Electroweak-Charged Bound States As LHC Probes of Hidden Forces

TUM-HEP-1103-17, UMD-PP-017-032

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

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+,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 b¯b, 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.

I. INTRODUCTION

New hidden particles that couple weakly to the Stan- dard Model (SM), but interact strongly with other beyond-the-SM (BSM) states, play important roles in theories addressing the electroweak hierarchy problem, such as neutral naturalness [1, 2] and natural supersymmetry (SUSY) [3–5], as well as in models that explain cosmological anomalies [6–8]. Examples of such particles, which in this paper are called hidden force carriers, include hadrons bound by a new confining interaction, or the physical excitations associated with a new scalar or vector force. Testing the existence of hidden force carriers is an important task of the Large Hadron Collider (LHC). Since these typically have small couplings to the SM sector, FIG. 1. The collider processes studied in this paper. Here however, their direct production is very suppressed. Nev- +,0 ertheless, in many motivated BSM scenarios other new ψ are the mediators, new particles that carry SM electroweak (but not color) charge, which we take to be vector- particles exist, charged under at least some of the SM like fermions. Their Drell-Yan pair production leads to the symmetries, that can serve as mediators to access the formation of electroweak-charged bound states due to a hid- hidden force carrier at the LHC. In this paper we focus den force. The annihilation of the electrically charged bound arXiv:1710.06437v2 [hep-ph] 20 Apr 2018 on the challenging, but motivated, case where the me- state Υ± produces a W ±X pair, where X is the hidden force diators, labeled ψ, have SM electroweak (and not color) carrier. We take X to be either a real scalar φ, which decays charges. Once a ψψ¯ pair is produced via the electroweak back to the SM via mass mixing with the SM-like Higgs, or interactions, it can form a bound state held together by a dark photon γd that decays via kinetic mixing with the SM ¯ the hidden force. Since the hidden force carrier X has a photon. The φ → bb and γd → `` decays are selected, which large coupling to the mediators, it is produced with siz- can be either prompt or displaced on collider timescales. able probability in the ensuing bound state annihilation, possibly in association with other SM object(s) to en- sure electroweak charge conservation. X can then decay through its small coupling to SM particles, yielding either prompt or displaced signatures in the LHC detectors. For concreteness, in this paper we consider the cases where the hidden force carrier is either a real scalar or a ∗ Email: llfl[email protected]; [email protected]; yht- dark photon, X = φ, γd, while the mediators are a pair of [email protected]; [email protected] vector-like fermions ψ+,0, with the superscript indicating 2 the SM electric charge. The relevant LHC processes are plified models sketched in Fig. 1, we apply the results shown in Fig. 1: A ψ+ψ¯0 (or ψ0ψ¯−) pair is produced just to two explicit, motivated models that contain strongly below threshold in the charged Drell-Yan (DY) process coupled hidden forces as well as electroweak-charged me- and forms a vector bound state Υ± due to the hidden diators. This serves as an illustration of the potential force. The bound state then undergoes annihilation de- impact of the searches we propose. cay into W ±X on prompt collider timescales. The mo- The first model example is λ-SUSY [5], where the Higgs tivation for focusing on the electrically charged bound quartic coupling can be naturally raised by adding to the ∗ state is twofold: First, its production mediated by W superpotential a term ∼ λSHuHd, with S a singlet su- exchange has larger cross section compared to the neutral perfield and large λ ∼ O(1). If the scalar singlet s is channel via γ∗/Z∗, and second, selecting the W → `ν de- light, it mediates a strong force that can lead to the for- cay provides a hard prompt lepton with sizable branching mation of Higgsino bound states at the LHC, which then ratio, ensuring efficient triggering and powerful suppres- decay into W s with large branching fraction. The singlet sion of the SM backgrounds. decays to SM particles via mixing with the Higgs. In this We assume that φ decays back to the SM via a small case we thus identify the mediators with the Higgsinos, ˜ mass mixing with the 125 GeV Higgs boson, whereas γd ψ → h, and the hidden force carrier with the light sin- decays via kinetic mixing with the SM photon. We con- glet scalar, φ → s. This scenario was first discussed in centrate on the mass region 10 GeV . mX . 100 GeV, Ref. [13]. Here we present a more detailed assessment of which offers the best opportunities for detection of the the future LHC constraints on the model. hidden force carriers at the LHC and is motivated by con- As a second example we consider non-SUSY ultraviolet crete models, for example, of neutral naturalness. There- (UV) extensions of the Twin Higgs model [1], where new ¯ fore φ → bb and γd → `` are selected as the most promis- vector-like fermions appear that are charged under both ing final states. We allow for these decays to be either the SM and twin gauge symmetries [1, 14]. Some of these prompt or displaced. exotic fermions, labeled K, carry SM electroweak and For prompt X decays, we show that the resonant twin color charges, and can have masses in the few hun- Υ± → WX signals can be tested by performing sim- dred GeV range without conflicting with experiment or ple extensions of the existing ATLAS and CMS diboson significantly increasing the fine-tuning in the Higgs mass, searches. In the case of (W → `ν)(φ → b¯b), we show as discussed in Ref. [15]. Once they are pair produced that extending the ATLAS W h search [9] to look for b¯b in the charged DY process, the exotic fermions form a resonances with mass different from mh provides a pow- vector bound state under the twin color force, which can erful coverage. Notice that, in a similar spirit, ATLAS then annihilate into a W plus twin gluons. In the Fra- has very recently published a search for resonances that ternal version of the Twin Higgs model (FTH) [16], the decay into Xh, with X a new particle decaying to light hadronization of the twin gluons can lead to the produc- PC ++ quarks [10]. For (W → `ν)(γd → ``), where the SM back- tion of the lightest glueball, which has J = 0 and grounds are small, we perform a simple estimate based decays into SM particles by mixing with the Higgs. The on the ATLAS WZ search [11, 12] to show the sensitivity glueball decay length strongly depends on its mass, and to dilepton resonances with mass different from mZ . Our can be either prompt or macroscopic. In this scenario ± analyses of the Υ → W φ, W γd channels provide further we thus identify the mediators with the exotic fermions, motivation to extend the program of diboson searches to ψ → K, and the hidden force carrier with the lightest ˆ cover resonances that decay into BSM particles. twin glueball, φ → G0++ . For displaced X decays, we propose searches that re- Notice that, in the broad setup we are considering, the quire a hard prompt lepton from the W in combination (scalar or fermion) neutral mediator ψ0 can also be the with a reconstructed (b¯b) or (``) displaced vertex. The dark matter candidate. The production and decay of the hard lepton guarantees efficient triggering on the sig- ψ0ψ¯0 bound state then gives an example of dark matter nal events, and the resulting signatures are essentially annihilation at colliders that does not leave a missing background-free. We perform simplified projections to energy signature [13, 17, 18]. estimate the reach achievable at the LHC. The remainder of this paper is organized as follows. It is important to emphasize that the resonant In Sec. II we analyze the Υ± → WX processes in the Υ± → WX signals studied in this paper allow for the context of simplified models. We perform projections reconstruction of the mass of both the bound state and to estimate the LHC sensitivity in the four final states the hidden force carrier. If we make the assumption that considered, given by X = φ or γd, each with prompt the decay channels available to the bound state are WX or displaced decay. We also discuss the sensitivity to and the “irreducible” ff¯ 0 (with f, f 0 SM fermions) medi- the irreducible Υ± → ff¯ 0 decays, focusing on the clean- ated by an off-shell W , then from the measurement of the est `ν channel, and compare it with the reach in the signal rate the size of the coupling between the hidden Υ± → WX processes. In Sec. III we apply our results force carrier and the mediators can be inferred. Thus the to the λ-SUSY model. We show that for large λ, the sig- discovery of the bound state signals would also offer the nals arising from the charged Higgsino bound state Υ± h˜ opportunity to measure the strength of the hidden force. have better reach than the standard monojet and disap- After carrying out our collider analyses within the sim- pearing track searches. In addition, in the typical case of 3

