Electroweak-Charged Bound States as LHC Probes of Hidden Forces
We explore the LHC reach on beyond-the-Standard Model (BSM) particles 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 that carry SM electroweak charges. The most promising signal is the Drell-Yan production of a pair, which forms an electrically charged vector bound state due to the hidden force and later undergoes resonant annihilation into . We analyze this final state in detail in the cases where is a real scalar that decays to , or a dark photon that decays to dileptons. For prompt 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 , we propose new searches where the requirement of a prompt hard lepton originating from the 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 -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 and , thus providing a wealth of information about the hidden sector.
New hidden particles that couple weakly to the Standard 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 Chacko et al. (2006); Burdman et al. (2007) and natural supersymmetry (SUSY) Batra et al. (2004); Maloney et al. (2006); Barbieri et al. (2007), as well as in models that explain cosmological anomalies Tulin et al. (2013); Hochberg et al. (2014); Kaplinghat et al. (2016). 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, however, their direct production is very suppressed. Nevertheless, in many motivated BSM scenarios other new particles exist, charged under at least some of the SM symmetries, that can serve as mediators to access the hidden force carrier at the LHC. In this paper we focus on the challenging, but motivated, case where the mediators, labeled , have SM electroweak (and not color) charges. Once a pair is produced via the electroweak interactions, it can form a bound state held together by the hidden force. Since the hidden force carrier has a large coupling to the mediators, it is produced with sizable probability in the ensuing bound state annihilation, possibly in association with other SM object(s) to ensure electroweak charge conservation. 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 dark photon, , while the mediators are a pair of vector-like fermions , with the superscript indicating the SM electric charge. The relevant LHC processes are shown in Fig. 1: A (or ) pair is produced just below threshold in the charged Drell-Yan (DY) process and forms a vector bound state due to the hidden force. The bound state then undergoes annihilation decay into on prompt collider timescales. The motivation for focusing on the electrically charged bound state is twofold: First, its production mediated by exchange has larger cross section compared to the neutral channel via , and second, selecting the decay provides a hard prompt lepton with sizable branching ratio, ensuring efficient triggering and powerful suppression of the SM backgrounds.
We assume that decays back to the SM via a small mass mixing with the Higgs boson, whereas decays via kinetic mixing with the SM photon. We concentrate on the mass region , which offers the best opportunities for detection of the hidden force carriers at the LHC and is motivated by concrete models, for example, of neutral naturalness. Therefore and are selected as the most promising final states. We allow for these decays to be either prompt or displaced.
For prompt decays, we show that the resonant signals can be tested by performing simple extensions of the existing ATLAS and CMS diboson searches. In the case of , we show that extending the ATLAS search ATLAS Collaboration (2015a) to look for resonances with mass different from provides a powerful coverage. Notice that, in a similar spirit, ATLAS has very recently published a search for resonances that decay into , with a new particle decaying to light quarks Aab (a). For , where the SM backgrounds are small, we perform a simple estimate based on the ATLAS search ATLAS Collaboration (2013, 2014a) to show the sensitivity to dilepton resonances with mass different from . Our analyses of the channels provide further motivation to extend the program of diboson searches to cover resonances that decay into BSM particles.
For displaced decays, we propose searches that require a hard prompt lepton from the in combination with a reconstructed or 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 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 and the “irreducible” (with SM fermions) mediated by an off-shell , then from the measurement of the signal rate the size of the coupling between the hidden force carrier and the mediators can be inferred. Thus the discovery of the bound state signals would also offer the opportunity to measure the strength of the hidden force.
After carrying out our collider analyses within the simplified models sketched in Fig. 1, we apply the results to two explicit, motivated models that contain strongly coupled hidden forces as well as electroweak-charged mediators. This serves as an illustration of the potential impact of the searches we propose.
The first model example is -SUSY Barbieri et al. (2007), where the Higgs quartic coupling can be naturally raised by adding to the superpotential a term , with a singlet superfield and large . If the scalar singlet is light, it mediates a strong force that can lead to the formation of Higgsino bound states at the LHC, which then decay into with large branching fraction. The singlet decays to SM particles via mixing with the Higgs. In this case we thus identify the mediators with the Higgsinos, , and the hidden force carrier with the light singlet scalar, . This scenario was first discussed in Ref. Tsai et al. (2016). Here we present a more detailed assessment of the future LHC constraints on the model.
As a second example we consider non-SUSY ultraviolet (UV) extensions of the Twin Higgs model Chacko et al. (2006), where new vector-like fermions appear that are charged under both the SM and twin gauge symmetries Chacko et al. (2006); Cheng et al. (2016). Some of these exotic fermions, labeled , carry SM electroweak and twin color charges, and can have masses in the few hundred GeV range without conflicting with experiment or significantly increasing the fine-tuning in the Higgs mass, as discussed in Ref. Cheng et al. (2017). Once they are pair produced in the charged DY process, the exotic fermions form a vector bound state under the twin color force, which can then annihilate into a plus twin gluons. In the Fraternal version of the Twin Higgs model (FTH) Craig et al. (2015), the hadronization of the twin gluons can lead to the production of the lightest glueball, which has and decays into SM particles by mixing with the Higgs. The glueball decay length strongly depends on its mass, and can be either prompt or macroscopic. In this scenario we thus identify the mediators with the exotic fermions, , and the hidden force carrier with the lightest twin glueball, .
Notice that, in the broad setup we are considering, the (scalar or fermion) neutral mediator can also be the dark matter candidate. The production and decay of the bound state then gives an example of dark matter annihilation at colliders that does not leave a missing energy signature Shepherd et al. (2009); An et al. (2016); Tsai et al. (2016).
The remainder of this paper is organized as follows. In Sec. II we analyze the processes in the context of simplified models. We perform projections to estimate the LHC sensitivity in the four final states considered, given by or , each with prompt or displaced decay. We also discuss the sensitivity to the irreducible decays, focusing on the cleanest channel, and compare it with the reach in the processes. In Sec. III we apply our results to the -SUSY model. We show that for large , the signals arising from the charged Higgsino bound state have better reach than the standard monojet and disappearing track searches. In addition, in the typical case of prompt decays the search has better sensitivity compared to . In Sec. IV our results are applied to the UV-extended FTH model. Here we find that, even though the branching fraction of the exotic fermion bound state into +twin glueball is suppressed to the few percent level, this signal provides an interesting complementarity to if the lightest twin glueball decays at a macroscopic distance, giving rise to a displaced vertex. Our concluding remarks are given in Sec. V.
Ii Simplified model analysis
In this section we study the LHC sensitivity to the processes
where decays as
with . Here (in the following we often drop the electric charge and write just ) is a bound state with that carries unit charge under the SM , whereas is a real scalar (real vector) hidden force carrier. As discussed in the Introduction, we make the assumption that couples to SM particles dominantly through mass mixing with the SM Higgs (kinetic mixing with the SM photon). Then, in the mass region the most promising decays of the force carriers are those in Eq. (2). We study the four types of signals in Eqs. (1) and (2) at the TeV LHC and set model-independent bounds on , where , as functions of the masses of the bound state and of the force carrier. We also compare the reach in these channels to that in
which constitutes the irreducible signal of spin- electroweak-charged bound states.
Since in Secs. III and IV we interpret our results in explicit models, it is useful to summarize the formulas that give the production cross section and branching ratios as functions of the underlying parameters. Given two Dirac fermions with approximately degenerate mass and coupled to the SM boson as , the cross section for production of their vector bound state in quark-antiquark annihilation is
where , is the parton luminosity, is the collider center of mass energy, and the bound state mass was approximated with . An analogous expression holds for the production of the charge conjugate . The factor in Eq. (4) accounts for the number of hidden degrees of freedom: for example, if are identified with the Higgsinos, while in the case of exotic fermions that transform in the fundamental of a confining hidden . For definiteness, henceforth we assume , which applies for both the Higgsino and exotic fermion bound states. is the wavefunction at the origin, whose value depends on the details of the hidden force. In the Coulomb approximation we have
where is the hidden force coupling strength, and is a model-dependent constant. For an hidden force, , where is the quadratic Casimir of the representation where transforms (see e.g. Refs. Kats and Schwartz (2010); Kats and Strassler (2012)). For a - or scalar-mediated force, we can instead set provided the charges are absorbed in the definition of the force coupling strength . In these cases, if the force carrier is not massless the formation of bound states can happen only if its wavelength is larger than the Bohr radius, namely , or equivalently .
In this paper we consider scenarios with small mass splitting between and , . The bound state annihilation rate is depending on whether the dominant channel is via a coupling , as in -SUSY, or , as in the UV-extended FTH 111Notice that in the former case we have assumed that does not run below the scale , as it is the case in -SUSY.. In order for the bound state annihilation to take place before the charged constituent decays as , must be larger than
This sets an upper bound on the mass splitting (for )
In the region that we consider in this work, the existing disappearing track constraint ATLAS Collaboration (2017a); CMS Collaboration (2015a) applies if ns, corresponding to mass splittings smaller than those typically found in our parameter space.
ii.1 with prompt
In this case the LHC sensitivity can be estimated by adapting the strategy used in the search for resonances that decay into ATLAS Collaboration (2015a), to allow for an invariant mass of the pair different from .
The signal is simulated using a simple FeynRules Alloul et al. (2014) model of a charged spin-1 resonance coupled to SM quarks as and to as . For both the signal and backgrounds, we generate parton level events with MadGraph5 Alwall et al. (2014), shower them using PYTHIA6 Sjostrand et al. (2006) and pass the result to Delphes3 de Favereau et al. (2014) for the detector simulation. We adopt most of the Delphes3 configurations proposed in the Snowmass 2013 energy frontier studies Avetisyan et al. (2013); Anderson et al. (2013). However, since the -tagging performance has recently been improved by employing multivariate techniques ATLAS Collaboration (2014b), in our analysis we assume the -tagging efficiency to be , with rate for a light flavor jet to be mis-tagged as -jet. Jets are reconstructed using the anti- algorithm with distance parameter .
In the event selection we require the (sub-)leading -jet to have GeV and . To suppress the background, we also impose that , where is the number of jets. In addition, the selection requires one lepton with and , as well as , where is the modulus of the missing transverse energy (MET) vector. The MET vector is identified with the neutrino transverse momentum, and the reconstructed transverse mass and transverse momentum of the must satisfy and , respectively 222The transverse mass is defined as , where is the azimuthal separation between the MET vector and the lepton momentum.. To identify the force carrier we require . In order to reconstruct the full -momentum of the candidate, we extract the longitudinal component of the neutrino momentum by solving 333Following Ref. ATLAS Collaboration (2015a), if the quadratic equation has two real solutions for , then we take the one with smaller absolute value. If the solutions are complex, we take the real part.. This allows us to calculate the invariant mass of the system for each event. In addition, to improve the resolution on we apply a standard kinematic fitting procedure that corrects the -jet momenta by imposing (for more details on the procedure, see for example the CMS search for resonances decaying into CMS Collaboration (2014)).
The largest SM background is , followed by jets. We also include production, but its contribution is subdominant. In the calculation of the signal significance, the distribution of the total background is fitted with an exponential function, shown by the orange curve in Fig. 2. For the signal, the width of the peak is dominated by detector effects and insensitive to the small intrinsic width of the resonance. We then require .
The resulting bounds on are shown as contours in the plane in the left panel of Fig. 3. We stress that although we have imposed different cuts on the and invariant masses for each hypothetical combination of considered, the bounds were calculated using local, and not global, significance. It can be clearly seen that for a fixed , the cross section limit deteriorates when is decreased. This happens because in our analysis we require two separate -jets with , which significantly reduces the selection efficiency for large and light . For this reason we chose to show our results only for , below which the efficiency becomes very small 444Notice also that if , important, albeit model-dependent, constraints can arise from the decay.. The sensitivity can be extended to larger and smaller through the application of jet substructure techniques Butterworth et al. (2008), which go beyond the scope of this paper but can be efficiently implemented in the actual experimental analysis, similarly to the very recent ATLAS searches for resonances decaying to ATLAS Collaboration (2017b) and Aab (a).
ii.2 with prompt
The projected bounds on the prompt signal are obtained by rescaling the results of the TeV ATLAS search for resonances in the tri-lepton channel ATLAS Collaboration (2013, 2014a). Notice that even though one neutrino is present in the final state, the kinematics can be fully reconstructed ATLAS Collaboration (2014a) by solving the equation for , with the same procedure described in Sec. II.1.
We summarize here the rescaling procedure. The SM background, which is dominated by + production, is very suppressed if the invariant mass of the pair is away from the peak. To estimate it we perform a simulation of SM at parton level, in the SM at TeV, and use it to compute for each hypothesis the ratio of the cross section in an invariant mass window to the cross section on the peak, namely . Then, the total background given as a function of in Table 2 of the ATLAS note ATLAS Collaboration (2013) is rescaled to a collider energy of using the parton luminosity, as well as to the appropriate integrated luminosity, and multiplied times to obtain our background prediction as a function of . The total signal acceptance times efficiency for a with mass , , was given in Table 7 of Ref. ATLAS Collaboration (2013). To take into account the variation of the invariant mass shape, for different from we multiply by the ratio of the maximum values of the corresponding signal templates, shown in Fig. 5 of the same reference. The resulting acceptance times efficiency, which was calculated for LHC energy of TeV, is employed in our TeV projection. In addition, we include the effect of the lepton isolation cuts as a function of the boost factor of , by requiring an angular separation . After including this correction, our estimate of the signal acceptance times efficiency for GeV varies from at to at . Our rescaling method relies on the assumption of a bump-hunt-type search in a narrow window around the putative , which is a reasonable approach given the good experimental resolution achievable in this final state. At the same time, however, some caveats apply to the extrapolation of the TeV analysis to TeV. In particular, we have implicitly assumed that the variation of trigger thresholds and selection cuts on the leptons and missing energy will not significantly affect our results.
The resulting bounds on are shown in the right panel of Fig. 3. We again emphasize that they were computed using local significance. The sensitivity is weaker for light and heavy , where the leptons from the dark photon decay are collimated, and for , where the background is largest.
ii.3 with displaced
If the hidden force carrier has a macroscopic decay length, we can search for the signal in final states containing a prompt hard lepton stemming from the and a displaced or decay.
For , our analysis follows the discussion in Ref. Cheng et al. (2016), which in turn was based on the existing ATLAS searches for hadronic displaced vertices (DV) ATLAS Collaboration (2015b, c). We generate the signal process at the parton level, and require one prompt lepton with and , thus ensuring that the signal events can be easily triggered on. An additional efficiency is assumed for the reconstruction of the prompt lepton. In addition, we require two ’s with and . For each event, we calculate the -momentum of in the lab frame, which together with the proper lifetime determines the probability distribution for the location of the displaced decay. The DV can be detected either in the inner detector (ID), if its radial distance satisfies , or in the hadronic calorimeter (HCAL) and muon spectrometer (MS) if . For the efficiency of the DV reconstruction we assume a constant in the ID volume and in the HCALMS, which are simple approximations of the results given in Refs. ATLAS Collaboration (2015b, c) 555In the analysis of the twin bottomonium signals of Ref. Cheng et al. (2016), the efficiency was very conservatively assumed to be also in the HCALMS. Based on the results of Ref. ATLAS Collaboration (2015c), we believe to be closer to the actual experimental performance..
Notice that the DVs can be identified even when the angular separation between the -jets is small. In the ID the impact parameter of charged tracks can be exploited, as done in Ref. ATLAS Collaboration (2015c). We can roughly estimate that for a distance cm between the location of the displaced decay and the primary vertex, the requirement ATLAS Collaboration (2015c) yields sensitivity to ’s with boost factor as large as . If the decay is inside the HCAL, the ratio of the energy deposits in the electromagnetic calorimeter and HCAL can be used to identify the signal. A detailed 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 boost-independent values for the efficiency.
The analysis of displaced is performed along similar lines. The same cuts and efficiency are applied on the prompt lepton originating from the . We focus on decays, requiring the two muons to satisfy and . Approximating the results of the searches in Refs. CMS Collaboration (2015b); ATLAS Collaboration (2016a), we assume that dimuon DVs can be reconstructed for with efficiency.
Although in general the searches for DVs at the LHC suffer from several backgrounds, such as the misidentification of prompt objects and the accidental crossing of uncorrelated tracks, these are strongly suppressed by the additional requirement of a prompt hard lepton. Therefore, in both our DV analyses we assume the background to be negligible, and accordingly we exclude at CL all parameter points that would yield a number of signal events larger than .
Even though each of the signals depends on three parameters, namely the masses and and the proper decay length , the problem can be simplified by observing that experimentally, the most important variable is the decay length of the long-lived particle in the lab frame. In the approximation that the is produced at rest, this is simply given by . Figure 4, where the bounds on the signal cross section are shown as functions of , confirms that this quantity determines the experimental efficiency to a good accuracy. A subleading dependence on can be observed, originating from the cuts on the prompt lepton, whereas varying leaves the efficiency essentially unaffected.
The has an irreducible decay width into SM fermions, via an off-shell boson. The most powerful probe of these decays is the channel, where the current upper limit on is of fb for , based on fb Aab (b). We obtain projections to larger integrated luminosity by rescaling the current cross section constraint . Even though this procedure is strictly correct only when systematic uncertainties are negligible, we have checked that applying it to the constraint from a previous ATLAS analysis based on fb ATLAS Collaboration (2016b) gives good agreement with the fb bound of Ref. Aab (b). This justifies our simplified treatment.
It is interesting to compare the sensitivity in the and final states. Focusing on prompt and decays, in Fig. 5 we show in the plane contours of the ratio
(where for we sum over all SM fermions) that yields with fb the same constraint on from the and final states. For the scalar we find that the ratio in Eq. (8) is in a large region of parameter space, thus indicating that the search for provides an important test of the bound state properties. On the other hand, the decay can compete with even if the relative branching fraction is at the percent level, thanks to the striking trilepton signature.
Here we discuss the concrete example of -SUSY Barbieri et al. (2007), where a coupling of the form is added to the minimal supersymmetric SM superpotential, with a singlet scalar superfield. A large helps to increase the Higgs mass to in a natural way Hall et al. (2012). If in addition the singlet scalar is light, it mediates a strong attractive force between the Higgsinos, that can lead to the formation of bound states in the process of DY Higgsino pair production Tsai et al. (2016). The charged bound state decays into with large branching fraction, and in turn the decays to through its mixing with the Higgs.
Before applying the results of our analysis of Sec. II, we briefly summarize some essential aspects of the model. We consider a general next-to-minimal supersymmetric SM superpotential and assume the gauginos to be heavy and out of the LHC reach 666The first term in the superpotential is normalized such that the coupling of the physical scalar singlet to the Higgsinos is simply .. We focus on the limit (where we have expanded the scalar component of the superfield as ), so the singlino is also decoupled from the light Higgsinos. As a consequence, the up- and down-type Higgsinos are nearly degenerate, and their DY production is unsuppressed. We can then treat as a Dirac fermion that receives a mass from the -term, and similarly for the charged Higgsinos. Electroweak radiative corrections split the masses of the neutral and charged Higgsinos by MeV, which clearly satisfies the condition in Eq. (7). The singlet scalar decays into SM particles through its mixing with the SM-like Higgs, which is constrained to be by the existing Higgs couplings measurements Farina et al. (2014). Since also generates a large coupling between the Higgs and two singlet scalars, we avoid bounds from the decay by requiring . Therefore, in our study we focus on the singlet scalar mass range
where the second inequality ensures that the bound state can form, as discussed below Eq. (5). The decay can easily have a small branching ratio, being suppressed by the - mixing and by the bottom Yukawa coupling.
The production and decay of is described by the upper diagram in Fig. 1, with the identifications . The decay is generically prompt, but it can also happen at a macroscopic distance if cancellations between the soft SUSY masses suppress the mixing between and to less than . We can then reinterpret our simplified model results in the -SUSY context, by comparing the model-independent limits calculated in Secs. II.1 and II.3 for the final state (with prompt or displaced decay, respectively) to the production cross section of calculated via Eqs. (4) and (5). We appropriately set and in those equations. Since the can annihilate into both and , in our signal predictions we include the corresponding branching ratio . Furthermore, we include the , which is the same as for a SM Higgs with mass given by , because couples to SM fields only via mixing with the Higgs.
In the left panel of Fig. 6 we show the constraints on obtained from the prompt channel with fb. Notice that the -contours also give at least a rough idea of the measurement of the hidden force coupling that can be obtained if an excess is observed. In the orange-shaded region the LHC will be able to entirely rule out the existence of Higgsino bound states, by pushing the exclusion on below the smallest value that allows bound state formation, namely . For example, for the reach extends up to Higgsino masses GeV. It is interesting to compare this to the reach of the monojet and disappearing track searches. The monojet channel has a CL reach of GeV at the LHC with ab, and a similar sensitivity is expected in the disappearing track search if the mass splitting generated by electroweak loops, MeV, is assumed Arkani-Hamed et al. (2016). Thus we find that if is large, the reach of the Higgsino bound state signal is far superior. In addition, since the values of probed by the analysis correspond to -, after including and comparing with Eq. (8) and Fig. 5 we find that the final state has better sensitivity than in this region of parameters.
For the large values of that can be probed by our analysis, perturbativity is lost at a relatively low scale , as illustrated in Fig. 7. For example, for (corresponding to ) we find , depending on the Higgsino mass and on the value of the parameter that controls the size of the term in the superpotential.
The large value of also affects the Higgs mass prediction. Since the - mixing is constrained to be small by LHC measurements Farina et al. (2014), we have approximately
where GeV. Therefore in the region where the bound state production is relevant, is required. The -SUSY region with large and large can produce dangerous corrections to the and parameters of electroweak precision tests. Nevertheless, these can be reduced by suppressing the mixing between the Higgsinos and the singlino, as we have assumed from the beginning, and by raising the masses of the squarks and the charged Higgs Franceschini and Gori (2011).
In the right panel of Fig. 6 we show the constraints obtained from the (prompt +displaced ) channel. Since the boost factor of is , the second inequality in Eq. (9) implies that . As discussed in Sec. II.3, the identification of the hadronic DV becomes very challenging if the decay takes place in the ID with . This is verified in the region of parameters with and (hatched in black), where new ideas are required to successfully reconstruct the narrow displaced jet in the ID.
Iv UV-extended Fraternal Twin Higgs
The signals we study also appear in several non-SUSY UV completions of the TH model, which contain exotic fermions charged under both the SM and twin gauge groups Chacko et al. (2006); Cheng et al. (2016). Some of these fermions, labeled (where the superscript indicates the SM electric charge), carry SM electroweak and twin color charges. As shown in Ref. Cheng et al. (2017), can have -breaking masses without violating experimental constraints, and without significantly increasing the fine-tuning of the Higgs mass. The exotic fermions can therefore be produced at the LHC through the DY process and form an electrically charged vector bound state due to the twin color force. If the lifetime of the constituents is sufficiently long, the bound state annihilates into resonant final states. The main channel is via an off-shell , but a sizable branching ratio also exists for the final state, where the two twin gluons can hadronize into the lightest twin glueball ; see Fig. 8. In turn, the twin glueball decays to via the Higgs portal, either promptly or at a macroscopic distance depending on the value of the twin confinement scale .
Before we interpret the bounds of Sec. II in this context, it is useful to recall some important features of the model. The has a small mass mixing with the twin top. Assuming , where is the global symmetry breaking scale, the level repulsion makes slightly lighter than , with mass splitting given by
Taking and a typical strength of the twin QCD coupling [where is related to the inverse Bohr radius of the bound state by an factor 777Precisely, , where is the Bohr radius and Kats and Strassler (2012)., and we have assumed GeV], the mass splitting in Eq. (11) satisfies Eq. (7) when the bound state mass is TeV. On the other hand, the neutral exotic fermion decays into , where the twin can be on- or off-shell, with amplitude suppressed by a mixing angle (for ). If , the corresponding lifetime is sufficiently long to allow for annihilation of the charged bound state. However, the twin bottom cannot be too heavy, to avoid introducing a new source of significant fine-tuning in the Higgs mass. Requiring this additional tuning to be better than restricts the parameter space for the bound state signals to , which we assume in the following.
Lattice computations Chen et al. (2006) give for the mass of the lightest glueball. The twin confinement scale depends on the number of flavors in the twin sector, as well as on the value of the twin QCD coupling in the UV, , where for definiteness we take . As to the field content, here we focus on the Fraternal Twin Higgs model, which includes twin copies of the third-generation fermions only. Concerning the value of , assuming exact symmetry at leads to GeV, whereas allowing for a difference between and yields , and therefore a lightest glueball mass in the range . The mixes with the SM-like Higgs through a twin top loop. In the region of larger mass, , it decays promptly, hence the dilepton channel Cheng et al. (2017) has far better sensitivity than due to the much larger branching fraction. Instead, a lighter glueball with mass undergoes displaced decays within the volume of the LHC detectors, yielding a signature that is striking enough to potentially overcome the branching fraction suppression. In this mass region the decay is dominantly into , with proper lifetime that can be approximated as Craig et al. (2015)
We then proceed to apply the bound from the (prompt +displaced ) analysis that was presented in Sec. II.3, with the identification .
The cross section for production is given by Eqs. (4) and (5) after we set , and replace . To estimate the relative branching ratio for the and decays, we exploit the similarity with the SM quarkonia. For example, for the we have (see e.g. Ref. Brambilla et al. ())
By replacing the photon with the and accounting for an extra factor , which arises because the couples only to left-handed fermions and with coupling strength , we arrive at
where the factor of accounts for the multiplicity of the SM fermion-antifermion final states available in the decay through the off-shell . The resulting branching ratio for varies from to in the mass range we study. We make the assumption that the twin gluons dominantly hadronize into a single lightest glueball , which is reasonable if the glueball production can be described by a thermal process with temperature Juknevich (2010). Notice, however, that our analysis strategy is not affected if additional glueballs are produced by the twin hadronization. Once the glueball mass is fixed, the running of is determined, which in turn sets the size of the wavefunction at the origin through Eq. (5) and the branching ratios via Eq. (14). Therefore in our analysis we take and as the two input parameters. Furthermore, for GeV we have for all the values of we consider, hence it is safe to apply the Coulomb approximation.
The results are shown in Fig. 9. Despite the suppressed branching ratio , this channel is competitive with , because the striking combination of a prompt lepton and a DV renders the final state essentially background-free. This decay is peculiar of the UV-extended FTH model. Similarly to the case of -SUSY, discussed at the end of Sec. III, if decays in the ID with boost factor the standard reconstruction of the hadronic DV fails. The corresponding region of parameter space is hatched in black in Fig. 9.
As a final comment, we observe that the signature of a prompt lepton+DV can also appear in other neutral naturalness scenarios. For example, in the Folded (F-) SUSY model Burdman et al. (2007) an F-stop/F-sbottom pair can be produced through DY or vector boson fusion Burdman et al. (2008). If the F-stop decays into a (likely off-shell) and an F-sbottom, the resulting F-sbottom pair forms a squirky bound state. The latter promptly annihilates into mirror glueballs, which in turn can yield displaced signatures by decaying through the Higgs portal Chacko et al. (2016).
In this paper we have presented a new strategy to search for hidden force carriers at the LHC. These particles have suppressed direct production cross sections, due to their small couplings to the SM particles, but can be produced through mediators that carry at least some of the SM charges. We focused on the cases where the hidden force carrier is either a real scalar or a dark photon , and the mediators are a pair of electroweak-charged vector-like fermions . Once a pair is produced in the DY process, the strong hidden force can bind it into an electrically charged spin- bound state , which promptly annihilates into . The corresponding signatures consist of a prompt lepton originating from the boson, and a prompt or displaced or decay. We analyzed these final states in detail, estimating the LHC reach within a simplified model approach. To illustrate the impact of our results, we also applied them to two motivated example models that contain hidden forces and can yield these signatures, namely -SUSY and the UV-extended Fraternal Twin Higgs. The resonant signals allow for the measurement of the mass of both the bound state and the force carrier, thus yielding critical insights on the structure of the hidden sector.
For displaced decays, we proposed new searches for and displaced vertices, where the simultaneous presence of a hard prompt lepton stemming from the ensures efficient triggering and essentially removes all SM backgrounds. As a consequence, the reach of these searches can compete with that of the irreducible signal even when the bound state decays to with subdominant branching fraction. Signals of this type are especially promising for testing models of neutral naturalness.
In the case of prompt decays, we showed that simple extensions of existing diboson searches would allow ATLAS and CMS to obtain a compelling reach. Furthermore, while the simplified analyses performed in this paper lose sensitivity when the decay products are collimated, the experimental collaborations have full capability to exploit this type of events, either by employing jet substructure variables in the decay or by resolving narrowly separated leptons that originate from . We believe that our results provide further motivation for extending the array of diboson searches to include heavy resonance decays to BSM particles.
We thank J. Collins, A. De Roeck, Y. Jiang, B. Shakya, C. Verhaaren, L.-T. Wang, and Y. Zhao for useful discussions. LL and RZ were supported in part by the US Department of Energy grant DE-SC-000999. The work of ES has been partially supported by the DFG Cluster of Excellence 153 “Origin and Structure of the Universe,” by the Collaborative Research Center SFB1258 and the COST Action CA15108. YT was supported in part by the National Science Foundation under grant PHY-1315155, and by the Maryland Center for Fundamental Physics. This work was performed in part at the Aspen Center for Physics, which is supported by the National Science Foundation grant PHY-1607611. ES (YT) is grateful to the MCFP (TUM Physics Department) for hospitality in the final stages of the project.
- Chacko et al. (2006) Z. Chacko, H.-S. Goh, and R. Harnik, Phys. Rev. Lett. 96, 231802 (2006), arXiv:hep-ph/0506256 .
- Burdman et al. (2007) G. Burdman, Z. Chacko, H.-S. Goh, and R. Harnik, JHEP 02, 009 (2007), arXiv:hep-ph/0609152 .
- Batra et al. (2004) P. Batra, A. Delgado, D. E. Kaplan, and T. M. P. Tait, JHEP 02, 043 (2004), arXiv:hep-ph/0309149 .
- Maloney et al. (2006) A. Maloney, A. Pierce, and J. G. Wacker, JHEP 06, 034 (2006), arXiv:hep-ph/0409127 .
- Barbieri et al. (2007) R. Barbieri, L. J. Hall, Y. Nomura, and V. S. Rychkov, Phys. Rev. D75, 035007 (2007), arXiv:hep-ph/0607332 .
- Tulin et al. (2013) S. Tulin, H.-B. Yu, and K. M. Zurek, Phys. Rev. D87, 115007 (2013), arXiv:1302.3898 [hep-ph] .
- Hochberg et al. (2014) Y. Hochberg, E. Kuflik, T. Volansky, and J. G. Wacker, Phys. Rev. Lett. 113, 171301 (2014), arXiv:1402.5143 [hep-ph] .
- Kaplinghat et al. (2016) M. Kaplinghat, S. Tulin, and H.-B. Yu, Phys. Rev. Lett. 116, 041302 (2016), arXiv:1508.03339 [astro-ph.CO] .
- ATLAS Collaboration (2015a) ATLAS Collaboration, Eur. Phys. J. C75, 263 (2015a), arXiv:1503.08089 [hep-ex] .
- Aab (a) ATLAS Collaboration, arXiv:1709.06783 [hep-ex] .
- ATLAS Collaboration (2013) ATLAS Collaboration, ATLAS-CONF-2013-015 (2013).
- ATLAS Collaboration (2014a) ATLAS Collaboration, Phys. Lett. B737, 223 (2014a), arXiv:1406.4456 [hep-ex] .
- Tsai et al. (2016) Y. Tsai, L.-T. Wang, and Y. Zhao, Phys. Rev. D93, 035024 (2016), arXiv:1511.07433 [hep-ph] .
- Cheng et al. (2016) H.-C. Cheng, S. Jung, E. Salvioni, and Y. Tsai, JHEP 03, 074 (2016), arXiv:1512.02647 [hep-ph] .
- Cheng et al. (2017) H.-C. Cheng, E. Salvioni, and Y. Tsai, Phys. Rev. D95, 115035 (2017), arXiv:1612.03176 [hep-ph] .
- Craig et al. (2015) N. Craig, A. Katz, M. Strassler, and R. Sundrum, JHEP 07, 105 (2015), arXiv:1501.05310 [hep-ph] .
- Shepherd et al. (2009) W. Shepherd, T. M. P. Tait, and G. Zaharijas, Phys. Rev. D79, 055022 (2009), arXiv:0901.2125 [hep-ph] .
- An et al. (2016) H. An, B. Echenard, M. Pospelov, and Y. Zhang, Phys. Rev. Lett. 116, 151801 (2016), arXiv:1510.05020 [hep-ph] .
- Kats and Schwartz (2010) Y. Kats and M. D. Schwartz, JHEP 04, 016 (2010), arXiv:0912.0526 [hep-ph] .
- Kats and Strassler (2012) Y. Kats and M. J. Strassler, JHEP 11, 097 (2012), [Erratum: JHEP 07, 009 (2016)], arXiv:1204.1119 [hep-ph] .
- (21) Notice that in the former case we have assumed that does not run below the scale , as it is the case in -SUSY.
- ATLAS Collaboration (2017a) ATLAS Collaboration, ATLAS-CONF-2017-017 (2017a).
- CMS Collaboration (2015a) CMS Collaboration, JHEP 01, 096 (2015a), arXiv:1411.6006 [hep-ex] .
