PHYSICAL REVIEW D 97, 015010 (2018)
Electroweak-charged bound states as LHC probes of hidden forces
† ‡ Lingfeng Li,1,* Ennio Salvioni,2, Yuhsin Tsai,3, and Rui Zheng1,§ 1Department of Physics, University of California, Davis, Davis, California 95616, USA 2Physics Department, Technical University of Munich, 85748 Garching, Germany 3Maryland Center for Fundamental Physics, Department of Physics, University of Maryland, College Park, Maryland 20742, USA
(Received 26 October 2017; published 19 January 2018)
We explore the LHC reach on beyond-the-standard model (BSM) particles X associated with a new strong force in a hidden sector. We focus on the motivated scenario where the SM and hidden sectors are connected by fermionic mediators ψ þ;0 that carry SM electroweak charges. The most promising signal is the Drell-Yan production of a ψ ψ¯ 0 pair, which forms an electrically charged vector bound state ϒ due to the hidden force and later undergoes resonant annihilation into W X. We analyze this final state in detail ¯ in the cases where X is a real scalar ϕ that decays to bb, or a dark photon γd that decays to dileptons. For prompt X decays, we show that the corresponding signatures can be efficiently probed by extending the existing ATLAS and CMS diboson searches to include heavy resonance decays into BSM particles. For long-lived X, we propose new searches where the requirement of a prompt hard lepton originating from the W boson ensures triggering and essentially removes any SM backgrounds. To illustrate the potential of our results, we interpret them within two explicit models that contain strong hidden forces and electroweak- charged mediators, namely λ-supersymmetry (SUSY) and non-SUSY ultraviolet extensions of the twin Higgs model. The resonant nature of the signals allows for the reconstruction of the mass of both ϒ and X, thus providing a wealth of information about the hidden sector.
DOI: 10.1103/PhysRevD.97.015010
I. INTRODUCTION Nevertheless, in many motivated BSM scenarios other new particles exist, charged under at least some of the SM New hidden particles that couple weakly to the standard symmetries, that can serve as mediators to access the model (SM), but interact strongly with other beyond-the-SM hidden force carrier at the LHC. In this paper we focus on (BSM) states, play important roles in theories addressing the challenging, but motivated, case where the mediators, the electroweak hierarchy problem, such as neutral natural- labeled ψ, have SM electroweak (and not color) charges. ness [1,2] and natural supersymmetry (SUSY) [3–5],aswell Once a ψψ¯ pair is produced via the electroweak inter- as in models that explain cosmological anomalies [6–8]. actions, it can form a bound state held together by the Examples of such particles, which in this paper are called hidden force. Since the hidden force carrier X has a large hidden force carriers, include hadrons bound by a new coupling to the mediators, it is produced with sizable confining interaction, or the physical excitations associated probability in the ensuing bound state annihilation, pos- with a new scalar or vector force. sibly in association with other SM object(s) to ensure Testing the existence of hidden force carriers is an electroweak charge conservation. X can then decay through important task of the Large Hadron Collider (LHC). its small coupling to SM particles, yielding either prompt or Since these typically have small couplings to the SM displaced signatures in the LHC detectors. sector, however, their direct production is very suppressed. For concreteness, in this paper we consider the cases where the hidden force carrier is either a real scalar or a dark photon, X ¼ ϕ; γ , while the mediators are a pair of * d [email protected] þ;0 † vectorlike fermions ψ , with the superscript indicating the [email protected] ‡ SM electric charge. The relevant LHC processes are shown [email protected] 0 0 − §[email protected] in Fig. 1:Aψ þψ¯ (or ψ ψ¯ ) pair is produced just below threshold in the charged Drell-Yan (DY) process and forms Published by the American Physical Society under the terms of a vector bound state ϒ due to the hidden force. The bound the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to state then undergoes annihilation decay into W X on the author(s) and the published article’s title, journal citation, prompt collider time scales. The motivation for focusing and DOI. Funded by SCOAP3. on the electrically charged bound state is twofold: First,
2470-0010=2018=97(1)=015010(12) 015010-1 Published by the American Physical Society LI, SALVIONI, TSAI, and ZHENG PHYS. REV. D 97, 015010 (2018)
motivation to extend the program of diboson searches to cover resonances that decay into BSM particles. For displaced X decays, we propose searches that require a hard prompt lepton from the W in combination with a reconstructed ðbb¯Þ or ðllÞ displaced vertex. The hard lepton guarantees efficient triggering on the signal events, and the resulting signatures are essentially background free. We perform simplified projections to estimate the reach achievable at the LHC. It is important to emphasize that the resonant ϒ → WX signals studied in this paper allow for the reconstruction of the mass of both the bound state and the hidden force carrier. If we make the assumption that the decay channels available to the bound state are WX and the “irreducible” þ;0 FIG. 1. The collider processes studied in this paper. Here ψ ff¯ 0 (with f, f0 SM fermions) mediated by an off-shell W, are the mediators, new particles that carry SM electroweak (but then from the measurement of the signal rate the size of the not color) charge, which we take to be vectorlike fermions. Their coupling between the hidden force carrier and the medi- Drell-Yan pair production leads to the formation of electroweak- charged bound states due to a hidden force. The annihilation of ators can be inferred. Thus the discovery of the bound state the electrically charged bound state ϒ produces a W X pair, signals would also offer the opportunity to measure the where X is the hidden force carrier. We take X to be either a real strength of the hidden force. scalar ϕ, which decays back to the SM via mass mixing with the After carrying out our collider analyses within the SM-like Higgs boson, or a dark photon γd that decays via kinetic simplified models sketched in Fig. 1, we apply the results ¯ mixing with the SM photon. The ϕ → bb and γd → ll decays to two explicit, motivated models that contain strongly are selected, which can be either prompt or displaced on collider coupled hidden forces as well as electroweak-charged time scales. mediators. This serves as an illustration of the potential impact of the searches we propose. its production mediated by W exchange has larger cross The first model example is λ-SUSY [5], where the Higgs section compared to the neutral channel via γ =Z , quartic coupling can be naturally raised by adding to the and second, selecting the W → lν decay provides a hard superpotential a term ∼λSHuHd, with S being a singlet prompt lepton with sizable branching ratio, ensuring superfield and large λ ∼ Oð1Þ. If the scalar singlet s is light, efficient triggering and powerful suppression of the SM it mediates a strong force that can lead to the formation of backgrounds. Higgsino bound states at the LHC, which then decay into We assume that ϕ decays back to the SM via a small mass Ws with large branching fraction. The singlet decays to SM mixing with the 125 GeV Higgs boson, whereas γd decays particles via mixing with the Higgs boson. In this case we via kinetic mixing with the SM photon. We concentrate on thus identify the mediators with the Higgsinos, ψ → h~, and 10 ≲ ≲ 100 the mass region GeV mX GeV, which offers the the hidden force carrier with the light singlet scalar, ϕ → s. best opportunities for detection of the hidden force carriers at This scenario was first discussed in Ref. [13]. Here we the LHC and is motivated by concrete models, for example, present a more detailed assessment of the future LHC ¯ of neutral naturalness. Therefore ϕ → bb and γd → ll are constraints on the model. selected as the most promising final states. We allow for these As a second example we consider non-SUSY ultraviolet decays to be either prompt or displaced. (UV) extensions of the twin Higgs model [1], where new For prompt X decays, we show that the resonant ϒ → vectorlike fermions appear that are charged under both the WX signals can be tested by performing simple extensions SM and twin gauge symmetries [1,14]. Some of these of the existing ATLAS and CMS diboson searches. In the exotic fermions, labeled K, carry SM electroweak and twin ¯ case of ðW → lνÞðϕ → bbÞ, we show that extending the color charges, and can have masses in the few hundred GeV ATLAS Wh search [9] to look for bb¯ resonances with mass range without conflicting with experiment or significantly different from mh provides a powerful coverage. Notice increasing the fine-tuning in the Higgs mass, as discussed that, in a similar spirit, ATLAS has very recently published in Ref. [15]. Once they are pair produced in the charged DY a search for resonances that decay into Xh, with X being process, the exotic fermions form a vector bound state a new particle decaying to light quarks [10].For under the twin color force, which can then annihilate into a ðW → lνÞðγd → llÞ, where the SM backgrounds are W plus twin gluons. In the fraternal version of the twin small, we perform a simple estimate based on the Higgs model (FTH) [16], the hadronization of the twin ATLAS WZ search [11,12] to show the sensitivity to gluons can lead to the production of the lightest glueball, PC þþ dilepton resonances with mass different from mZ.Our which has J ¼ 0 and decays into SM particles by analyses of the ϒ → Wϕ;Wγd channels provide further mixing with the Higgs boson. The glueball decay length
015010-2 ELECTROWEAK-CHARGED BOUND STATES AS LHC … PHYS. REV. D 97, 015010 (2018) strongly depends on its mass, and can be either prompt or are those in Eq. (2). We study the four types of signals in macroscopic. In this scenario we thus identify the mediators Eqs. (1) and (2) at the 13 TeV LHC and set model- with the exotic fermions, ψ → K, and the hidden force independent bounds on σðϒÞBRðϒ → WXÞBRðX → FÞ, ˆ ¯ carrier with the lightest twin glueball, ϕ → G0þþ . where F ¼ bb; ll, as functions of the masses of the bound Notice that, in the broad setup we are considering, the state and of the force carrier. We also compare the reach in (scalar or fermion) neutral mediator ψ 0 can also be the dark these channels to that in matter candidate. The production and decay of the ψ 0ψ¯ 0 pp → ϒ → lν; ð3Þ bound state then gives an example of dark matter annihi- lation at colliders that does not leave a missing energy which constitutes the irreducible signal of spin-1 electro- signature [13,17,18]. weak-charged bound states. The remainder of this paper is organized as follows. In Since in Secs. III and IV we interpret our results in Sec. II we analyze the ϒ → WX processes in the context explicit models, it is useful to summarize the formulas that of simplified models. We perform projections to estimate give the ϒ production cross section and branching ratios the LHC sensitivity in the four final states considered, given as functions of the underlying parameters. Given two Dirac −;0 by X ¼ ϕ or γ , each with prompt or displaced decay. We fermions ψ with approximately degenerate mass mψ and d pffiffiffi ϒ → ¯ 0 W þ − 0 also discuss the sensitivity to the irreducible ff coupled to the SM W boson as ðg= 2Þvψ ψ¯ =W ψ þ H:c:, decays, focusing on the cleanest lν channel, and compare it the cross section for production of their vector bound state with the reach in the ϒ → WX processes. In Sec. III we ϒþ in quark-antiquark annihilation is apply our results to the λ-SUSY model. We show that for 2 W 2 2 ψ 0 α vψ 1 4mψ large λ, the signals arising from the charged Higgsino σ π3 j ð Þj 0 W ud¯→ϒþ ¼ 3 Nc 2 Lud¯ ; ð4Þ ϒ 3mψ mW s s bound state ~ have better reach than the standard monojet 1 − 2 h 4mψ and disappearing track searches. In addition, in the typical R ¯ α ≡ 2 4π τ 1 ¯ τ case of prompt s → bb decays the ϒ → Ws search has where W g =ð Þ, Lud¯ ð Þ¼ τ ðdx=xÞ½uðxÞdð =xÞþ h~ ¯ uðτ=xÞdðxÞ is the parton luminosity, s is the collider better sensitivity compared to ϒ~ → lν. In Sec. IV our h center of mass energy, and the bound state mass was results are applied to the UV-extended FTH model. Here we approximated with Mϒ ≃ 2mψ . An analogous expression find that, even though the branching fraction of the exotic ϒ− ϒ holds for the production of the charge conjugate . fermion bound state K into W þ twin glueball is sup- 0 The factor Nc in Eq. (4) accounts for the number of hidden pressed to the few percent level, this signal provides an − 0 degrees of freedom: for example, N0 1 if ψ ; are ϒ → lν c ¼ interesting complementarity to K if the lightest twin identified with the Higgsinos, while N0 ¼ 3 in the case glueball decays at a macroscopic distance, giving rise to a c ¯ of exotic fermions that transform in the fundamental of a ðbbÞ displaced vertex. Our concluding remarks are given confining hidden SUð3Þ. For definiteness, henceforth we in Sec. V. W assume vψ ¼ 1, which applies for both the Higgsino and exotic fermion bound states. ψð0Þ is the wave function at II. SIMPLIFIED MODEL ANALYSIS the origin, whose value depends on the details of the hidden In this section we study the LHC sensitivity to the force. In the Coulomb approximation we have 2 3 3 processes jψð0Þj C αλ 3 ¼ ; ð5Þ mψ 8π pp → ϒ → W X; ð1Þ 2 where αλ ≡ λ =ð4πÞ is the hidden force coupling strength, where X ¼ ϕ; γd decays as and C is a model-dependent constant. For an SUðNÞ hidden force, C ¼ Cψ − Cϒ=2, where Cψ ðCϒÞ is the quadratic ¯ ϕ → bb ðprompt or displacedÞ; Casimir of the representation where ψðϒÞ transforms (see ð2Þ e.g. Refs. [19,20]). For a Uð1Þ- or scalar-mediated force, γd → ll ðprompt or displacedÞ; we can instead set C ¼ 1 provided the charges are absorbed with l ¼ e, μ. Here ϒ (in the following we often drop the in the definition of the force coupling strength αλ. In these electric charge and write just ϒ) is a bound state with JPC ¼ cases, if the force carrier is not massless the formation of 1−− that carries unit charge under the SM Uð1Þ , whereas bound states can happen only if its wavelength is larger em 1 2 α ϕðγ Þ is a real scalar (real vector) hidden force carrier. As than the Bohr radius, namely =mX > =ð λmψ Þ, or equiv- d α 2 ≃ α 4 discussed in the introduction, we make the assumption that alently mX 015010-3 LI, SALVIONI, TSAI, and ZHENG PHYS. REV. D 97, 015010 (2018) _ 1 is ϒ → Wϕ via a coupling λϕðψ¯ þψ − þ ψ¯ 0ψ 0Þ,asin Prompt W bb analysis , m 100 GeV, 300 fb ¯ 0 _ λ-SUSY, or ϒ → W → ff , as in the UV-extended SM tt Wj WZ 200 FTH [21]. In order for the bound state annihilation to take SM fit place before the charged constituent decays as ψ → 100 M 0.8 TeV ¯ 0 0 ðW → ff Þψ , Γϒ must be larger than M 1TeV 2 5 50 3G ðΔmψ Þ Γ ψ → ψ 0ff¯ 0 ≃ F : ð Þ 5π3 ð6Þ 50 GeV This sets an upper bound on the mass splitting (for 20 events Δmψ ≪ mW) N 10 4 3 5 4 5 Δmψ αλ f ; g= 300 GeV = 0 3 1=5 5 < 0.16ðNcC Þ : ð7Þ mψ 0.2 mψ 300 2 In the region mψ > GeV that we consider in this work, 600 800 1000 1200 1400 the existing disappearing track constraint [22,23] applies if MWbb GeV cτψ > 0.1 ns, corresponding to mass splittings smaller than those typically found in our parameter space. FIG. 2. Reconstructed MWbb for signal and backgrounds in the analysis of ϒ → Wϕ with prompt ϕ → bb¯, assuming 100 A. ϒ → W ϕ with prompt ϕ → bb¯ mϕ ¼ GeV. The signal distributions are shown for two representative parameter points with Mϒ ¼ 800, 1000 GeV, In this case the LHC sensitivity can be estimated by taking the hidden force coupling λ ¼ 2.5 and C ¼ 1. The orange adapting the strategy used in the search for resonances that curve shows the fitted total background that was used to calculate ¯ decay into ðW → lνÞðh → bbÞ [9], to allow for an invari- the signal significance. ¯ ant mass of the bb pair different from mh. The signal is simulated using a simple FeynRules [24] model of a charged spin-1 resonance coupled to SM calculate the invariant mass of the Wbb system for each μ þ −μ þ event. In addition, to improve the resolution on M we quarks as u¯γ PLdϒμ þ H:c: and to Wϕ as ϕW ϒμ þ Wbb H:c: For both the signal and backgrounds, we generate apply a standard kinematic fitting procedure that corrects 2 2 parton level events with MadGraph5 [25], shower them the b-jet momenta by imposing ðpb1 þ pb2 Þ ¼ mϕ (for using PYTHIA6 [26] and pass the result to Delphes3 [27] more details on the procedure, see for example the CMS for the detector simulation. We adopt most of the Delphes3 search for resonances decaying into hh [33]). configurations proposed in the Snowmass 2013 energy The largest SM background is tt¯, followed by W þ jets. frontier studies [28,29]. However, since the b-tagging We also include WðZ → bb¯Þ production, but its contribu- performance has recently been improved by employing tion is subdominant. In the calculation of the signal multivariate techniques [30], in our analysis we assume significance, the MWbb distribution of the total background the b-tagging efficiency to be 70%, with 1% rate for a light is fitted with an exponential function, shown by the orange flavor jet to be mistagged as a b-jet. Jets are reconstructed curve in Fig. 2. For the signal, the width of the MWbb using the anti-kT algorithm with distance parameter peak is dominated by detector effects and insensitive to R ¼ 0.5. the small intrinsic width of the resonance. We then require In the event selection we require the (sub-) leading b-jet MWbb ∈ ½Mϒ − 50 GeV;Mϒ þ 100 GeV . b ¯ to have pT > 100ð30Þ GeV and jη j < 2.5. To suppress the The resulting bounds on σðϒÞBRðϒ → WϕÞBRðϕ → bbÞ ¯ ≤ 3 tt background, we also impose that Nj , where Nj is are shown as contours in the ðmϕ;MϒÞ plane in the left the number of jets. In addition, the selection requires panel of Fig. 3. We stress that although we have imposed l 30 ηl 2 5 one lepton with pT > GeV and j j < . , as well as different cuts on the bb and Wbb invariant masses for ET > 30 GeV, where ET is the modulus of the missing each hypothetical combination of ðmϕ;MϒÞ considered, the transverse energy (MET) vector. The MET vector is bounds were calculated using local, and not global, identified with the neutrino transverse momentum, and significance. It can be clearly seen that for a fixed the reconstructed transverse mass and transverse momen- Mϒ ≳ 800 GeV, the cross section limit deteriorates when W ∈ 10 100 tum of the W must satisfy mT ½ ; GeV and mϕ is decreased. This happens because in our analysis we W 200 Δ ≳ 0 5 pT > GeV, respectively [31]. To identify the force require two separate b-jets with Rbb . , which sig- carrier ϕ we require mbb − mϕ ∈ ½−15; 10 GeV. In order nificantly reduces the selection efficiency for large Mϒ and to reconstruct the full 4-momentum of the W candidate, we light ϕ. For this reason we chose to show our results only extract the longitudinal component of the neutrino momen- for mϕ > 60 GeV, below which the efficiency becomes 2 2 tum by solving ðpν þ plÞ ¼ mW [32]. This allows us to very small [34]. The sensitivity can be extended to larger 015010-4 ELECTROWEAK-CHARGED BOUND STATES AS LHC … PHYS. REV. D 97, 015010 (2018) _ 95 CL exclusion on pp BR W bb fb 95 CL exclusio n o n pp BR W fb 1600 1600 2 1 300 fb 1 0.3 3ab 1 1400 1400 300 fb 1 10 5 2 3ab 1 1200 1200 50 0.6 0.6 Ge V Ge V 1000 1000 M 20 M 1 15 800 5 800 0.4 0.15 0.1 0.4 0.15 0.1 0.05 2 10 600 600 15 5 20 70 80 90 100 110 120 130 140 20 40 60 80 100 120 140 m Ge V m d Ge V FIG. 3. Left: Projected 95% C.L. bounds on σðϒÞBRðϒ → WϕÞBRðϕ → bb¯Þ from the LHC search for prompt ϕ → bb¯ and W → lν. See Sec. II A for details. Right: Projected 95% C.L. bounds on σðϒÞBRðϒ → WγdÞBRðγd → ee þ μμÞ from the LHC search for prompt 0 γd → ll and W → l ν. See Sec. II B for details. In both analyses, the invariant mass cuts were varied according to the hypothetical masses of the BSM particles. However, the cross section limits were computed using local, and not global, significance. Mϒ and smaller mϕ through the application of jet sub- shape, for Mϒ different from 800 GeV we multiply structure techniques [35], which go beyond the scope of A × ϵð800Þ by the ratio of the maximum values of the this paper but can be efficiently implemented in the actual corresponding signal templates, shown in Fig. 5 of the same experimental analysis, similarly to the very recent ATLAS reference. The resulting acceptance times efficiency, which searches for resonances decaying to ðW → qq¯ 0Þðh → bb¯Þ was calculated for LHC energy of 8 TeV, is employed in our [36] and ðX → qq¯ 0Þðh → bb¯Þ [10]. 13 TeV projection. In addition, we include the effect of the lepton isolation cuts as a function of the boost factor of γd,by requiring an angular separation ΔRll > 0.3. After including B. ϒ → W γd with prompt γd → ll this correction, our estimate of the signal acceptance times The projected bounds on the prompt ðγ →llÞðW →l0νÞ d efficiency for mγ ¼ 60 GeV varies from ≈7% at Mϒ ¼ signal are obtained by rescaling the results of the 8 TeV d 800 GeV to ≈0.7% at Mϒ ¼ 1.5 TeV. Our rescaling ATLAS search for WZ resonances in the trilepton channel method relies on the assumption of a bump-hunt-type search [11,12]. Notice that even though one neutrino is present in in a narrow M ll window around the putative Mϒ, which is the final state, the kinematics can be fully reconstructed W 2 2 z a reasonable approach given the good experimental reso- [12] by solving the equation ðpν þ pl0 Þ ¼ m for pν, with W lution achievable in this final state. At the same time, the same procedure described in Sec. II A. however, some caveats apply to the extrapolation of the We summarize here the rescaling procedure. The SM 8 TeV analysis to 13 TeV. In particular, we have implicitly background, which is dominated by W þ Zð Þ=γ produc- tion, is very suppressed if the invariant mass of the ll pair is assumed that the variation of trigger thresholds and selection away from the Z peak. To estimate it we perform a cuts on the leptons and missing energy will not significantly simulation of SM pp → Wll at parton level, in the SM affect our results. The resulting bounds on σðϒÞBRðϒ → Wγ ÞBRðγ → at 13 TeV, and use it to compute for each mγ hypothesis the d d d ee þ μμÞ are shown in the right panel of Fig. 3. We again ratio rðmγ Þ of the cross section in an invariant mass window d emphasize that they were computed using local signifi- mll − mγ < 10 GeV to the cross section on the Z peak, j d j γ ϒ − 10 cance. The sensitivity is weaker for light d and heavy , namely jmll mZj < GeV. Then, the total background where the leptons from the dark photon decay are colli- given as a function of M in Table 2 of the ATLAS note WZ mated, and for mγ ∼ m , where the background is largest. [11] is rescaled to a collider energy of 13 TeV using the qq¯ 0 d Z parton luminosity, as well as to the appropriate integrated ¯ C. ϒ → W ϕðγdÞ with displaced ϕ → bbðγd → llÞ luminosity, and multiplied times rðmγd Þ to obtain our background prediction as a function of MWγd . The total If the hidden force carrier has a macroscopic decay signal acceptance times efficiency for a W0 with mass length, we can search for the ϒ signal in final states 800 GeV, A × ϵð800Þ, was given in Table 7 of Ref. [11]. containing a prompt hard lepton stemming from the W and ¯ To take into account the variation of the invariant mass a displaced ϕ → bb or γd → ll decay. 015010-5 LI, SALVIONI, TSAI, and ZHENG PHYS. REV. D 97, 015010 (2018) FIG. 4. Left: 95% C.L. upper bound on σðϒÞBRðϒ → WϕÞBRðϕ → bb¯Þ from the LHC search for prompt W → lν and displaced ¯ ϕ → bb. The quantity cτϕMϒ=ð2mϕÞ approximates the decay length of ϕ in the lab frame. The result is insensitive to mϕ, as can be seen from the small deviation between the solid (s) and dashed (d) curves. The local minimum on the left corresponds to decays inside the ID, while the minimum on the right corresponds to the HCAL þ MS. Right: 95% C.L. upper bound on σðϒÞBRðϒ → WγdÞBRðγd → μμÞ from the LHC search for prompt W → lν and displaced γd → μμ. Both analyses are described in Sec. II C. We assume the searches to be background free; hence the cross section bounds for 3000 fb−1 are simply obtained by dividing those in the plots by a factor 10. ϕ → ¯ For bb, our analysis follows the discussion in The analysis of displaced γd → ll is performed along Ref. [14], which in turn was based on the existing similar