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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 j j − HD j Dj j j j Dj + λ H 4 + λ H 4: (2) j j Dj Dj The SM and dark Higgs acquire vacuum expectation val- Z A′ ues (VEVs) H = (0; v=p2) and H = v =p2, 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 "Y and θZ ) FIG. 1: Feynman diagram illustrating dark Higgs (h ) Zµ Zµ (θZ + " 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 + "A0 ; (5) off-shell. ! µ where " "Y cos θ , θ is the weak mixing angle, and ≡ W W 2 " tan θW mZ 3 cays into leptons and a dark gauge boson [30], as well θZ = 2 2 + (" ) (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 ("), 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, ". 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.
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