- Alloul et al. (2014) A. Alloul, N. D. Christensen, C. Degrande, C. Duhr, and B. Fuks, Comput. Phys. Commun. 185, 2250 (2014), arXiv:1310.1921 [hep-ph] .
- Alwall et al. (2014) J. Alwall et al., JHEP 07, 079 (2014), arXiv:1405.0301 [hep-ph] .
- Sjostrand et al. (2006) T. Sjostrand, S. Mrenna, and P. Z. Skands, JHEP 05, 026 (2006), arXiv:hep-ph/0603175 .
- de Favereau et al. (2014) J. de Favereau et al., JHEP 02, 057 (2014), arXiv:1307.6346 [hep-ex] .
- Avetisyan et al. (2013) A. Avetisyan et al., in Proceedings, 2013 Community Summer Study: Snowmass on the Mississippi: Minneapolis, MN, USA (2013) , arXiv:1308.1636 [hep-ex] .
- Anderson et al. (2013) J. Anderson et al., in Proceedings, 2013 Community Summer Study: Snowmass on the Mississippi: Minneapolis, MN, USA (2013) , arXiv:1309.1057 [hep-ex] .
- ATLAS Collaboration (2014b) ATLAS Collaboration, ATLAS-CONF-2014-004 (2014b).
- (31) The transverse mass is defined as , where is the azimuthal separation between the MET vector and the lepton momentum.
- (32) Following Ref. ATLAS Collaboration (2015a), if the quadratic equation has two real solutions for , then we take the one with smaller absolute value. If the solutions are complex, we take the real part.
- CMS Collaboration (2014) CMS Collaboration, CMS-PAS-HIG-14-013 (2014).
- (34) Notice also that if , important, albeit model-dependent, constraints can arise from the decay.
- Butterworth et al. (2008) J. M. Butterworth, A. R. Davison, M. Rubin, and G. P. Salam, Phys. Rev. Lett. 100, 242001 (2008), arXiv:0802.2470 [hep-ph] .
- ATLAS Collaboration (2017b) ATLAS Collaboration, Phys. Lett. B774, 494 (2017b), arXiv:1707.06958 [hep-ex] .
- ATLAS Collaboration (2015b) ATLAS Collaboration, Phys. Lett. B743, 15 (2015b), arXiv:1501.04020 [hep-ex] .
- ATLAS Collaboration (2015c) ATLAS Collaboration, Phys. Rev. D92, 012010 (2015c), arXiv:1504.03634 [hep-ex] .
- (39) In the analysis of the twin bottomonium signals of Ref. Cheng et al. (2016), the efficiency was very conservatively assumed to be also in the HCALMS. Based on the results of Ref. ATLAS Collaboration (2015c), we believe to be closer to the actual experimental performance.
- CMS Collaboration (2015b) CMS Collaboration, Phys. Rev. D91, 052012 (2015b), arXiv:1411.6977 [hep-ex] .
- ATLAS Collaboration (2016a) ATLAS Collaboration, ATLAS-CONF-2016-042 (2016a).
- Aab (b) ATLAS Collaboration, arXiv:1706.04786 [hep-ex] .
- ATLAS Collaboration (2016b) ATLAS Collaboration, ATLAS-CONF-2016-061 (2016b).
- Hall et al. (2012) L. J. Hall, D. Pinner, and J. T. Ruderman, JHEP 04, 131 (2012), arXiv:1112.2703 [hep-ph] .
- (45) The first term in the superpotential is normalized such that the coupling of the physical scalar singlet to the Higgsinos is simply .
- Farina et al. (2014) M. Farina, M. Perelstein, and B. Shakya, JHEP 04, 108 (2014), arXiv:1310.0459 [hep-ph] .
- Arkani-Hamed et al. (2016) N. Arkani-Hamed, T. Han, M. Mangano, and L.-T. Wang, Phys. Rept. 652, 1 (2016), arXiv:1511.06495 [hep-ph] .
- Franceschini and Gori (2011) R. Franceschini and S. Gori, JHEP 05, 084 (2011), arXiv:1005.1070 [hep-ph] .
- (49) Precisely, , where is the Bohr radius and Kats and Strassler (2012).
- Chen et al. (2006) Y. Chen et al., Phys. Rev. D73, 014516 (2006), arXiv:hep-lat/0510074 .
- (51) N. Brambilla et al. (Quarkonium Working Group), arXiv:hep-ph/0412158 .
- Juknevich (2010) J. E. Juknevich, Ph.D. thesis, Rutgers U. (2010).
- Burdman et al. (2008) G. Burdman, Z. Chacko, H.-S. Goh, R. Harnik, and C. A. Krenke, Phys. Rev. D78, 075028 (2008), arXiv:0805.4667 [hep-ph] .
- Chacko et al. (2016) Z. Chacko, D. Curtin, and C. B. Verhaaren, Phys. Rev. D94, 011504 (2016), arXiv:1512.05782 [hep-ph] .