JHEP09(2017)076 e Springer May 1, 2017 July 26, 2017 : : September 1, 2017 September 18, 2017 : : , Revised , Received Accepted Published Matthew McCullough, , d searches (dMETs). Our approach is e Published for SISSA by https://doi.org/10.1007/JHEP09(2017)076 T / E Kristian Hahn, albert.de.roeck@cern.ch , b,c [email protected] , and Tien-Tien Yu d [email protected] , . Albert De Roeck, 3 a Kevin Sung 1704.06515 f The Authors. Beyond Standard Model, Dark matter, Hadron-Hadron scattering (experi- c

We propose a systematic programme to search for long-lived neutral particle , [email protected] E-mail: [email protected] [email protected] [email protected] Evanston, Illinois 60208, U.S.A. Theoretical Physics Department, CERN, CH-1211 Gen`eve23, Switzerland PRISMA Cluster of Excellence55099 & Mainz, Institute Germany of Physics, Johannes Gutenberg University, Prince Consort Road, London, SW7Physics 2AZ, Department, U.K. CERN, CH-1211 Gen`eve23, Switzerland Antwerp University, B2610 Wilrijk, Belgium Department of Physics and Astronomy, