, V0→V V/V H, caused by Z−Z0and W−W0mixing. These models are considered as benchmark scenarios for diboson resonances having spin-1 (W0→ WZ or WH,Z0→WW or ZH), produced predominantly via quark-antiquark annihilation (q¯q0→W0,q¯q→Z0). Many of the searches for new physics at the LHC amount to looking for “heavy stuff”, states or resonances at masses above the scale of the electroweak vector bosons and the Higgs boson. This would be unstable and decay to jets, (add to lepton pair and neutrino pair or one can simply say fermion-antifermion pairs, f=ν, `, q), to two SU(2)Lvector bosons (V V ) or to one such vector boson plus a Higgs boson (V H). If the “heavy stuff” is a gauge bosons associated with some 269 270 I. A. Serenkova additional symmetry groups, the decay could be to two fermions, to two vector bosons or to a vector boson and a Higgs boson. Events of the latter kind, pp →V0X→V HX, (1) have been searched for in the resonance masses range between ∼1.0and 5.0TeV in ATLAS and CMS detectors at the LHC with a total integrated luminosity of 137−139 fb−1. No significant excess is observed and 95% C.L. upper limits are placed on the production cross section times branching fraction of neutral and charged spin-1 resonances. These limits [7, 8] are converted into constraints on the parameter space (mixing vs. resonance mass) of extended gauge models. A heavy vector boson Z00associated with some new gauge group could mix with the familiar ones of SU(2)L Z=Z0cos φ+Z00sin φ , (2a) Z0=−Z0sin φ+Z00cos φ , (2b) and similar for the charged ones, Wand W0. Here, the superscript “0” refers to the “pure” gauge bosons, in the absence of any mixing. This mixing can be constrained from the non-observation of significant excess of events of the kind (1) above the estimated background. Such mixing is also constrained by the analysis of electroweak precision data and by analysis of data on the processes pp →Z0X→WWX, and pp →W0X→WZX, (3) where Z0and W0decaying to pairs of electroweak vector bosons (jointly referred to as Vin the following with V=W, Z), and SM Higgs (H) bosons. In the simplest models under study such as the Sequential Standard Model (SSM) [9] new neutral Z0 SSM and charged W0 SSM bosons have couplings to fermions that are identical to those of the SM Zand Wbosons, but for which the trilinear couplings Z0WW and W0WZ are absent, gZ0WW = 0 and gW0WZ = 0. This suppression may arise naturally in an EGM: if the new gauge bosons and the SM ones belong to different gauge groups, a vertex such as Z0WW (W0WZ) is forbidden. They can only be induced after symmetry breaking due to mixing of the gauge eigenstates. The properties of possible Z0and W0 bosons are also constrained by measurements of electroweak (EW) processes at low energies, i.e., at energies much below their masses. Such bounds on the Z-Z0(W-W0) mixing are mostly due to the constraints on deviation in Z(W) properties from the SM predictions. In particular, limits from direct hadron production with subsequent diboson decay at the Tevatron [10] and from virtual effects at LEP, through interference or mixing with the Zboson, imply that any new Z0boson is rather heavy and mixes very little with the Zboson. The measurements show that the mixing angles, referred to as ξZ-Z0and ξW-W0, between the gauge eigenstates must be smaller than about 10−3and 10−2, respectively [5]. Previous analyses of the Z-Z0and WW0mixing [11, 12] were carried out using the diboson production data set corresponding to the time-integrated luminosity of ∼36 fb−1 collected in 2015 and 2016 with the ATLAS and CMS collaborations at √s=13 TeV where, in the former case, electroweak Zand Wgauge bosons decay into the semileptonic channel or into the dijet final state. Further updated results were obtained using the diboson and dilepton Run 2 production data set corresponding to an integrated luminosity of 139 fb−1[13, 14] recorded by the ATLAS detector. In the analysis presented here, we utilize the full Run 2 