lines. The same cuts and efficiency are applied on the ATLAS searches for hadronic displaced vertices (DV) prompt lepton originating from the W. We focus on γd → μμ [37,38]. We generate the signal process at the parton level, decays, requiring the two muons to satisfy jημj < 2.0 and l μ l μ and require one prompt lepton ¼ e, with pT > p > 30 GeV. Approximating the results of the searches in l T 100 GeV and jη j < 2.5, thus ensuring that the signal Refs. [40,41], we assume that dimuon DVs can be recon- events can be easily triggered on. An additional 90% structed for 1 cm 015010-6 ELECTROWEAK-CHARGED BOUND STATES AS LHC … PHYS. REV. D 97, 015010 (2018) Reach in W Xversus λ ∼ 1 0.9 0.1 0.7 with S being a singlet scalar superfield. A large Oð Þ helps to increase the Higgs mass to 125 GeV in a natural 1400 way [44]. If in addition the singlet scalar s is light, it 0.5 mediates a strong attractive force between the Higgsinos, that can lead to the formation of bound states in the process 1200 _ X bb of DY Higgsino pair production [13]. The charged bound 0.05 X state ϒ decays into Ws with large branching fraction, h~ Ge V ¯ 1000 0.02 and in turn the s decays to bb through its mixing with the M Higgs boson. Before applying the results of our analysis of Sec. II, 800 we briefly summarize some essential aspects of the model. We consider a general next-to-minimalpffiffiffi supersymmetric standard model superpotential W ¼ 2λSHuHd þ ξFS þ 600 μ0 2 2 κ 3 3 0.02 0.25 S = þ S = and assume the gauginos to be heavy and 70 80 90 100 110 120 130 140 out of the LHC reach [45]. We focus on the limit 2κhsiþ 0 m X Ge V μ ≫ λv (where we have expanded the scalar component u;d pffiffiffi of the superfield S as s → hsiþs= 2), so the singlino FIG. 5. Contours of the ratio in Eq. (8) that gives at the LHC −1 is also decoupled from the light Higgsinos. As a conse- with 300 fb the same bound on σðϒÞ from the ϒ → WX and ϒ → lν final states. Here we consider prompt ϕ → bb¯ and quence, the up- and down-type Higgsinos are nearly γ → ll decays. degenerate, and their DY production is unsuppressed. d ~ 0 ~ 0 We can then treat ðhu; hdÞ as a Dirac fermion that receives μ a mass mh~ from the -term, and similarly for the charged −1 OðfewÞ fb for Mϒ ∼ 1 TeV, based on 36.1 fb [42]. Higgsinos. Electroweak radiative corrections split the We obtain projections to larger integrated luminosity ffiffiffiffiL masses of the neutral and charged Higgsinos by p Δ ≃ 350 by rescaling the current cross section constraint ∝ 1= L. mh~ MeV, which clearly satisfies the condition Even though this procedure is strictly correct only when in Eq. (7). The singlet scalar s decays into SM particles systematic uncertainties are negligible, we have checked through its mixing with the SM-like Higgs, which is that applying it to the constraint from a previous ATLAS constrained to be ≲20% by the existing Higgs couplings analysis based on 13.3 fb−1 [43] gives good agreement measurements [46]. Since λ also generates a large coupling with the 36.1 fb−1 bound of Ref. [42]. This justifies our between the Higgs boson and two singlet scalars, we avoid → 2 simplified treatment. bounds from the h ss decay by requiring ms >mh= . It is interesting to compare the sensitivity in the ϒ → Therefore, in our study we focus on the singlet scalar lν and ϒ → W X final states. Focusing on prompt ϕ → mass range ¯ bb and γ → ll decays, in Fig. 5 we show in the ðm ;MϒÞ m m~ αλ d X h 015010-7 LI, SALVIONI, TSAI, and ZHENG PHYS. REV. D 97, 015010 (2018) _ _ 1 1 95 CL exclusio n o n ,W prompt bb, 300 fb 95 CL exclusio n o n ,W bb DV,300fb 1600 1.2 1600 0.4 0.4 1 0.5 0.3 1400 1400 0.75 1200 1200 0.6 Ge V Ge V h h 0.5 1000 1000 M M 800 4 m s 0.4 800 LHC 0.3 M h 0.2 600 600 0.3 0.1 70 80 90 100 110 120 130 140 1 10 100 1000 104 m Ge V s c s M h 2m s cm ¯ −1 FIG. 6. Left: 95% C.L. upper bound on αλ in λ-SUSY from the search for prompt ðW → lνÞðs → bbÞ at the LHC with 300 fb . In the orange-shaded region the LHC can fully rule out the existence of Higgsino bound states, by setting a limit on αλ that is below the smallest value required for bound state formation, 4m =Mϒ . Right: 95% C.L. upper bound on αλ in λ-SUSY from the search for prompt s h~ ¯ −1 W → lν and displaced s → bb at the LHC with 300 fb . The relation αλ > 4m =Mϒ that makes bound state formation possible is s h~ implicitly assumed to hold. In the region to the left (right) of the vertical dashed line, s decays in the ID (HCAL þ MS). In the region hatched in black the s decays in the ID with boost factor ≳10, making the identification of the DV challenging (see text for details). both Ws and ff¯ 0, in our signal predictions we include For the large values of λ that can be probed by our ϒ → ≃ α Λ the corresponding branching ratio BRð h~ WsÞ λ= analysis, perturbativity is lost at a relatively low scale ,as ¯ illustrated in Fig. 7. For example, for αλ 0.4 (corre- ðαλ þ 6αWÞ. Furthermore, we include the BRðs → bbÞ, ¼ sponding to λ ≃ 2.2) we find 2 TeV ≲ Λ ≲ 10 TeV, which is the same as for a SM Higgs with mass given by ms, because s couples to SM fields only via mixing with the depending on the Higgsino mass and on the value of the 3 Higgs boson. parameter κ that controls the size of the S term in the λ In the left panel of Fig. 6 we show the constraints on αλ superpotential. The large value of also affects the Higgs obtained from the prompt ðW → lνÞðs → bb¯Þ channel with mass prediction. Since the h-s mixing is constrained to be −1 300 fb . Notice that the αλ-contours also give at least a small by LHC measurements [46], we have approximately rough idea of the measurement of the hidden force coupling 2 ∼ λ2 2 22β 2 22β that can be obtained if an excess is observed. In the orange- mh v sin þ mZcos ; ð10Þ shaded region the LHC will be able to entirely rule out the existence of Higgsino bound states, by pushing the exclusion on αλ below the smallest value that allows bound state min formation, namely α ¼ 2m =m~ ¼ 4m =Mϒ . For exam- λ s h s h~ ple, for αλ ¼ 0.4 the reach extends up to Higgsino masses ∼ 500 mh~ GeV. It is interesting to compare this to the reach of the monojet and disappearing track searches. The monojet ≃ 200 channel has a 95% C.L. reach of mh~ GeV at the LHC with 3 ab−1, and a similar sensitivity is expected in the disappearing track search if the mass splitting generated Δ ≃ 350 by electroweak loops, mh~ MeV, is assumed [47]. Thus we find that if λ is large, the reach of the Higgsino bound state signal is far superior. In addition, since the values of αλ probed by the analysis correspond to ϒ → ≃ 0 6– 0 8 → ¯ FIG. 7. Estimate of the scale Λ where perturbativity is lost in the BRð h~ WsÞ . . , after including BRðs bbÞ λ-SUSY model, as a function of the low-energy value of αλ, for and comparing with Eq. (8) and Fig. 5 we find that the ϒ~ → κ Λ ¯ h representative values of . is defined as the scale where the two- ðW → lνÞðs → bbÞ final state has better sensitivity than loop contributions to the running of λ and κ become of the same ϒ → lν h~ in this region of parameters. size as the one-loop terms. 015010-8 ELECTROWEAK-CHARGED BOUND STATES AS LHC … PHYS. REV. D 97, 015010 (2018) qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 macroscopic distance depending on the value of the twin where v ¼ 2ðv þ v Þ ≃ 246 GeV. Therefore in the u d Λˆ λ ≳ 2 confinement scale . region where the bound state production is relevant, Before we interpret the bounds of Sec. II in this context, tan β ≳ 10 is required. The λ-SUSY region with large λ and β it is useful to recall some important features of the model. large tan can produce dangerous corrections to the S and The K0 has a small mass mixing with the twin top. T parameters of electroweak precision tests. Nevertheless, Assuming mK− 015010-9 LI, SALVIONI, TSAI, and ZHENG PHYS. REV. D 97, 015010 (2018) → 95 CLexclusionontheUV-extendedFTH We then proceed to apply the bound from the ðprompt W 1200 lνÞþðdisplaced ϕ → bb¯Þ analysis that was presented in Exotic fermions decay ϕ → ˆ _ Sec. II C, with the identification G. 1100 1 ϒ W bb DV 300 fb The cross section for K production is given by Eqs. (4) 300 fb 1 0 ˆ 1 and (5) after we set Nc ¼ 3, C ¼ 4=3 and replace αλ → αs. 1000 36 fb ¯ 0 To estimate the relative branching ratio for the ϒK → ff and ϒ → Wgˆ gˆ decays, we exploit the similarity with the 900 K Ge V SM quarkonia. For example, for the J=ψ we have (see e.g. 800 Ref. [51]) M Γ ψ → γ 8 π2 − 9 α2 700 ðJ= ggÞ ≃ sðmbÞ þ − : ð13Þ ΓðJ=ψ → γ → e e Þ 9 π α 600 By replacing the photon with the W and accounting for an 500 2 extra factor 2 , which arises because the W couples only toffiffiffi 10 20 30 40 50 p m Ge V left-handed fermions and with coupling strength g= 2, G we arrive at FIG. 9. 95% C.L. exclusions on the UV-extended fraternal twin 2 2 Higgs from the LHC searches for signals of the exotic fermion Γ ϒ → ˆ ˆ 32 π − 9 αˆ − 1 ð W g gÞ sðmK Þ ϒ 1 ≃ ; ð14Þ bound state K. We set f ¼ TeV. In black, we show the ¯ 0 9 π α 12 Γðϒ → W → ff Þ W exclusion from the search for prompt W → lν and displaced Gˆ → bb¯ with 300 fb−1. The maximum of reach on the left (right) 1 12 where the factor of = accounts for the multiplicity of the τ ˆ 2 ˆ ∼ 400 10 corresponds to c GðMϒK = mGÞ ð Þ cm, which optimizes SM fermion-antifermion final states available in the decay the sensitivity in the HCAL þ MS (ID). In the region hatched in through the off-shell W. The resulting branching ratio for black the Gˆ decays in the ID with boost factor ≳10, making the ϒK → W gˆ gˆ varies from 1% to 5% in the mass range identification of the DV challenging (see text for details). In we study. We make the assumption that the twin gluons orange, we show the current and projected exclusions from the ˆ ϒ → lν dominantly hadronize into a single lightest glueball G, search for K . In the area shaded in grey, the exotic quarks which is reasonable if the glueball