± 2 R 1 prompt s → b¯b decays the Υ → W s search has better where α ≡ g /(4π), L ¯(τ) = (dx/x)[u(x)d¯(τ/x) + h˜ W ud τ sensitivity compared to Υ± → `ν. In Sec. IV our re- u(τ/x)d¯(x)] is the parton luminosity, s is the collider cen- h˜ sults are applied to the UV-extended FTH model. Here ter of mass energy, and the bound state mass was approx- we find that, even though the branching fraction of the imated with MΥ ' 2 mψ. An analogous expression holds − exotic fermion bound state Υ± into W + twin glueball is for the production of the charge conjugate Υ . The K 0 suppressed to the few percent level, this signal provides factor Nc in Eq. (4) accounts for the number of hidden ± 0 −,0 an interesting complementarity to Υ → `ν if the light- degrees of freedom: for example, Nc = 1 if ψ are iden- K 0 est twin glueball decays at a macroscopic distance, giving tified with the Higgsinos, while Nc = 3 in the case of rise to a (b¯b) displaced vertex. Our concluding remarks exotic fermions that transform in the fundamental of a are given in Sec. V. confining hidden SU(3). For definiteness, henceforth we W assume vψ = 1 , which applies for both the Higgsino and exotic fermion bound states. ψ(0) is the wavefunction II. SIMPLIFIED MODEL ANALYSIS at the origin, whose value depends on the details of the hidden force. In the Coulomb approximation we have In this section we study the LHC sensitivity to the processes |ψ(0)|2 C3α3 = λ , (5) ± ± 3 pp → Υ → W X, (1) mψ 8π where X = φ, γd decays as where α ≡ λ2/(4π) is the hidden force coupling ( λ φ → b¯b (prompt or displaced), strength, and C is a model-dependent constant. For an (2) γd → `` (prompt or displaced), SU(N) hidden force, C = Cψ − CΥ/2, where Cψ (CΥ) is the quadratic Casimir of the representation where ψ (Υ) with ` = e, µ. Here Υ± (in the following we often drop transforms (see e.g. Refs. [19, 20]). For a U(1)- or the electric charge and write just Υ) is a bound state scalar-mediated force, we can instead set C = 1 pro- with J PC = 1−− that carries unit charge under the SM vided the charges are absorbed in the definition of the U(1)em, whereas φ (γd) is a real scalar (real vector) hid- force coupling strength αλ. In these cases, if the force den force carrier. As discussed in the Introduction, we carrier is not massless the formation of bound states make the assumption that φ (γd) couples to SM parti- can happen only if its wavelength is larger than the cles dominantly through mass mixing with the SM Higgs Bohr radius, namely 1/mX > 2/(αλmψ), or equivalently (kinetic mixing with the SM photon). Then, in the mX < mψαλ/2 ' MΥαλ/4. mass region 10 GeV . mX . 100 GeV the most promis- In this paper we consider scenarios with ing decays of the force carriers are those in Eq. (2). We small mass splitting between ψ± and ψ0, study the four types of signals in Eqs. (1) and (2) at 0 < ∆mψ = mψ± − mψ0 mW . The bound state an- the 13 TeV LHC and set model-independent bounds on nihilation rate is Γ = N 0C3{α4 α /24, α3 α2 /4} m ¯ Υ c λ W λ W ψ σ(Υ) BR(Υ → WX) BR(X → F ), where F = bb, ``, as depending on whether the dominant channel is Υ → W φ functions of the masses of the bound state and of the force via a coupling λφ(ψ¯+ψ− + ψ¯0ψ0), as in λ-SUSY, or carrier. We also compare the reach in these channels to Υ → W ∗ → ff¯ 0, as in the UV-extended FTH [21]. In or- that in der for the bound state annihilation to take place before the charged constituent decays as ψ± → (W ∗ → ff¯ 0)ψ0, pp → Υ± → ` ν , (3) ΓΥ must be larger than which constitutes the irreducible signal of spin-1 electroweak-charged bound states. 3G2 (∆m )5 Γ(ψ± → ψ0ff¯ 0) ' F ψ . (6) Since in Secs. III and IV we interpret our results in 5π3 explicit models, it is useful to summarize the formulas that give the Υ± production cross section and branch- This sets an upper bound on the mass splitting (for ing ratios as functions of the underlying parameters. ∆m m ) Given two Dirac fermions ψ−,0 with approximately de- ψ W generate mass mψ and coupled to the SM W boson as √ − W ¯+ 0 {4,3}/5 4/5 (g/ 2)vψ ψ W/ ψ + h.c., the cross section for produc- ∆mψ 0 3 1/5 αλ 300 GeV + < 0.16 (NcC ) . tion of their vector bound state Υ in quark-antiquark mψ 0.2 mψ annihilation is (7)  2 In the region mψ > 300 GeV that we consider in this 2 W 2 ! work, the existing disappearing track constraint [22, 23] 3 |ψ(0)| 0 αW vψ 1 4mψ σud¯→Υ+ = π 3 Nc  2  Lud¯ , applies if cτ ± > 0.1 ns, corresponding to mass split- 3m mW s s ψ ψ 1 − 2 4mψ tings smaller than those typically found in our parameter (4) space. 4

_ ± ± -1 A. Υ → W φ with prompt φ → b¯b Prompt W + bb analysis , mΦ = 100 GeV , 300 fb

_ SM tt Wj WZ In this case the LHC sensitivity can be estimated by 200 SM fit adapting the strategy used in the search for resonances H L that decay into (W → `ν)(h → b¯b) [9], to allow for an 100 MU = 0.8 TeV ¯ M = 1 TeV invariant mass of the bb pair diﬀerent from mh. U The signal is simulated using a simple FeynRules [24] 50 model of a charged spin-1 resonance coupled to SM GeV 50

µ + −µ + quarks asuγ ¯ PLdΥµ +h.c. and to W φ as φW Υµ +h.c.. 20

For both the signal and backgrounds, we generate par- events N ton level events with MadGraph5 [25], shower them using 10 PYTHIA6 [26] and pass the result to Delphes3 [27] for the detector simulation. We adopt most of the Delphes3 5 configurations proposed in the Snowmass 2013 energy frontier studies [28, 29]. However, since the b-tagging 2 performance has recently been improved by employing 600 800 1000 1200 1400 multivariate techniques [30], in our analysis we assume MWbb GeV the b-tagging efficiency to be 70%, with 1% rate for a light flavor jet to be mis-tagged as b-jet. Jets are re- FIG. 2. Reconstructed MW bb for@ signalD and backgrounds in ± constructed using the anti-kT algorithm with distance the analysis of Υ → W φ with prompt φ → b¯b, assuming parameter R = 0.5. mφ = 100 GeV. The signal distributions are shown for two In the event selection we require the (sub-)leading b-jet representative parameter points with MΥ = 800, 1000 GeV, b taking the hidden force coupling λ = 2.5 and C = 1. The to have pT > 100 (30) GeV and |η | < 2.5. To suppress the tt¯ background, we also impose that N ≤ 3, where orange curve shows the fitted total background that was used j to calculate the signal significance. Nj is the number of jets. In addition, the selection re- ` ` quires one lepton with pT > 30 GeV and |η | < 2.5, as well as E/ T > 30 GeV, where E/ T is the modulus of the missing transverse energy (MET) vector. The MET vec- global, significance. It can be clearly seen that for a fixed tor is identified with the neutrino transverse momentum, MΥ & 800 GeV, the cross section limit deteriorates when and the reconstructed transverse mass and transverse mφ is decreased. This happens because in our analysis W we require two separate b-jets with ∆Rbb & 0.5, which momentum of the W must satisfy mT ∈ [10, 100] GeV and pW > 200 GeV, respectively [31]. To identify the significantly reduces the selection efficiency for large MΥ T and light φ. For this reason we chose to show our re- force carrier φ we require mbb − mφ ∈ [−15, 10] GeV. In order to reconstruct the full 4-momentum of the W sults only for mφ > 60 GeV, below which the efficiency candidate, we extract the longitudinal component of the becomes very small [34]. The sensitivity can be ex- 2 2 tended to larger MΥ and smaller mφ through the ap- neutrino momentum by solving (pν + p`) = mW [32]. This allows us to calculate the invariant mass of the W bb plication of jet substructure techniques [35], which go system for each event. In addition, to improve the res- beyond the scope of this paper but can be efficiently im- olution on M we apply a standard kinematic fitting plemented in the actual experimental analysis, similarly W bb to the very recent ATLAS searches for resonances decay- procedure that corrects the b-jet momenta by imposing 0 0 2 2 ing to (W → qq¯ )(h → b¯b) [36] and (X → qq¯ )(h → b¯b) (pb1 + pb2 ) = mφ (for more details on the procedure, see for example the CMS search for resonances decaying into [10]. hh [33]). The largest SM background is tt¯, followed by W + jets. ± ± We also include W (Z → b¯b) production, but its contribu- B. Υ → W γd with prompt γd → `` tion is subdominant. In the calculation of the signal significance, the MW bb distribution of the total background The projected bounds on the prompt 0 is fitted with an exponential function, shown by the or- (γd → ``)(W → ` ν) signal are obtained by rescal- ange curve in Fig. 2. For the signal, the width of the ing the results of the 8 TeV ATLAS search for WZ MW bb peak is dominated by detector effects and insen- resonances in the tri-lepton channel [11, 12]. Notice that sitive to the small intrinsic width of the resonance. We even though one neutrino is present in the final state, then require MW bb ∈ [MΥ − 50 GeV,MΥ + 100 GeV]. the kinematics can be fully reconstructed [12] by solving 2 2 z The resulting bounds on σ(Υ)BR(Υ → W φ)BR(φ → the equation (pν + p`0 ) = mW for pν , with the same ¯ bb) are shown as contours in the (mφ,MΥ) plane in the procedure described in Sec. II A. left panel of Fig. 3. We stress that although we have im- We summarize here the rescaling procedure. The SM posed different cuts on the bb and W bb invariant masses background, which is dominated by W + Z(∗)/γ∗ produc- for each hypothetical combination of (mφ,MΥ) consid- tion, is very suppressed if the invariant mass of the `` pair ered, the bounds were calculated using local, and not is away from the Z peak. To estimate it we perform a 5

_ 95% CL exclusion on Σ pp®U ´BR U®W+bb fb 95% CL exclusion on Σ pp®U ´BR U®W+{{ fb 1600 1600 - 2 1 300 fb 1 H L H L @ D H L H L0.3@ D 3 ab-1 1400 1400 300 fb-1 10 5 2 3 ab-1 1200 1200

D 50 D 0.6 0.6 GeV GeV @ @

U 1000 U 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

mΦ GeV mΓd GeV

FIG. 3. Left: Projected 95% CL bounds@ D on σ(Υ)BR(Υ → W φ)BR(φ → b¯b) from the LHC@ searchD for prompt φ → b¯b and W → `ν. See Sec. II A for details. Right: Projected 95% CL bounds on σ(Υ)BR(Υ → W γd)BR(γd → ee + µµ) from the LHC 0 search for prompt γd → `` and W → ` 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. simulation of SM pp → W `` at parton level, in the SM significantly affect our results. at 13 TeV, and use it to compute for each mγd hypoth- The resulting bounds on σ(Υ)BR(Υ → W γd)BR(γd → esis the ratio r(mγd ) of the cross section in an invariant ee + µµ) are shown in the right panel of Fig. 3. We mass window |m`` − mγd | < 10 GeV to the cross section again emphasize that they were computed using local on the Z peak, namely |m`` − mZ | < 10 GeV. Then, the significance. The sensitivity is weaker for light γd and total background given as a function of MWZ in Table 2 heavy Υ, where the leptons from the dark photon decay of the ATLAS note [11] is rescaled to a collider energy of are collimated, and for mγd ∼ mZ , where the background 13 TeV using the qq¯0 parton luminosity, as well as to the is largest. appropriate integrated luminosity, and multiplied times r(mγd ) to obtain our background prediction as a function of M . The total signal acceptance times efficiency for ± ± W γd C. Υ → W φ (γd) with displaced φ → b¯b (γd → ``) a W 0 with mass 800 GeV, A × (800), was given in Ta- ble 7 of Ref. [11]. To take into account the variation of the If the hidden force carrier has a macroscopic decay invariant mass shape, for MΥ different from 800 GeV we ± multiply A × (800) by the ratio of the maximum values length, we can search for the Υ signal in final states containing a prompt hard lepton stemming from the W of the corresponding signal templates, shown in Fig. 5 of ¯ the same reference. The resulting acceptance times effi- and a displaced φ → bb or γd → `` decay. ¯ ciency, which was calculated for LHC energy of 8 TeV, For φ → bb, our analysis follows the discussion in is employed in our 13 TeV projection. In addition, we Ref. [14], which in turn was based on the existing ATLAS include the effect of the lepton isolation cuts as a func- searches for hadronic displaced vertices (DV) [37, 38]. We generate the signal process at the parton level, and re- tion of the boost factor of γd , by requiring an angular ` quire one prompt lepton ` = e, µ with pT > 100 GeV separation ∆R`` > 0.3. After including this correction, ` our estimate of the signal acceptance times efficiency for and |η | < 2.5, thus ensuring that the signal events can be easily triggered on. An additional 90% efficiency is mγ = 60 GeV varies from ≈ 7% at MΥ = 800 GeV to d assumed for the reconstruction of the prompt lepton. ≈ 0.7% at MΥ = 1.5 TeV. Our rescaling method relies b on the assumption of a bump-hunt-type search in a nar- In addition, we require two b’s with |η | < 2.0 and pb > 30 GeV. For each event, we calculate the 4- row MW `` window around the putative MΥ , which is a T reasonable approach given the good experimental reso- momentum of φ in the lab frame, which together with lution achievable in this final state. At the same time, the proper lifetime cτφ determines the probability dis- however, some caveats apply to the extrapolation of the tribution for the location of the displaced decay. The 8 TeV analysis to 13 TeV. In particular, we have implic- DV can be detected either in the inner detector (ID), if itly assumed that the variation of trigger thresholds and its radial distance r satisfies 1 cm < r < 28 cm, or in selection cuts on the leptons and missing energy will not the hadronic calorimeter (HCAL) and muon spectrome- ter (MS) if 200 cm < r < 750 cm. For the efficiency of 6

FIG. 4. Left: 95% CL upper bound on σ(Υ)BR(Υ → W φ)BR(φ → b¯b) from the LHC search for prompt W → `ν and displaced φ → b¯b. The quantity cτφ MΥ/(2mφ) 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+MS. Right: 95% CL upper bound on σ(Υ)BR(Υ → W γd)BR(γd → µµ) from the LHC search for prompt W → `ν 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. the DV reconstruction we assume a constant 10% in the Even though each of the signals depends on three pa- ID volume and 40% in the HCAL+MS, which are simple rameters, namely the masses MΥ and mX and the proper approximations of the results given in Refs. [37, 38] [39]. decay length cτX , the problem can be simplified by ob- Notice that the DVs can be identified even when the serving that experimentally, the most important variable angular separation between the b-jets is small. In the is the decay length of the long-lived particle in the lab ± ID the impact parameter d0 of charged tracks can be ex- frame. In the approximation that the Υ is produced ploited, as done in Ref. [38]. We can roughly estimate at rest, this is simply given by cτX MΥ/(2mX ). Figure 4, that for a distance ∼ 10 cm between the location of the where the bounds on the signal cross section are shown as displaced decay and the primary vertex, the requirement functions of cτX MΥ/(2mX ), confirms that this quantity d0 > 1 cm [38] yields sensitivity to φ’s with boost factor determines the experimental efficiency to a good accu- as large as 10. If the decay is inside the HCAL, the ratio racy. A subleading dependence on MΥ can be observed, of the energy deposits in the electromagnetic calorimeter originating from the cuts on the prompt lepton, whereas and HCAL can be used to identify the signal. A detailed varying mX leaves the efficiency essentially unaffected. understanding of the dependence of the reconstruction efficiency on the boost factor requires further studies, which are beyond the scope of this paper. Here we simply give an estimate, by assuming the above-mentioned D. Υ± → `ν boost-independent values for the efficiency. The analysis of displaced γd → `` is performed along similar lines. The same cuts and efficiency are applied The Υ± has an irreducible decay width into SM on the prompt lepton originating from the W . We focus fermions, via an off-shell W boson. The most power- ± on γd → µµ decays, requiring the two muons to satisfy ful probe of these decays is the Υ → `ν channel, where |ηµ| < 2.0 and pµ > 30 GeV. Approximating the results the current upper limit on σ(Υ±)BR(Υ± → `ν) is of T −1 of the searches in Refs. [40, 41], we assume that dimuon O(few) fb for MΥ ∼ 1 TeV, based on 36.1 fb [42]. We DVs can be reconstructed for 1 cm < r < 750 cm with obtain projections to larger integrated luminosity L√by 40% efficiency. rescaling the current cross section constraint ∝ 1/ L . Although in general the searches for DVs at the LHC Even though this procedure is strictly correct only when suffer from several backgrounds, such as the misidentifi- systematic uncertainties are negligible, we have checked cation of prompt objects and the accidental crossing of that applying it to the constraint from a previous AT- −1 uncorrelated tracks, these are strongly suppressed by the LAS analysis based on 13.3 fb [43] gives good agree- −1 additional requirement of a prompt hard lepton. There- ment with the 36.1 fb bound of Ref. [42]. This justifies fore, in both our DV analyses we assume the background our simplified treatment. to be negligible, and accordingly we exclude at 95% CL It is interesting to compare the sensitivity in the Υ± → all parameter points that would yield a number of signal `ν and Υ± → W ±X final states. Focusing on prompt ¯ events larger than 3. φ → bb and γd → `` decays, in Fig. 5 we show in the 7

(mX ,MΥ) plane contours of the ratio next-to-minimal√ supersymmetric SM superpotential 0 2 3 W = 2λSHuHd + ξF S + µ S /2 + κS /3 and assume BR(Υ± → W ±X) BR(X → F ) (8) the gauginos to be heavy and out of the LHC reach [45]. ± ± ± 0 0 BR(Υ → W X) BR(X → F ) + BR(Υ → ff¯ ) We focus on the limit 2κhsi + µ λvu,d (where we have expanded the√ scalar component of the superfield S as (where for Υ± → ff¯ 0 we sum over all SM fermions) that s → hsi + s/ 2), so the singlino is also decoupled from yields with L = 300 fb−1 the same constraint on σ(Υ±) the light Higgsinos. As a consequence, the up- and down- from the WX and `ν final states. For the scalar φ we type Higgsinos are nearly degenerate, and their DY pro- ˜0 ˜0 find that the ratio in Eq. (8) is < 0.5 in a large region duction is unsuppressed. We can then treat (hu, hd) as a of parameter space, thus indicating that the search for Dirac fermion that receives a mass mh˜ from the µ-term, Υ → W φ provides an important test of the bound state and similarly for the charged Higgsinos. Electroweak ra- properties. On the other hand, the Υ → W γd decay diative corrections split the masses of the neutral and can compete with Υ → `ν even if the relative branching charged Higgsinos by ∆mh˜ ' 350 MeV, which clearly fraction is at the percent level, thanks to the striking satisfies the condition in Eq. (7). The singlet scalar s de- trilepton signature. cays into SM particles through its mixing with the SM- like Higgs, which is constrained to be < 20% by the ex- ± ± ± ∼ Reach in U ®W X versus U ® {Ν isting Higgs couplings measurements [46]. Since λ also 0.9 0.1 0.7 generates a large coupling between the Higgs and two 1400 singlet scalars, we avoid bounds from the h → ss decay 0.5 by requiring ms > mh/2. Therefore, in our study we focus on the singlet scalar mass range

1200 _ X®bb mh mh˜ αλ D 0.05 < ms < , (9) X®{{ 2 2 GeV @ 1000 0.02 U where the second inequality ensures that the bound state M can form, as discussed below Eq. (5). The decay h → ss∗ → 4b can easily have a small branching ratio, being 800 suppressed by the h-s mixing and by the bottom Yukawa coupling. The production and decay of Υ± is described by 600 h˜ 0.02 0.25 the upper diagram in Fig. 1, with the identifications 0 ± ˜0 ˜± ¯ 70 80 90 100 110 120 130 140 (ψ , ψ , φ) → (hu,d, hu,d, s). The s → bb decay is gener- mX GeV ically prompt, but it can also happen at a macroscopic distance if cancellations between the soft SUSY masses FIG. 5. Contours of the ratio in Eq.@ (8)D that gives at the LHC suppress the mixing between h and s to less than ∼ −1 with 300 fb the same bound on σ(Υ) from the Υ → WX 10−5. We can then reinterpret our simplified model re- ¯ and Υ → `ν final states. Here we consider prompt φ → bb sults in the λ-SUSY context, by comparing the model- and γd → `` decays. independent limits calculated in Secs. II A and II C for the (W → `ν)(φ → b¯b) final state (with prompt or displaced φ decay, respectively) to the production cross sec-

tion of Υh˜ calculated via Eqs. (4) and (5). We appropri- III. λ - SUSY 0 ately set Nc = 1 and C = 1 in those equations. Since the Υ± can annihilate into both W s and ff¯ 0, in our signal h˜ Here we discuss the concrete example of λ-SUSY [5], predictions we include the corresponding branching ra- where a coupling of the form ∼ λSHuHd is added to tio BR(Υh˜ → W s) ' αλ/(αλ + 6 αW ). Furthermore, we the minimal supersymmetric SM superpotential, with S include the BR(s → b¯b), which is the same as for a SM a singlet scalar superfield. A large λ ∼ O(1) helps to Higgs with mass given by ms, because s couples to SM increase the Higgs mass to 125 GeV in a natural way [44]. fields only via mixing with the Higgs. If in addition the singlet scalar s is light, it mediates a In the left panel of Fig. 6 we show the constraints ¯ strong attractive force between the Higgsinos, that can on αλ obtained from the prompt (W → `ν)(s → bb) −1 lead to the formation of bound states in the process of channel with 300 fb . Notice that the αλ-contours DY Higgsino pair production [13]. The charged bound also give at least a rough idea of the measurement of state Υ± decays into W s with large branching fraction, h˜ the hidden force coupling that can be obtained if an ex- and in turn the s decays to b¯b through its mixing with cess is observed. In the orange-shaded region the LHC the Higgs. will be able to entirely rule out the existence of Higgsino Before applying the results of our analysis of bound states, by pushing the exclusion on αλ below the Sec. II, we briefly summarize some essential as- smallest value that allows bound state formation, namely pects of the model. We consider a general αmin = 2m /m = 4m /M . For example, for α = 0.4 λ s h˜ s Υh˜ λ 8

_ _ -1 % Α + -1 95% CL exclusion on ΑΛ , W + prompt bb, 300 fb 95 CL exclusion on Λ , W bb DV, 300 fb 1600 1.2 1600 0.4 0.4 1 H L 0.5 0.3 1400 1400

0.75 D D 1200 1200 0.6 GeV GeV @ @ h h 0.5 U U 1000 1000 M M

800 4 ms 0.4 ΑΛ < 800 LHC 0.3 MUh

H L 0.2 600 600 0.3 0.1 70 80 90 100 110 120 130 140 1 10 100 1000 104 m GeV s cΤs MUh 2ms cm

@ D FIG. 6. Left: 95% CL upper bound on αλ in λ-SUSY from the search for prompt (W →H `ν)( s →L @b¯b)D at the LHC with 300 −1 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 /M . Right: 95% CL upper bound on α in λ-SUSY s Υh˜ λ from the search for prompt W → `ν and displaced s → b¯b at the LHC with 300 fb−1. The relation α > 4m /M that λ s Υh˜ makes bound state formation possible is implicitly assumed to hold. In the region to the left (right) of the vertical dashed line, s decays in the ID (HCAL+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).

the reach extends up to Higgsino masses mh˜ ∼ 500 GeV. It is interesting to compare this to the reach of the monojet and disappearing track searches. The monojet channel has a 95% CL reach of mh˜ ' 200 GeV at the LHC with 3 ab−1, and a similar sensitivity is expected in the disappearing track search if the mass splitting generated by electroweak loops, ∆mh˜ ' 350 MeV, is assumed [47]. Thus we find that if λ is large, the reach of the Hig- gsino bound state signal is far superior. In addition, since the values of αλ probed by the analysis correspond ¯ to BR(Υh˜ → W s) ' 0.6 - 0.8, after including BR(s → bb) and comparing with Eq. (8) and Fig. 5 we find that the ¯ Υh˜ → (W → `ν)(s → bb) final state has better sensitivity than Υh˜ → `ν in this region of parameters. For the large values of λ that can be probed by our analysis, perturbativity is lost at a relatively low scale FIG. 7. Estimate of the scale Λ where perturbativity is lost in the λ-SUSY model, as a function of the low-energy value Λ, as illustrated in Fig. 7. For example, for αλ = 0.4 of α , for representative values of κ. Λ is defined as the scale (corresponding to λ ' 2.2) we find 2 TeV . Λ . 10 TeV, λ depending on the Higgsino mass and on the value of the where the two-loop contributions to the running of λ and κ become of the same size as the one-loop terms. parameter κ that controls the size of the S3 term in the superpotential. The large value of λ also affects the Higgs mass prediction. Since the h-s mixing is constrained to be small by LHC measurements [46], we have approximately between the Higgsinos and the singlino, as we have assumed from the beginning, and by raising the masses of 2 2 2 2 2 2 mh ∼ λ v sin 2β + mZ cos 2β , (10) the squarks and the charged Higgs [48]. where v = p2(v2 + v2) ' 246 GeV. Therefore in the re- In the right panel of Fig. 6 we show the constraints ob- u d ¯ gion λ & 2 where the bound state production is relevant, tained from the (prompt W → `ν) + (displaced s → bb) channel. Since the boost factor of s is γs ' MΥ /(2ms), tan β & 10 is required. The λ-SUSY region with large λ h˜ > −1 and large tan β can produce dangerous corrections to the the second inequality in Eq. (9) implies that γs ∼ 2αλ . S and T parameters of electroweak precision tests. Nev- As discussed in Sec. II C, the identification of the ertheless, these can be reduced by suppressing the mixing hadronic DV becomes very challenging if the s → b¯b de- 9 cay takes place in the ID with γs >∼ 10. This is verified in the region of parameters with cτ (M /2m ) < 30 cm s Υh˜ s ∼ and αλ . 0.2 (hatched in black), where new ideas are required to successfully reconstruct the narrow displaced jet in the ID.

IV. UV-EXTENDED FRATERNAL TWIN HIGGS FIG. 8. The signal of the exotic fermion bound state in the UV-extended Fraternal Twin Higgs. The outgoing twin glu- The signals we study also appear in several non-SUSY ons (curly lines) hadronize into twin glueballs. The lightest UV completions of the TH model, which contain exotic ˆ ¯ glueball G0++ decays to bb through the Higgs portal, either fermions charged under both the SM and twin gauge promptly or at a macroscopic distance. groups [1, 14]. Some of these fermions, labeled K−, 0 (where the superscript indicates the SM electric charge), carry SM electroweak and twin color charges. As shown Lattice computations [50] give m ˆ ' 6.8Λˆ for the mass −, 0 G in Ref. [15], K can have Z2-breaking masses 1 TeV of the lightest glueball. The twin confinement scale de- without violating experimental constraints, and with- pends on the number of flavors in the twin sector, as well out significantly increasing the fine-tuning of the Higgs as on the value of the twin QCD coupling in the UV, mass. The exotic fermions can therefore be produced gˆs(ΛUV), where for definiteness we take ΛUV = 5 TeV. at the LHC through the DY process and form an elec- As to the field content, here we focus on the Fraternal ± trically charged vector bound state ΥK due to the twin Twin Higgs model, which includes twin copies of the color force. If the lifetime of the constituents is suffi- third-generation fermions only. Concerning the value ciently long, the bound state annihilates into resonant ofg ˆs, assuming exact Z2 symmetry at ΛUV leads to final states. The main channel is ff¯ 0 via an off-shell W , Λˆ ' 5 GeV, whereas allowing for a 10% difference be- but a sizable branching ratio also exists for the W gˆgˆ fi- tween gs(ΛUV) andg ˆs(ΛUV) yields Λˆ ∈ [1, 20] GeV, and nal state, where the two twin gluons can hadronize into therefore a lightest glueball mass in the range 7 GeV ˆ ˆ . the lightest twin glueball G ≡ G0++ ; see Fig. 8. In turn, m 140 GeV. The Gˆ mixes with the SM-like Higgs ¯ Gˆ . the twin glueball decays to bb via the Higgs portal, either h through a twin top loop. In the region of larger promptly or at a macroscopic distance depending on the mass, 60 GeV m 140 GeV, it decays promptly, ˆ . Gˆ . value of the twin confinement scale Λ. hence the dilepton channel ΥK → `ν [15] has far bet- Before we interpret the bounds of Sec. II in this con- ter sensitivity than ΥK → W Gˆ due to the much larger text, it is useful to recall some important features of branching fraction. Instead, a lighter glueball with mass the model. The K0 has a small mass mixing with 15 GeV . mGˆ . 50 GeV undergoes displaced decays the twin top. Assuming mK− < mtf/v, where f is within the volume of the LHC detectors, yielding a sig- the global symmetry breaking scale, the level repulsion nature that is striking enough to potentially overcome 0 − makes K slightly lighter than K , with mass splitting the branching fraction suppression. In this mass region mK− = mK0 + ∆mK given by the decay is dominantly into b¯b, with proper lifetime that can be approximated as [16] ∆m m2 K ' t . (11) 2 2 2 2 7 4 mK− 2(mt f /v − mK− ) 5 GeV f cτGˆ ∼ 1 cm . (12) m ˆ /6.8 1 TeV Taking f/v ' 4 and a typical strength of the twin QCD G couplingα ˆs(qrms) ∼ 0.2 [where qrms is related to the in- We then proceed to apply the bound from the verse Bohr radius of the bound state by an O(1) factor (prompt W → `ν) + (displaced φ → b¯b) analysis that [49], and we have assumed Λˆ = 5 GeV], the mass splitting was presented in Sec. II C, with the identification φ → Gˆ. in Eq. (11) satisfies Eq. (7) when the bound state mass is MΥ < 1.2 TeV. On the other hand, the neutral exotic The cross section for ΥK production is given by K 0 fermion K0 decays into Wˆ ˆb, where the twin W can be Eqs. (4) and (5) after we set Nc = 3, C = 4/3 and re- on- or off-shell, with amplitude suppressed by a mixing place αλ → αˆs . To estimate the relative branching ratio ± ¯ 0 ± for the ΥK → ff and ΥK → W gˆgˆ decays, we exploit the angle ' v/f (for mK− mtf/v). If mK0 < mWˆ + mˆb, the corresponding lifetime is sufficiently long to allow for similarity with the SM quarkonia. For example, for the annihilation of the charged bound state. However, the J/ψ we have (see e.g. Ref. [51]) twin bottom cannot be too heavy, to avoid introducing a 2 2 Γ(J/ψ → γgg) 8 π − 9 α (mb) new source of significant fine-tuning in the Higgs mass. ' s . (13) Γ(J/ψ → γ∗ → e+e−) 9 π α Requiring this additional tuning to be better than 10% restricts the parameter space for the bound state signals By replacing the photon with the W and accounting for 2 to MΥK < 1.1 TeV, which we assume in the following. an extra factor 2 , which arises because the W couples 10

95% CL exclusion on the UV-extended FTH is competitive with ΥK → `ν, because the striking com- 1200 Exotic fermions decay bination of a prompt lepton and a DV renders the ﬁnal state essentially background-free. This decay is peculiar _ 1100 -1 UK ® W + bb DV 300 fb of the UV-extended FTH model. Similarly to the case of -1 ˆ UK ® {Ν 300 fb λ-SUSY, discussed at the end of Sec. III, if G decays in 1000 U ® Ν 36H fbL-1 H L K { the ID with boost factor & 10 the standard reconstruc- H L D tion of the hadronic DV fails. The corresponding region 900 H L of parameter space is hatched in black in Fig. 9. GeV @