CMS and ATLAS data set on diboson resonance production published recently in Refs. [7, 8] for the V V and V H channels corresponding to an integrated luminosity of 137 fb−1. Another class of models considered here are those inspired by Grand Unified Theories (GUT), which are motivated by gauge unification or a restoration of the left–right symmetry violated by the weak interaction. Examples Нелинейные явления в сложных системах Т. 28, № 3, 2025 Improved Constraints on the Heavy Gauge Bosons Decaying into a Vector Boson and a Higgs Boson at the LHC 271 considered in this paper include the Z0bosons of the E6-motivated [6] theories and highmass neutral bosons of the left-right (LR) symmetric extensions of the SM, based on the SU(2)LNSU(2)RNU(1)B−Lgauge group, where B−Lrefers to the difference between baryon and lepton numbers. The paper is organized as follows. In Sect. 2 we present the theoretical framework, then, in Sects. 3 and 4 we review the production and decay of W0and Z0, respectively. Finally, Sect. 5 contains concluding remarks. 2. V–V0mixing As mentioned above, in the SSM, the coupling constants of the W0and Z0bosons with SM fermions are identical to the corresponding SM couplings, while the W0and Z0couplings to, respectively, WZ and WW vanish, gW0WZ = gZ0WW = 0. Such a suppression may arise in an EGM in a natural manner: if the new gauge bosons and those of the SM belong to different gauge groups, vertices such as W0W Z and Z0W W do not arise. They can only occur after symmetry breaking due to mixing of the gauge eigenstates. Triple gauge boson couplings (such as W0WZ and Z0WW) as well as the vector-vector-scalar couplings (like W0WH and Z0ZH) arise from the symmetry breaking and may contribute to the W0and Z0decays, respectively. The vertices are then suppressed by a factor of the order of (MW/MV0)2, where V0represents a W0or a Z0 boson. In an EGM [9], the trilinear gauge boson couplings are modified by mixing factors ξV-V0=C ×(MW/MV0)2,(4) where Cis a scaling constant that sets the coupling strength. Note that the EGM can be parametrized either in terms of (MV0,C)or in terms of (MV0, ξV−V0). Specifically, in an EGM the standard-model trilinear gauge boson coupling strength gWWZ (=ecot θW), is replaced by gW0WZ =ξW-W0·gWWZ in the W Z channel and gZ0WW =ξZ-Z0·gWWZ in the WW channel. We follow a parametrization of the trilinear gauge boson couplings W0WZ and Z0WW for analyzing and interpreting the CDF data on p¯p→W0X→ WZX and p¯p→Z0X→W+W−Xwhich are expressed in terms of two free parameters, ξW-W0(ξZ-Z0) and MW0(MZ0). Such W0and Z0, described in terms of the two parameters (mass and mixing), are here referred to as EGM bosons. The parametrization is presented in [10]. Then, we will set two-dimensional limits, by using the CMS and ATLAS resonant diboson production data [7, 8] collected in the full Run 2 data set with time-integrated luminosity of 137 fb−1and 139 fb−1, respectively. The presented analysis in the EGM with two free parameters is more general than the previous ones where the only parameter is the V0mass. As for the SSM, one has V0 SSM ≡ V0 EGM when ξV-V0= 0. Note that the parametrization of boson mixing introduced by Altarelli et al. [9], though being simplified, has a well-motivated theoretical basis. To be specific, we briefly consider Z0– Z00mixing within the framework of models with extended gauge sector. The mass eigenstates Z and Z0are admixtures of the weak eigenstates Z0of SU(2) ×U(1) and Z00of the extra U(1)0, respectively: Z=Z0cos φ+Z00sin φ , (5a) Z0=−Z0sin φ+Z00cos φ . (5b) In each case there is a relation between the Z0Z00mixing angle φand the masses MZand MZ0 [6]: tan2φ=M2 Z0−M2 Z M2 Z0−M2 Z0≃2MZ0∆MZ0Z M2 Z0 ,(6) where the downward shift ∆MZ0Z=MZ0−MZ> 0, and MZ0is the mass of the Zboson in the absence of mixing, i.e., for φ= 0, given by MZ0=MW √ρ0cos θW ,(7) in terms of the charged (MW) gauge boson mass and the ρ0parameter. The mixing angle Nonlinear Phenomena in Complex Systems Vol. 28, no. 3, 2025 272 I. A. Serenkova φwill play an important role in our analysis. Such mixing effects reflect the underlying gauge symmetry and/or the structure of the Higgs sector of the model as the ρ0parameter depends on the ratios of the Higgs vacuum expectation values and on the total and third components of weak isospin of the Higgs fields. For each type of Z00boson, defined by its gauge couplings, there are three classes of models, which differ in the assumptions concerning the quantum numbers of the Higgs fields which generate the Z-boson mass matrix [6]. (i) The least constrained (ρ0free) model makes no assumption concerning the Higgs sector. It allows arbitrary SU(2) representations for the Higgs fields, and is the analogue of allowing ρ06= 1 in the SU(2) ×U(1) model. In this case MZ,MZ0 and φare all free parameters. (ii) If one assumes that all SU(2) breaking is due to Higgs doublets and singlets (ρ0= 1 model), there are only two free parameters, which we identify as φand MZ0. We will adopt this parametrization throughout the paper. (iii) Finally, in specific models one specifies not only the SU(2) assignments but the U(1)0 assignments of the Higgs fields. Since the same Higgs multiplets generate both MZ and φ, one has an additional constraint. To a good approximation, for MZMZ0, in specific “minimal-Higgs models”, one has an additional constraint φ≃ −s2 WPihΦii2Ii 3LQ0 i PihΦii2(Ii 3L)2=PM2 Z M2 Z0 ,(8) where sWis the sine of the electroweak angle. In these models φand MZ0 are not independent and there is only one (e.g., MZ0) free parameter. This parametrization is of the form presented in Eq. (4). Furthermore, hΦiiare the Higgs (doublet) vacuum expectation values spontaneously breaking the symmetry, and Q0 iare their charges with respect to the additional U(1)0. In these models the same Higgs multiplets are responsible for both generation of the mass MZand for the strength of the Z0-Z00mixing. Thus Pis a model-dependent constant. This Z0-Z00mixing induces a change in the couplings of the two bosons to fermions. From Eq. (5), one obtains the vector and axial-vector couplings of the Zand Z0bosons to fermions: vf=v0 fcos φ+v00 fsin φ,af=a0 fcos φ+a00 fsin φ, (9a) v0 f=v00 fcos φ−v0 fsin φ,a0 f=a00 fcos φ−a0 fsin φ, (9b) with unprimed and primed couplings referring to Z0and Z00, respectively, and found, e.g. in [6]. An important property of the models under consideration is that the gauge eigenstate Z00does not couple to the W+W−pair since it is neutral under SU(2). Therefore the W-pair production is sensitive to a Z0only to the extent that there is a non-zero Z0-Z00mixing. From Eq. (5), one obtains: gWWZ = cos φ gWWZ0,(10a) gWWZ0=−sin φ gW W Z0,(10b) where gWWZ0=ecot θW. Also, gW W γ =e. In many extended gauge models, while the couplings to fermions are not much different from those of the SM, the Z0WW coupling is substantially suppressed with respect to that of the SM. In fact, in the extended gauge models the SM trilinear gauge boson coupling strength, gWWZ0, is replaced by gW WZ0→ξZ−Z0·gW W Z0, where ξZ−Z0≡ |sin φ|(see Eq. (10b)) is the mixing factor. We will set cross section limits on such Z0as functions of the mass MZ0and ξZ−Z0. In addition, we study W-W0mixing in the process pp →V0X→V HX within the framework of the EGM model. Mass mixing may be induced between the electrically charged gauge bosons at the tree level. The physical (mass) Нелинейные явления в сложных системах Т. 28, № 3, 2025 Improved Constraints on the Heavy Gauge Bosons Decaying into a Vector Boson and a Higgs Boson at the LHC 273 eigenstates of Wand W0are admixtures of the weak eigenstates denoted as ˆ Wand ˆ W0, respectively, and obtained by a rotation of those fields: W±=ˆ W±cos θWW0+ˆ W0±sin θWW0,(11a) W0± =−ˆ W±sin θWW0+ˆ W0±cos θWW0,(11b) in analogy with Eq. (5). Upon diagonalization of their mass matrix, the couplings of the observed Wboson are shifted from the SM values. The mixing parameter ξW−W0between gauge eigenstates can be defined as ξW−W0≡ |sin θWW0|. 