production can be decay before the bound state annihilation takes place. described by a thermal process with temperature ∼Λˆ ≪ mGˆ [52]. Notice, however, that our analysis strategy is not decays into a (likely off-shell) W and an F-sbottom, the affected if additional glueballs are produced by the twin resulting F-sbottom pair forms a squirky bound state. hadronization. Once the glueball mass is fixed, the running The latter promptly annihilates into mirror glueballs, which of αˆ s is determined, which in turn sets the size of the wave in turn can yield displaced signatures by decaying through function at the origin through Eq. (5) and the ϒK branching the Higgs portal [54]. ratios via Eq. (14). Therefore in our analysis we take MϒK and mGˆ as the two input parameters. Furthermore, for ˆ ˆ V. DISCUSSION Λ ≲ 10 GeV we have a0Λ ≪ 1 for all the values of mK− we consider; hence it is safe to apply the Coulomb In this paper we have presented a new strategy to search approximation. for hidden force carriers at the LHC. These particles have The results are shown in Fig. 9. Despite the suppressed suppressed direct production cross sections, due to their ˆ branching ratio BRðϒK → WGÞ ∼ few%, this channel is small couplings to the SM particles, but can be produced competitive with ϒK → lν, because the striking combina- through mediators that carry at least some of the SM tion of a prompt lepton and a DV renders the final state charges. We focused on the cases where the hidden force ϕ γ essentially background free. This decay is peculiar of the carrier X is either a real scalar or a dark photon d, and the UV-extended FTH model. Similarly to the case of λ-SUSY, mediators are a pair of electroweak-charged vectorlike ψ þ;0 ψ ψ¯ 0 discussed at the end of Sec. III,ifGˆ decays in the ID with fermions . Once a pair is produced in the DY boost factor ≳10 the standard reconstruction of the had- process, the strong hidden force can bind it into an ronic DV fails. The corresponding region of parameter electrically charged spin-1 bound state ϒ , which promptly space is hatched in black in Fig. 9. annihilates into W X. The corresponding signatures con- As a final comment, we observe that the signature of a sist of a prompt lepton originating from the W boson, and ¯ prompt lepton þ DV can also appear in other neutral a prompt or displaced ϕ → bb or γd → ll decay. We naturalness scenarios. For example, in the folded (F-) analyzed these final states in detail, estimating the LHC SUSY model [2] an F-stop/F-sbottom pair can be produced reach within a simplified model approach. To illustrate through DY or vector boson fusion [53]. If the F-stop the impact of our results, we also applied them to two 015010-10 ELECTROWEAK-CHARGED BOUND STATES AS LHC … PHYS. REV. D 97, 015010 (2018) motivated example models that contain hidden forces resolving narrowly separated leptons that originate from λ and can yield these signatures, namely -SUSY and the γd → ll. We believe that our results provide further UV-extended fraternal twin Higgs. The resonant signals motivation for extending the array of diboson searches allow for the measurement of the mass of both the bound to include heavy resonance decays to BSM particles. state and the force carrier, thus yielding critical insights on the structure of the hidden sector. ACKNOWLEDGMENTS For displaced X decays, we proposed new searches for ðbb¯Þ and ðllÞ displaced vertices, where the simultaneous We thank J. Collins, A. De Roeck, Y. Jiang, B. Shakya, presence of a hard prompt lepton stemming from the W C. Verhaaren, L.-T. Wang, and Y. Zhao for useful dis- ensures efficient triggering and essentially removes all SM cussions. L. L. and R. Z. were supported in part by the U.S. backgrounds. As a consequence, the reach of these searches Department of Energy Award No. DE-SC-000999. The can compete with that of the irreducible ϒ → lν signal work of E. S. has been partially supported by the DFG even when the bound state decays to W X with subdomi- Cluster of Excellence 153 “Origin and Structure of the nant branching fraction. Signals of this type are especially Universe,” by the Collaborative Research Center Grant promising for testing models of neutral naturalness. No. SFB1258 and the COST Action Grant No. CA15108. In the case of prompt X decays, we showed that simple Y. T. was supported in part by the National Science extensions of existing diboson searches would allow Foundation under Grant No. PHY-1315155, and by the ATLAS and CMS to obtain a compelling reach. Maryland Center for Fundamental Physics. This work was Furthermore, while the simplified analyses performed in performed in part at the Aspen Center for Physics, which is this paper lose sensitivity when the X decay products are supported by the National Science Foundation Grant collimated, the experimental collaborations have full No. PHY-1607611. E. S. (Y. 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