Rare $ Z $ Boson Decays to a Hidden Sector

SLAC-PUB-17159

Rare Z Boson Decays to a Hidden Sector

Nikita Blinov,1 Eder Izaguirre,2 and Brian Shuve3, 1 1SLAC National Accelerator Laboratory, 2575 Sand Hill Rd., Menlo Park, CA 94025, USA 2Brookhaven National Laboratory, Upton, NY 11973, USA 3Harvey Mudd College, 301 Platt Blvd., Claremont, CA 91711, USA (Dated: November 15, 2017) We demonstrate that rare decays of the Standard Model Z boson can be used to discover and characterize the nature of new hidden-sector particles. We propose new searches for these particles in soft, high-multiplicity leptonic ﬁnal states at the Large Hadron Collider. The proposed searches are sensitive to low-mass particles produced in Z decays, and we argue that these striking signatures can shed light on the hidden-sector couplings and mechanism for mass generation.

I. INTRODUCTION In this study, we focus on rare Z boson decays, which are most important in vector-portal models of hidden sectors. The Large Hadron Collider (LHC) is now probing the To achieve optimal sensitivity to hidden sectors at the Standard Model (SM) and its possible extensions at en- LHC, it is essential that the experiments are able to ergies exceeding the electroweak scale. The lack of any efficiently trigger on and reconstruct new low-mass ob- definitive discoveries beyond the Higgs boson, however, jects. Dedicated search and reconstruction strategies are suggests that new physics within the reach of the LHC needed to uncover evidence for low-mass particles, espe- may appear in unexpected places. It is now widely ap- cially if the particles are boosted and fail conventional preciated that some classes of signatures are challeng- isolation criteria. Such strategies have been success- ing to probe at a hadron collider. These include new fully implemented in several contexts, such as for lepton electroweak multiplets with masses near the electroweak jets [19–21]; compressed stops [22, 23]; long-lived, low- scale [1–4]; particles produced via the strong interac- mass particles decaying in the ATLAS hadronic calorime- tions that decay to approximately degenerate states [5]; ter and muon spectrometer [24]; and searches by the “stealth” spectra [6]; or all-hadronic final states [7]. LHCb collaboration for long-lived particles in the for- In this paper, we focus on searches for low-mass par- ward direction [25]. However, comprehensive studies are ticles, which can likewise be difficult to find at the LHC. needed to ensure that signals are not lost at trigger or The signatures of new light particles are manifold and are event reconstruction level, and we undertake such a study sensitive to both the manner of production (i.e., whether with a focus on high-multiplicity (6+ particle) decays of the low-mass states are produced directly or in the de- the Z boson into hidden sector particles. cays of heavier particles), as well as whether there exists We take as a concrete example a minimal hidden sec- a single new particle [8, 9] or an entire hidden sector or tor with a spontaneously broken Abelian gauge interac- “hidden valley” [10–12]. When the new low-mass parti- tion [26, 27]. The new gauge boson (the dark photon, cles decay back into SM final states, the result is typically A0), couples to the SM via kinetic mixing with the hy- a high-multiplicity final state [10, 12–14]. Since the en- percharge boson, resulting in Z decays into the hidden ergy in the event is divided among many particles, the sector. We show that Z decays into A0 in association with final-state particles are typically soft and could be lost the dark Higgs boson, hD, lead to striking signatures such in the enormous multijet backgrounds or contaminated as multiple resonances, high multiplicities of soft leptons, by pile-up. However, hidden sectors can also give rise and long-lived particles. The decay Z A0hD is a dark → to spectacular signatures such as high multiplicities of version of the Higgs-strahlung process and additionally leptons, displaced vertices, and other non-standard phe- allows for a direct test of the mass generation mecha- arXiv:1710.07635v2 [hep-ph] 11 Nov 2017 nomena [10–12, 15–17]. These can be used to suppress nism in the hidden sector. If the dark Higgs decays via the sizable SM backgrounds, provided the signals are suf- hD A0A0 as illustrated in Fig. 1, then A0 decays into → ficiently energetic to be efficiently reconstructed. SM particles can yield a final state with as many as six Due to its high luminosity, the LHC is an exquisite tool leptons. for studying hidden-sector particles that are too heavy We show that searches for dark Higgs-strahlung in rare to be produced in other intensity-frontier experiments. Z decays can be competitive with and exceed the sensi- Through Phase II, the LHC will produce unprecedented tivity of existing and proposed search strategies for dark numbers of electroweak and Higgs bosons, exceeding the gauge and Higgs bosons, while also yielding new infor- statistics from LEP by many orders of magnitude. By mation. Because the decay Z A0h is sensitive to the → D looking for new states produced in the rare decays of hidden-sector gauge coupling, αD, a discovery of a signal SM particles, we may probe ever-smaller couplings be- in this process provides complementary information to tween SM particles and hidden sectors. The production direct searches for A0. Previous proposals entailed look- of hidden-sector particles in the decays of the SM Higgs ing for A0 at the LHC via its contribution to Drell-Yan boson has been well studied (see, for example, Ref. [18]). production above 10 GeV [28, 29], in rare 3-body Z de- 2

V is the scalar potential A′ V (H,H ) = µ2 H 2 µ2 H 2 + κ H 2 H 2 D − H | | − HD | D| | | | D| + λ H 4 + λ H 4. (2) | | D| D| The SM and dark Higgs acquire vacuum expectation val- Z A′ ues (VEVs) H = (0, v/√2) and H = v /√2, break- h i h Di D ing the electroweak and U(1)D gauge symmetries, respec- hD tively. As a result, gauge eigenstates undergo mixing [26]. For a recent review of the model, see Ref. [32]. The kinetic and mass terms for the gauge bosons can be simultaneously diagonalized using the transformation A′ (to leading order in εY and θZ )

FIG. 1: Feynman diagram illustrating dark Higgs (h ) Zµ Zµ (θZ + ε tan θW)Aµ0 , (3) D → − and dark photon (A ) production in rare Z boson 0 Aµ0 Aµ0 + θZ Zµ, (4) decays. The dark photons in hD decay can be on- or → Aµ Aµ + ε A0 , (5) off-shell. → µ where ε εY cos θ , θ is the weak mixing angle, and ≡ W W 2 ε tan θW mZ 3 cays into leptons and a dark gauge boson [30], as well θZ = 2 2 + (ε ) (6) − m m 0 O as in decays of the SM Higgs boson [18, 31–33]. Finally, Z − A Ref. [34] evaluated the prospects for discovering A0 and is the gauge-boson mixing angle. The Z and A0 bosons hD via Higgs-strahlung at future lepton colliders, where have masses equal to the unshifted values at (ε), while they focused on decays to invisible hidden-sector states. the photon A remains exactly massless. O While our study is phenomenologically driven, we The scalar states can also undergo mixing after gauge- demonstrate sensitivity to models of hidden sectors that symmetry breaking. The mass eigenstates are are well motivated by various shortcomings of the SM, h cos θ sin θ h(0) especially the need to account for dark matter but also h h , h = θ − θ (0) (7) potentially outstanding problems in neutrino physics and D sin h cos h hD other areas. Indeed, low-mass dark matter scenarios are (0) (0) typically only viable with additional low-mass mediators where h , hD are the CP -even gauge eigenstate com- in the hidden sector [8, 35, 36]. Hidden sectors can also ponents of H and HD, respectively. In the limit of small generically arise in ultraviolet completions of the SM such mixed quartic coupling κ, the h hD mixing angle is − as string theory [37–39]. given by We outline our benchmark hidden-sector model in Sec- κ vv sin θ D . (8) tion II. We then enumerate the signatures of rare Z decay h 2 2 ≈ 2 λDvD λv into the hidden sector, focusing on signals with high lep- − ton multiplicities and hidden-sector resonances. We give Except where otherwise noted, we assume that the dom- projected LHC sensitivities to prompt hidden-sector sig- inant hidden-sector portal to the SM is via the coupling nals in Section III and we discuss displaced signals in between gauge bosons, ε. Section IV. Our outlook is given in Sec. V. Because the U(1)D gauge symmetry is spontaneously broken, the masses of hidden-sector particles are related to the symmetry-breaking parameter. In particular, the dark Higgs VEV gives a mass to the dark gauge boson, II. AN ABELIAN HIDDEN SECTOR leading to a dark Higgs-strahlung hD A0 A0 vertex by analogy with the symmetry breaking− pattern− in the SM. The benchmark model we consider is one of the sim- After the vector and scalar eigenstates mix, we obtain plest examples of a hidden sector: a minimal U(1)D gauge the following mass-basis Lagrangian: interaction spontaneously broken by a non-decoupled µ µ µ L gh A0Z h A0 Z +gh A0A0 h A0 A0 +g 0 ¯ A0 fγ¯ f, Higgs field. The model is specified by the following La- D D µ D D µ A ff µ ⊃ (9) grangian: along with additional terms that are not relevant for the phenomenology we study. The approximate couplings 1 µν εY µν L Fµν0 F 0 + Fµν0 B may be expressed simply in the mA0 mZ limit, ⊃ −4 2 2 + ∂µH ie A0 H V (H,H ), (1) g 0 = 2e θ cos θ m 0 , (10) | D − D µ D| − D hDA Z D Z h A 2 0 0 µν µν ghDA A = eDvD, (11) where F 0 (B ) is the U(1)D (hypercharge) field g 0 ¯ = εeQf . (12) strength, eD = √4παD is the U(1)D gauge coupling, and A ff 3

The first term in Eq. (9) gives rise to Z boson decay into Electroweak Precision Observables (EWPO): hD and A0 with rate Precision tests of electroweak symmetry breaking set stringent bounds for mA0 < mZ . Bounds from EWPO 2 2 2 2αD θZ cos θh mA0 0 arise predominantly from the mass mixing of A0 with ΓZ A hD = [1+ → 3mZ Z, although other EWPO observables get modified by 2 2 2 2 # m m 0 m 0 virtue of the fact that electrically charged SM particles ( Z + A hD ) mA mhD 2 −2 β , , (13) acquire an effective millicharge under the A0 (see for in- 8m m 0 m m Z A Z Z stance, Ref. [43] and a newer analysis including prospects for future improvements in EWPO at high-energy lepton where β(x, y) = [(1 (x y)2)(1 (x + y)2)]1/2. This − − − colliders by Ref. [32]). rate vanishes as mA0 0, but becomes appreciable as → mA0 increases above 10 GeV, which is precisely where ∼ LHC Constraints: The A0 mediates new contributions constraints from low-energy colliders become ineffective. to Drell-Yan production of leptons at the LHC. A rein- The decays of the A0 and the hD depend on the spec- terpretation of a CMS study of the Drell-Yan process at trum of the hidden sector. When A0 and hD are the √s = 7 TeV [44] sets constraints on the A0 mass via a lightest states, they decay back into SM particles. The A0 dilepton resonance search [28] (see Ref. [28] and an up- decays dominantly into electrically charged SM fermion dated analysis by Ref. [32] on future prospects for Drell- pairs via the coupling in Eq. (12). When kinematically Yan sensitivity to A0). A recent LHCb search for inclusive allowed, the dark Higgs can decay into one or two on- Drell-Yan production of dark photons has set powerful ( ) shell A0 via hD A0A0 ∗ , and the A0 in turn decays into constraints in the mA0 10 70 GeV mass range with → 0 1 ∼ − SM fermions. Finally, if mhD < mA , then the hD can 1.5 fb− of data at √s = 13 TeV [45]. In the case where decay via two off-shell A0, although radiative corrections hD has an appreciable mixing with hSM, there are also typically induce a comparable decay via scalar mixing. constraints on the hidden sector via hSM A0A0 [32, 46]; Having defined the model, we can consider new search in the limit of small scalar mixing that is→ our focus, the strategies for discovering the hidden sector through the latter searches do not apply any meaningful constraint. process, Z A0hD. The specific signatures depend on → 0 the mass hierarchy of the A0 and hD. For mA < mhD , the ( ) decay hD A0A0 ∗ is kinematically allowed and occurs III. PROMPT MULTILEPTON SIGNALS FROM → relatively rapidly, giving rise to prompt signals. We pro- RARE Z DECAYS pose searches for such prompt signatures in Section III. If instead m 0 > m , then the h lifetime is typically A hD D We have argued that the dark sector benchmark model long; we explore this scenario in Section IV. Before we in Eq. (1) gives rise to striking signatures in the decay of study the Z A0hD signal, however, we first summarize the SM Z boson via Z A0h . Studying this process existing constraints→ on the model. → D would allow for not only the discovery of A0 and hD, but can also provide information about the hidden sector couplings and mass generation mechanisms. We now A. Existing Constraints examine in detail the phenomenology of this rare Z decay.

0 0 We focus on masses mA , mhD & 1 GeV which are Fully On-Shell Decays: If mhD > 2mA , then the fol- most relevant for the LHC. lowing decay chain occurs:

+ Low-Energy e e− Colliders: The clean environment pp Z A0hD A0A0A0. (14) + → → → and high luminosities of low-energy e e− colliders allow for powerful searches for A0 and hD for masses The A0 can decay to various SM final particles. In prin- below 10 GeV. The kinetic-mixing coupling of A0 to ciple, this gives final-state signatures with three A0 res- fermions is studied in the radiative return reaction onances, as well as the intermediate hD resonance. In + + e e− A0γ, A0 ` `− for electron and muon the case of fully leptonic decays, this is an extremely final states.→ In particular,→ the analysis from Ref. [40] clean and spectacular signature. In practice, other Z puts mass-dependent upper bounds on ε in the range decays may give better model sensitivity because of the 4 3 3 10− 10− for masses mA0 . 10 GeV. BaBar and small probability that each A0 decays leptonically, as well Belle× also− constrain hidden sectors through searches for the efficiency penalties associated with reconstructing all + the dark Higgs-strahlung process, e e− A0hD [41, 42]. six soft leptons. Combinatorics may also present a chal- These searches constrain the combination→ of couplings lenge to reconstructing the signal. However, even the 2 9 α ε 10− , with the precise limits depending on mA0 more inclusive case with Z h A0, h 4` (with the D . → D D → and mhD . Belle II is expected to significantly extend this other A0 decaying to arbitrary final states) features two sensitivity to hidden sectors below 10 GeV, although leptonically-decaying A0 resonances that together recon- in all cases B-factories lose sensitivity for mA0 > 10 GeV. struct the hD. We therefore investigate signatures with at least four leptons from the hD decay. 4

Due to the limited available phase space in six-body particles that decay to three or more leptons [50]. We Z decays, it is beneficial to use multilepton triggers with re-interpret the results of the low-E/ T, 4-lepton signal re- low pT thresholds. The current triggers that best fit these gions in terms of our signal model. In order to derive the requirements are the three-lepton triggers. For ATLAS, constraints from the CMS search, we must apply lepton these are [47] identification efficiencies, which are somewhat small for leptons with low pT. Because Ref. [50] only provides the three loose e’s: p 15, 8, 8 GeV at L1 (17, 10, • T ≥ low-pT lepton tagging efficiencies for the most pessimistic 10 at HLT), working point, we must use the pessimistic values and obtain a conservative result. The true signal efficiency three µ’s: p > 6 GeV (3 6 at HLT). • T × is almost certainly better than what we find, because For CMS, we examine the thresholds from a multilepton Ref. [50] states that a looser set of lepton identification analysis such as ZZ 4` [48], which used criteria are used for searches with four leptons, but does → not specifically state what these efficiencies are. three e’s: pT 15, 8, 5 GeV. We find that the Signal Region (SR) H of Ref. [50], • ≥ which requires 4 leptons and fewer than two opposite- While this analysis was conducted at √s = 8 TeV, sign, same-flavor (OSSF) lepton pairs, is most sensitive the CMS dilepton trigger thresholds did not increase to the hidden sector topology we study. In this case, the appreciably between 8 TeV and 13 TeV [49, 50], and we Z A0hD 6` decay can pass the CMS signal selections use this as a proxy for what can currently be expected if two→ of the→ leptons are lost and only one OSSF pair is in terms of trigger thresholds. We note that trilepton 1 reconstructed. Using the CLs method [56], we estimate thresholds may go up in the high-luminosity phase of a constraint on the dark photon kinetic mixing, ε, at the the LHC; however, in this case 4-lepton triggers could 95% confidence level (c.l.). alternatively be used to keep pT thresholds low. The limits from the CMS multilepton search are better than the constraints from EWPO, but somewhat worse Partially off-shell decays: m 0 < m < m 0 When A hD 2 A , than the recent bounds from LHCb [45], and so we do the decay h A0A0 is kinematically forbidden, but the D → not show them explicitly. However, as argued above our semi-off-shell decay h A0A0∗ A0ff¯ (where f is D → → re-interpretation is almost certainly more conservative a SM fermion) can occur. While ΓhD is suppressed by than the actual analysis, and the existing CMS search 2 a factor of ε for semi-off-shell decays compared to the may in fact place limits on the dark Abelian Higgs model case of fully on-shell decays, we find that the decay still that are competitive with LHCb. Crucially, the CMS occurs promptly for the parameters of relevance to the search is not optimized for the hidden-sector signal, LHC. Thus, the reaction proceeds as follows: and so the fact that it is already somewhat competitive with existing dedicated searches for A0 affirms the pp Z A0h A0A0ff.¯ (15) → → D → important role of rare Z decays in probing hidden sectors. The principal difference between the semi-off-shell and Proposal for New Multilepton Search: Our signal fully on-shell decays is that one of the pairs of SM features distinctive kinematics and multiple resonances particles no longer reconstructs a resonance. As we in h A A 4` decays. These features can be ex- shall soon see, however, the backgrounds are sufficiently D 0 0 ploited→ to significantly→ reduce both the background and low that we do not necessarily need to impose a m 0 A the uncertainty on its estimate compared to the CMS resonance reconstruction requirement on the leptons SUSY signal regions while maximizing signal efficiency. within h 4` decays, and so the fully and partially D We define a signal region for the decay mode Z on-shell h →decays can be studied simultaneously. De- D A h , h A A 4`, while remaining agnostic about→ pending on how actual experimental conditions compare 0 D D 0 0 the third A→ decay→ mode. The selections for our signal to Monte Carlo simulations, these two cases may need 0 region are: to be studied separately. Trigger selection: Require four muons with p > • T Simulations: In performing our analysis, we gen- 7 GeV or any four leptons with pT > 15, 8, 7, 5 erate parton-level events at leading order with GeV. All leptons must be in the central part of the MadGraph5 aMC@NLO [51]. To capture the effects of detector ( η < 2.5). initial-state radiation on signal acceptance, we generate | | events with up to one extra parton and match them to Isolation: Require that each lepton be isolated from • hadronic activity or photons. We do this by finding the showered events using the shower-kT scheme [52]. We use the parton shower program Pythia 8.2 [53–55].

Reinterpretation of Existing Searches: Existing 1 There is also a signal region with two OSSF pairs (SR G) [50], searches by ATLAS and CMS are already sensitive to sig- which features a larger signal acceptance but signiﬁcantly larger nals with high lepton multiplicities. For example, CMS backgrounds (and systematic uncertainties). As a result, the has a search for new electroweak supersymmetric (SUSY) signal sensitivity is better for SR H. 5

the scalar sum pT of all hadrons or photons within rate. We first express the expected sensitivity in terms ∆R = 0.3 of the lepton and requiring that the sum of the Z A0hD branching fraction, which we show for 1 → be either less than 5 GeV or less than 20% of the 40 fb− in Fig. 2. This sensitivity depends only on the A0 lepton pT. and hD masses and not separately on the hidden-sector couplings. In Fig. 3, we show the estimated sensitivity A0 Signal Selection: Require at least 2 OSSF lepton to the kinetic mixing parameter, ε, for various values • pairs (each pair forms an A candidate). 0 of αD. Looking forward, in Fig. 4 we demonstrate for the particular case α = 0.1 the sensitivity that can be Suppression of Z backgrounds: Veto events with D achieved if the same trigger and analysis selections can be • any OSSF dilepton pair satisfying m m < 2` Z maintained throughout Run 3 and the High-Luminosity 5 GeV. Also, since the signal arises from| Z− 4|` + LHC integrated luminosity benchmarks. For comparison X decays, veto events with any m +5 GeV→> m . 4` Z with our results, we display the projected sensitivity from Suppression of combinatorics: When re- dilepton resonance searches. • constructing A0 candidates among possible We emphasize that beyond allowing for a discovery of OSSF dilepton pairs, A0 candidates are chosen A0 and hD, such a search can yield additional informa- such that the dilepton pairs minimize mi mj , tion about the dark sector. In particular, the Z branch- | − | where i and j refer to the A0 candidates and mi ing ratio into A0hD is sensitive to the dark coupling, αD, and mj refer to their respective masses. which is readily seen in Fig. 3. Thus, a combined discovery of A0 in Drell-Yan production direct production and We find the efficiency of these selections is 20 50% via Z A0hD would allow for the determination of the ≈0 − → for signal events (depending on the masses mA and mhD ) hidden-sector coupling, αD. The Z hDA0 branching and about 1% for background. fraction in Eq. (13) depends linearly on→ α and quadrat- ≈ D Additionally, we exploit the fact that the four leptons ically on ε, and so the reach in ε for other values of αD in hD 4` decays reconstruct mhD . A typical 4-lepton can be obtained by rescaling our limits on ε by 1/√αD. invariant→ mass resolution is approximately [57]

∆m4` = 0.13 GeV + 0.065mhD . (16) IV. DISPLACED DARK HIGGS DECAYS

Therefore, for each signal hypothesis mass mh , we D The results of Sec. III focused exclusively on the case define a bin centered at mass mhD and width given by Eq. (16), and consider only events inside this bin. This where hD can decay into at least one on-shell A0. In this section we study the opposite mass hierarchy: m < eliminates much of the remaining background. We com- hD mA0 . In this regime, the decays Z A0h are still al- ment that all of our selection criteria are approximate → D lowed for m > m 0 + m , but the h can only decay and should be re-optimized by the experimental collab- Z A hD D orations once more accurate, data-driven background radiatively or via entirely off-shell A0. Consequently, the estimates are obtained. hD decay is typically displaced from the primary interaction point. These signatures benefit from smaller back- Backgrounds: The dominant SM background by far grounds compared to the prompt final states described in is the γ/Z-initiated inclusive pp 4` + X final state.2 Section III. We now discuss the salient phenomenological Other backgrounds, such as tt¯ →and multi-boson pro- features. m < m 0 h duction, are subdominant after the cuts we apply and In the parameter space hD A , the D can still could be further suppressed by additional requirements decay into a two-body final state. For one possibility, hD decays through a loop of virtual A0 into SM fermions. on b-jets, the maximum allowed lepton pT, and the This partial width scales approximately as [13] maximum E/ T. 2 4 4 2 α Q αDε m Sensitivity Projections: We now make projections for h ff¯ f f m Γ( D ) 2 hD (17) the sensitivity of the above proposed search to the dark → ∼ 32π mA0 4 Abelian Higgs model. In addition to the selections de- 1 αD ε 15 GeV 1 m− 2 scribed above, we apply a flat event-level 50% penalty ∼ 0.1 10− mA0 for reconstructing the four soft leptons. We evaluate the maximum number of allowed signal events at 95% c.l. when summing over SM final-state fermions and taking 0 4 assuming Poisson statistics and a background-only hy- mA mhD . At this order of ε , there is also a tree-level ∼ pothesis, and extract an estimated limit on the signal four-body decay of the hD via two off-shell A0. However, for the moderate dark Higgs masses that we are interested in, the loop decay typically dominates. So far, we have assumed that the mixing between the 2 This was also found to be the dominant background in both hD and the SM Higgs is zero, and consequently the only CMS low–E/ T 4-lepton searches (with either < 2 or = 2 OSSF allowed hD decay modes are via its coupling with A0. pairs) [50]. However, a mixing between the hD and the SM Higgs is 6

3 10− 1 = 40 fb− L 4 10− ) D h 0 A 5

→ 10− Z

BR( 10 6 − 20 mhD = 15 30 40 7 50 10− 101

mA0 [GeV]

1 FIG. 2: Projected 95% c.l. sensitivity of an LHC search with = 40 fb− at √s = 13 TeV for Z h A0 4` + X L → D → where 4` are required to reconstruct mhD . The sensitivity is expressed in terms of the accessible branching fraction of Z h A0 decays. → D

1 10−

αD = 0.01 EWPO

2 αD = 0.1 10− LHCb

αD = 1 ε 1 BaBar DY14 40 fb− 10 3 − m = hD 20 30 50 1 = 40 fb− 4 L 10− 101 102

mA0 [GeV]

1 FIG. 3: Projected 95% c.l. sensitivity of an LHC search with = 40 fb− at √s = 13 TeV for Z h A0 4` + X L → D → where 4` are required to reconstruct mhD . Each curve is labeled by the value of mhD in GeV. The dotted line gives the sensitivity of the Drell-Yan search from Ref. [32]. We also show existing constraints from electroweak precision observables [32], BaBar [40] and LHCb [45]. The three sets of lines from bottom (dark) to top (light) correspond to αD = 1, 0.1, and 0.01. induced by a loop of dark vectors. This mixing is given where Λ is an ultraviolet (UV) energy scale. The decay by h ff¯ due to the the mixing in Eq. (19) is parametri- D → cally similar to the A0-loop-induced and four-body decay 2 2 V (H,HD) κ(µ) H HD , (18) modes. The precise value of this loop-induced mixing de- ⊃ | | | | pends explicitly on the UV value of κ. The mixing κ can where the renormalization-scale-dependent mixing term in principle be zero in the infrared, but this represents a scales as tuning of model parameters. Thus, the decay width of h for m 0 > m (and whether it proceeds radiatively α α ε2 µ D A hD κ(µ) D log + κ(Λ), (19) or via Higgs mixing) depends sensitively on the value of ∼ (4π)2 Λ 7

1 10−

EWPO

2 10− LHCb 1 300 fb− 1 DY14 300 fb− ε BaBar 3 1 10− 1 − 3 ab− LHCb 15 fb 1 DY14 3 ab− 30 50 mhD = 20 αD = 0.1 4 10− 101 102

mA0 [GeV]

1 FIG. 4: Sensitivity projections for the Z hDA0 4` + X search for integrated luminosity of 300 fb− (upper dark 1 → → lines) and 3000 fb− (lower faint lines) at √s = 13 TeV and αD = 0.1. The dotted green line shows the projected 1 LHCb sensitivity with 15 fb− from Ref. [29], while the dashed lines show the projections for the proposed Drell-Yan search from Ref. [32]. Notation and existing bounds are the same as in Fig. 3.

κ in the UV and its renormalization-group evolution. hadrons) originating from a displaced vertex as follows. Because of this model dependence, we take a bottom- The signal events are selected using standard dilepton up approach and focus on the plausible signatures of hD triggers [50] decay for m < m 0 , all of which feature decays of h hD A D two OSSF muons with p > 17, 8 GeV, or at a displaced vertex for the parameter space that is ac- • T cessible to the LHC. The dominant displaced signatures two OSSF electrons with pT > 23, 12 GeV. that can arise are: • We further require the track transverse impact parame- Displaced decay of hD into SM fermions according ters, d , to lie within 1 mm < d < 200 mm (motivated • 0 0 to Eq. (17). The branching fractions into heavy- collectively| | by the ATLAS [58]| and| CMS [59] d recon- | 0| flavor objects (b, c, and τ) are comparable: the struction capability). We further require the point of hD color factors and/or heavier masses of the b/c are decay to occur within 200 mm of the primary vertex in compensated by the smaller electric charges. This both the transverse and longitudinal directions. Finally, case will arise when the branching ratio given by we apply an efficiency for selection of a displaced vertex. Eq. (17) dominates. The hD will then give (at This efficiency depends on the details of the experimen- least) two displaced tracks, which can be leptons tal search, and in particular the need to reject certain or hadrons. The combined final state from the rare backgrounds. In existing searches, the efficiencies for dis- Z decay is two prompt leptons in association with placed vertices in the inner detector vary widely from the two or more displaced tracks. 10 30% [58] through to 50% [59]. The signal also features∼ − a resonant A mass∼ that can be reconstructed Displaced decay of h through Higgs mixing in 0 • D in the prompt leptons: therefore, backgrounds are lower Eq. (18). This decay occurs predominantly into than for inclusive displaced vertex searches, and data- bottom quarks. We require displaced tracks from driven background estimation is more straightforward in the b-quark hadronization but apply no b-tagging the variable m`+`− from the prompt leptons. There- requirements. The displaced vertex comes in asso- fore, we prioritize signal efficiency and choose to apply ciation with prompt leptons from the A0 decay in + a flat 50% vertex tagging efficiency. The sensitivity of Z A0h ` `−h . → D → D this search is estimated by requiring an observation of 10 signal events, assuming no background. The sub-dominant decay of hD into four SM • fermions can give a rather striking final state; we In Fig. 5 we show the projected sensitivity in two ways. do not consider it further, although it could give In the top panel we compute the sensitivity to ε in the rise to an interesting signature for future study. (mA0 , ε) plane, where for each choice of masses we have selected the hD lifetime that gives the optimal reach in ε.

We estimate the sensitivity for a prompt, two-lepton In the bottom panel we select a speciﬁc value of mhD and 0 ﬁnal state in association with displaced tracks (leptons or show the expected sensitivity in the (mA , cτhD ) plane. 8

1 Optimal cτh , = 40 fb− 1 D 10− L EWPO

2 10− LHCb ε

mhD = 15 20 3 30 10− 40

αD = 0.1 4 10− 101 102

mA0 [GeV]

1 αD = 0.1, mh = 15 GeV, = 40 fb− 7 D L 10 2.4 6 10 1.6 105 0.8 104

0.0 ε

[mm] 3 10 10 D h 0.8 log 2 − cτ 10 1.6 101 − 2.4 100 −

1 3.2 10− − 20 30 40 50 60 70

mA0 [GeV]

0 FIG. 5: Projected sensitivity to the scenario where mhD < mA , which gives rise to displaced decays of the dark 1 Higgs. Projections are shown for √s = 13 TeV and = 40 fb− . In the top panel, we compute the sensitivity for 10 0 L 0 signal events after cuts to ε in the (mA , ε) plane for diﬀerent values of mhD (labeled in GeV); for each mA point we have selected the hD lifetime that gives the optimal reach in ε. In the bottom panel we compute the expected 0 sensitivity in the (mA , cτhD ) plane for mhD = 15 GeV. The projected reach of the displaced search exceeds the existing constraints from electroweak precision observables (LHCb prompt search, showing the envelope of the exclusion contour) within the solid (dotted) black contours.

The projected sensitivity of this search exceeds the cur- sectors. Using a dark Abelian Higgs model as a bench- rent limits from EWPO (LHCb) inside the solid black mark, we have demonstrated how studying rare Z decays (dotted) contours. With current levels of data, one can into hidden sector particles can allow for the discovery of 3 already probe ε at or better than the level of 10− . exotic particles through the same interactions responsible for generating hidden-sector particle masses.

Z decays into hidden-sector particles typically give rise V. DISCUSSION AND CONCLUSIONS to large multiplicities of soft particles. When the hidden- sector particles can decay leptonically, such as in the dark In this article, we have shown that rare decays of the Abelian Higgs scenario, this results in striking events Standard Model Z boson are powerful probes of hidden with up to six soft leptons. We have demonstrated a 9 range of prompt and displaced signatures that can oc- of the dark photon and dark Higgs. A comprehensive cur in this model, providing a path for experimentally characterization of the properties of the hidden sector is discovering or constraining these new particles. therefore possible at the LHC. Finally, we have focused on the speciﬁc case where the Crucial to the success of the strategies we outline in Z boson can decay to a dark gauge boson and a dark this article is the fact that trigger and reconstruction scalar where both are on-shell. There exist spectra where thresholds for leptons must be kept low. Because the Z this is not the case, such as when m < m 0 + m , boson mass-energy is distributed among six or more par- Z A hD and there may yet be other interesting signatures of dark ticles, a moderate increase in trigger thresholds would Higgs-strahlung originating from oﬀ-shell Z production. greatly curtail the sensitivity of ATLAS or CMS to high- Indeed, the signatures we discuss in this article should multiplicity hidden-sector signatures. While the high- be applicable to more general mass hierarchies, and we luminosity running of the LHC will introduce new chal- encourage ATLAS, CMS, and LHCb to avoid overly opti- lenges such as increased pile-up, we urge the experimen- mizing their search strategies to the particular examples tal collaborations to consider maintaining low-threshold, studied here where possible. high-multiplicity triggers where possible (including potentially triggers requiring four or more leptons) in order to retain sensitivity to well-motivated hidden-sector mod- ACKNOWLEDGMENTS els. Furthermore, our study has focused on only one particular high-multiplicity hidden-sector signature: models We would like to thank Justin Chiu, Michel Lefebvre, giving rise to even higher multiplicities are possible, moti- Michael Peskin and Maxim Pospelov for helpful conver- vating keeping high-multiplicity trigger thresholds as low sations. EI is supported by the United States Depart- as possible. ment of Energy under Grant Contract desc0012704. NB The searches we propose are complementary to existing is supported by the United States Department of Energy proposals for observation of the direct production of the under Contract No. DE-AC02-76SF00515. We express dark photon, A0. A discovery in both channels could our gratitude to the Aspen Center for Physics, where allow for the determination of the A0 mixing with the part of this work was completed and which is supported SM, the hidden-sector gauge coupling, and the masses by National Science Foundation grant PHY-1607761.

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