3. Hadron production and decay of W0boson In this section, we consider the simplest EGM model which predicts charged heavy gauge bosons. At the lowest order in the EGM, W0 production and decay into WZ and WH in proton-proton collisions occur through quarkantiquark annihilation in the s-channel. Adopting the Narrow-Width Approximation (NWA), one can factorize the process (1) into the W0 production and the W0decay, σ(pp →W0X→WZ X) = σ(pp →W0X) ×BR(W0→WZ),(12a) σ(pp →W0X→WH X) = σ(pp →W0X)× BR(W0→WH).(12b) Here, σ(pp →W0X)is the total (theoretical) W0production cross section, BR(W0→WZ) = ΓWZ W0/ΓW0and similarly BR(W0→WH) = ΓWH W0/ΓW0with ΓW0the total width of the W0. In the EGM the W0bosons can decay into pairs of SM fermions (charged leptons, neutrinos and quarks), gauge bosons WZ and WH. Specifically, in the calculation of the total width ΓW0we consider the following channels: W0→f¯ f0,WZ, and WH, where fis a SM fermion (f=`, ν, q). Note, that here the ` includes τleptons as well. Only the familiar left-handed neutrinos are considered, possible right-handed exotic neutrinos are assumed to be kinematically unavailable as final states. Also, we shall ignore the couplings to other beyondSM particles such as SUSY partners and exotic fermions. As a result, the total decay width of the W0boson is taken to be ΓW0=X f Γf¯ f0 W0+ ΓWZ W0+ ΓWH W0.(13) The presence of the last two decay channels, which are often neglected at low and moderate values of MW0, is due to W-W0mixing which is constrained to be tiny. In particular, for the range of MW0values below ∼2TeV, the dependence of ΓW0on the values of ξW-W0(within its allowed range) induced by ΓWZ W0and ΓWH W0is unimportant because PfΓf¯ f0 W0highly dominates over the diboson partial widths as illustrated in fig. 1 for a representative value of the mixing parameter. Therefore, in this mass range, one can approximate the total width as ΓW0≈PfΓf¯ f0 W0= 3.5% ×MW0[11], where the sum runs over SM fermions only. For heavier W0bosons, the diboson decay channels, WZ and WH, start to play an important role, and we are no longer able to ignore them [11–14]. To be specific, we assume that both partial widths are comparable, ΓW H W0≃ΓWZ W0 for heavy MW0, as required by the Equivalence theorem. The partial width of the W0→WZ decay channel in the EGM can be written as [9, 11, 13]: Nonlinear Phenomena in Complex Systems Vol. 28, no. 3, 2025 274 I. A. Serenkova ΓWZ W0=αem 48 cot2θWMW0 M4 W0 M2 WM2 Z"1−M2 Z−M2 W M2 W02 −4M2 W M2 W0#3/2 ×"1 + 10 M2 W+M2 Z M2 W0+M4 W+M4 Z+ 10M2 WM2 Z M4 W0#·ξ2 W-W0.(14) For a fixed mixing factor ξW-W0and at large MW0, the total width increases rapidly with the W0mass because of the quintic dependence of the WZ mode on the W0mass ΓW Z W0∝ MW0M4 W0/(M2 WM2 Z), corresponding to the production of longitudinally polarized Wand Z in the channel W0→WLZL[9]. In this case, the WZ mode (as well as WH) becomes dominant and BR(W0→WZ)→0.5, while the fermionic decay channels, PfΓf¯ f0 W0∝MW0, are increasingly suppressed, as illustrated in fig. 1. 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 -4 10 -3 10 -2 10 -1 10 1 BR WH+WZ ff WH M (TeV) w' = 3 10 w-w' -3 . W' WH+WZ EGM → W' Σ ff EGM - - - W' WH → EGM → ' ' FIG. 1. Branching ratios BR(W0→Pf¯ f0)(solid), BR(W0→WH)(dash-dotted), and BR(W0→WH+ WZ)(dashed) vs MW0in the EGM where the W-W0 mixing factor is taken to be ξW-W0= 3 ·10−3. It is assumed that BR(W0→WZ) = BR(W0→WH). The data we consider were collected with the CMS and ATLAS detectors during the 2015–2018 running period of the LHC, referred to as Run 2 and correspond to a time-integrated luminosity of 137 fb−1and 139 fb−1, respectively. The CMS and ATLAS experiments have presented the recent search for diboson resonances based on the full Run 2 datasets in the semileptonic final states [7, 8] and set limits on the W0production cross sections times branching fraction in the process pp →W0X→WH X for MW0in the 1.0 TeV – 4.5-5 TeV