K As a ﬁnal comment, we observe that the signature of U 800

M a prompt lepton + DV can also appear in other neutral naturalness scenarios. For example, in the Folded (F-) 700 SUSY model [2] an F-stop/F-sbottom pair can be produced through DY or vector boson fusion [53]. If the F- 600 stop decays into a (likely off-shell) W and an F-sbottom, the resulting F-sbottom pair forms a squirky bound state. 500 10 20 30 40 50 The latter promptly annihilates into mirror glueballs, m ` GeV which in turn can yield displaced signatures by decay- G ing through the Higgs portal [54]. @ D FIG. 9. 95% CL exclusions on the UV-extended Fraternal Twin Higgs from the LHC searches for signals of the exotic V. DISCUSSION ± fermion bound state ΥK. We set f = 1 TeV. In black, we show the exclusion from the search for prompt W → `ν and In this paper we have presented a new strategy to displaced Gˆ → b¯b with 300 fb−1. The maximum of reach on search for hidden force carriers at the LHC. These par- the left (right) corresponds to cτGˆ (MΥK /2mGˆ ) ∼ 400 (10) cm, which optimizes the sensitivity in the HCAL+MS (ID). In the ticles have suppressed direct production cross sections, region hatched in black the Gˆ decays in the ID with boost due to their small couplings to the SM particles, but can be produced through mediators that carry at least some factor & 10, making the identification of the DV challenging (see text for details). In orange, we show the current and of the SM charges. We focused on the cases where the ± projected exclusions from the search for ΥK → `ν. In the hidden force carrier X is either a real scalar φ or a dark area shaded in grey, the exotic quarks decay before the bound photon γd, and the mediators are a pair of electroweak- state annihilation takes place. charged vector-like fermions ψ+,0. Once a ψ±ψ¯0 pair is produced in the DY process, the strong hidden force can bind it into an electrically charged spin-1 bound state only√ to left-handed fermions and with coupling strength Υ±, which promptly annihilates into W ±X. The cor- g/ 2, we arrive at responding signatures consist of a prompt lepton orig- ± ± 2 2 Γ(Υ → W gˆgˆ) 32 π − 9 αˆ (m − ) 1 inating from the W boson, and a prompt or displaced ' s K , (14) ¯ ± ± ∗ 0 φ → bb or γd → `` decay. We analyzed these final states Γ(Υ → W → ff¯ ) 9 π αW 12 in detail, estimating the LHC reach within a simplified where the factor of 1/12 accounts for the multiplicity of model approach. To illustrate the impact of our results, the SM fermion-antifermion final states available in the we also applied them to two motivated example models decay through the off-shell W . The resulting branch- that contain hidden forces and can yield these signatures, ± ± ing ratio for ΥK → W gˆgˆ varies from 1% to 5% in the namely λ-SUSY and the UV-extended Fraternal Twin mass range we study. We make the assumption that the Higgs. The resonant signals allow for the measurement twin gluons dominantly hadronize into a single lightest of the mass of both the bound state and the force car- glueball Gˆ, which is reasonable if the glueball production rier, thus yielding critical insights on the structure of the can be described by a thermal process with temperature hidden sector. ˆ ∼ Λ mGˆ [52]. Notice, however, that our analysis strat- For displaced X decays, we proposed new searches for egy is not affected if additional glueballs are produced by (b¯b) and (``) displaced vertices, where the simultaneous the twin hadronization. Once the glueball mass is fixed, presence of a hard prompt lepton stemming from the the running ofα ˆs is determined, which in turn sets the W ensures efficient triggering and essentially removes size of the wavefunction at the origin through Eq. (5) and all SM backgrounds. As a consequence, the reach of the ΥK branching ratios via Eq. (14). Therefore in our these searches can compete with that of the irreducible ± analysis we take MΥK and mGˆ as the two input param- Υ → `ν signal even when the bound state decays to ˆ ˆ ± eters. Furthermore, for Λ . 10 GeV we have a0Λ 1 W X with subdominant branching fraction. Signals of for all the values of mK− we consider, hence it is safe to this type are especially promising for testing models of apply the Coulomb approximation. neutral naturalness. The results are shown in Fig. 9. Despite the suppressed In the case of prompt X decays, we showed that sim- branching ratio BR(ΥK → W Gˆ) ∼ few %, this channel ple extensions of existing diboson searches would allow 11

ATLAS and CMS to obtain a compelling reach. Fur- C. Verhaaren, L.-T. Wang, and Y. Zhao for useful dis- thermore, while the simpliﬁed analyses performed in this cussions. LL and RZ were supported in part by the US paper lose sensitivity when the X decay products are col- Department of Energy grant DE-SC-000999. The work limated, the experimental collaborations have full capa- of ES has been partially supported by the DFG Clus- bility to exploit this type of events, either by employing ter of Excellence 153 “Origin and Structure of the Uni- jet substructure variables in the φ → b¯b decay or by re- verse,” by the Collaborative Research Center SFB1258 solving narrowly separated leptons that originate from and the COST Action CA15108. YT was supported γd → ``. We believe that our results provide further mo- in part by the National Science Foundation under grant tivation for extending the array of diboson searches to PHY-1315155, and by the Maryland Center for Funda- include heavy resonance decays to BSM particles. mental Physics. This work was performed in part at the Aspen Center for Physics, which is supported by the Na- tional Science Foundation grant PHY-1607611. ES (YT) Acknowledgments is grateful to the MCFP (TUM Physics Department) for hospitality in the ﬁnal stages of the project. We thank J. Collins, A. De Roeck, Y. Jiang, B. Shakya,

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