range. In fig. 2, we show the observed 95% C.L. upper limits on the production cross section times the branching fraction, σ95% ×BR(W0→WH), as functions of the W0mass. The area below the long-dashed curve labelled “NWA” corresponds to the region where the W0resonance width is predicted to be less than 5% of its mass, corresponding to the best detector resolution of the searches, where the narrow-width assumption is satisfied. We also show a curve labelled “Unitarity limit” that corresponds to the unitarity bound (see, e.g. [11, 13]). The intersection points of the measured upper limits on the production cross section with these theoretical cross sections for various values of ξW-W0give the corresponding upper bounds on ξW-W0, displayed in fig. 3. Our results extend the sensitivity much beyond the corresponding CDF Tevatron results as well as the ATLAS and CMS sensitivity attained at 7 and 8 TeV. Also, for the first time, we set W0limits as functions of the mass MW0and mixing factor ξW-W0from the study of the diboson production and subsequent decay into semileptonic final states at the LHC at 13 TeV with the full CMS Run 2 datasets. The exclusion region obtained in this way on the parameter space of the W0 naturally supersedes the corresponding exclusion area obtained for time-integrated luminosity of 36.1 fb−1at CMS in the semileptonic channel as reported in [12, 14–17]. The limits on the Нелинейные явления в сложных системах Т. 28, № 3, 2025 Improved Constraints on the Heavy Gauge Bosons Decaying into a Vector Boson and a Higgs Boson at the LHC 275 1 1.5 2 2.5 3 3.5 4 4.5 5 -4 10 -3 10 -2 10 -1 10 1 W' WH EGM CMS, ATLAS, observed 95% C.L., 13 TeV, 139 fb -1 observed.95% C.L., 13 TeV, 137 fb -1 Unitarity limit NWA BR (W' WH) [pb] + M (TeV) w' 3 10 5 10 10-3 -4 -4 . . = 1.5 10 w-w' .-3 FIG. 2. 95% C.L. upper limits on σ95% ×BR(W0→ WH), showing CMS and ATLAS data on the semileptonic final states for 137 fb−1and 139 fb−1. The theoretical production cross sections σ(pp → W0X)×BR(W0→WH)for the EGM. W0parameters presented in this section obtained from the diboson WH production in semileptonic final states, corresponding to a time-integrated luminosity of 137 fb−1(CMS) and 139 fb−1 (ATLAS). 4. Hadron production and decay of Z0boson We shall next consider Z0boson production in pp collision and its subsequent decay into diboson channels, Z0→W+W−and Z0→ZH. Specificlly, we concentrate on the models with extended gauge sector predicting the existence of Z0bosons, such as E6, left-right symmetric LR and the EGM. The processes under study are: σ(pp →Z0X→W+W−X) = σ(pp →Z0X) ×BR(Z0→W+W−),(15a) σ(pp →Z0X→ZH X) = σ(pp →Z0X) ×BR(Z0→ZH).(15b) Here, σ(pp →Z0X)is the total (theoretical) Z0 production cross section, BR(Z0→W+W−) = ΓWW Z0/ΓZ0and BR(Z0→ZH) = ΓZH Z0/ΓZ0with FIG. 3. 95% C.L. exclusion regions in the twodimensional (MW0,ξW-W0) plane obtained from the precision electroweak data (horizontal dashed straight line labeled “EW”), direct search constraints from the Tevatron in p¯p→WZX (dark shaded area) as well as from the LHC searches for pp →WZX at 7 TeV and 8 TeV (Run 1) (gray area) and at 13 TeV from W0→WH production in semileptonic final states using the full Run 2 ATLAS and CMS datasets. The region above each curve for the WZH channel is excluded. ΓZ0the total width of the Z0. Among the Z0 models, we start out with a discussion of the EGM. In the computation of the total width ΓZ0we take into account the following channels: Z0→f¯ f,W+W−, and ZH [13, 14], where H is the SM Higgs boson and frefers to the SM fermions (f=l, ν, q). Throughout the paper we shall ignore the couplings of the Z0to any beyondNonlinear Phenomena in Complex Systems Vol. 28, no. 3, 2025 276 I. A. Serenkova 1 1.5 2 2.5 3 3.5 4 4.5 5 -4 10 -3 10 -2 10 -1 10 1 CMS, Z' ZH BR (Z' ZH) [pb] M (TeV) z' + ATLAS, observed 95% C.L., 13 TeV, 139 fb -1 Unitarity limit NWA 3 10 3 10 10 -4 -4 -3 = 1.5 10 -3 z-z' . . . EGM observed. 95% C.L., 13 TeV, 137 fb -1 FIG. 4. 95% C.L. upper limits on σ95% ×BR(Z0→ ZH), showing CMS and ATLAS data on the semileptonic final states for 137 fb−1and 139 fb−1, respectively. . SM particles such as right-handed neutrinos, as well as to SUSY partners and any other exotic fermions. Any additional states may increase the width of the Z0. The total width ΓZ0of the Z0 boson can then be written as follows: ΓZ0=X f Γff Z0+ ΓWW Z0+ ΓZH Z0.(16) The two last terms are due to Z-Z0mixing. For the range of MZ0values below ∼3TeV, the dependence of ΓZ0on the values of ξZ-Z0(within its allowed range) is unimportant. Therefore, in this mass range, one can approximate the total width as ΓZ0≈PfΓff Z0, where the sum runs over SM fermions only. Within the approximation above, one can quantify the ratio of ΓZ0/MZ0for the benchmark EGM as 3%, whereas for the ψ, η, χ and LR models it varies from 0.5% to 2.0%. We note that the “Equivalence theorem” suggests a value for BR(Z0→ ZH)comparable to BR(Z0→W+W−), up to electroweak symmetry breaking effects and phase-space factors. Throughout this paper, for definiteness, we adopt a scenario where both partial widths are comparable, ΓZH Z0≃ΓWW Z0for heavy MZ0. For all MZ0values of interest for our analysis the width of the Z0boson is considerably FIG. 5. The Z0 EGM model: 95% C.L. exclusion regions in the two-dimensional (MZ0,ξZ-Z0) plane obtained after incorporating indirect constraints from electroweak precision data (dashed curve labeled “EW”), and direct search constraints from the Tevatron (dark shaded area) as well as from the LHC searches for pp →Z0→ZH in semileptonic final states using the full Run 2 CMS and ATLAS datasets. The region above the curves for ZH channels are excluded. smaller than the experimental mass resolution ∆M. We adopt the approximation ∆M/M ≈5%, as reported, e.g., in for reconstructing the diboson invariant mass of the ZH systems. The partial width of the Z0→W+W−decay channel can be written as: Нелинейные явления в сложных системах Т. 28, № 3, 2025 Improved Constraints on the Heavy Gauge Bosons Decaying into a Vector Boson and a Higgs Boson at the LHC 277 ΓWW Z0=α 48 cot2θWMZ0MZ0 MW41−4M2 W M2 Z03/2"1 + 20 MW MZ02 + 12 MW MZ04#ξ2 Z−Z0.(17) For a fixed mixing factor ξZ-Z0and at large MZ0where ΓWW Z0dominates over PfΓff Z0the total width increases rapidly with the mass MZ0because of the quintic dependence of the W+W−mode on the Z0mass. In this case, the W+W−mode (together with Z0→ZH) becomes dominant and BR(Z0→W+W−)→0.5(this value arises from the assumption ΓZH Z0= ΓWW Z0), while the fermionic decay channels (Γff Z0∝MZ0) are increasingly suppressed. In fig. 4, we consider the full CMS and ATLAS Run2 datasets of time integrated luminosity of 137 fb−1and 139 fb−1and show the observed 95% C.L. upper limits on the production cross section times the branching fraction, σ95% × BR(Z0 EGM →ZH), as functions of the Z0mass, obtained from the semileptonic final state. 1 1.5 2 2.5 3 3.5 4 4.5 5 -4 10 -3 10 -2 10 -1 10 1 CMS, Z' ZH ATLAS, observed 95%C.L., 13 TeV, 139 fb -1 observed. 95%C.L., 13 TeV, 137 fb -1 LR Unitarity limit NWA M (TeV) z' BR(Z' ZH) [pb] + 3 10 -4 5 10 -4 10 -3 . . = 1.5 10 -3 z-z' . FIG. 6. 95% C.L. upper limits on σ95% ×BR(Z0 LR → ZH), showing CMS and ATLAS data on the semileptonic final states for 137 fb−1and 139 fb−1, respectively. Different bounds on the Z0parameter space are collected in fig. 5, for the Z0 EGM model, FIG. 7. 95% C.L. upper limits on σ95% ×BR(Z0 LR → ZH), showing CMS and ATLAS data on the semileptonic final states for 137 fb−1and 139 fb−1, respectively. The theoretical production cross sections σ(pp →Z0X)×BR(Z0→WW )for the EGM for mixing factor ξZ-Z0. showing that at high masses, the limits on ξZ-Z0 obtained from the full Run 2 datasets collected at √s= 13 TeV and recorded by the CMS and ATLAS detectors are substantially stronger than that derived from the global analysis of the precision electroweak data (EW), as well as Nonlinear Phenomena in Complex Systems Vol. 28, no. 3, 2025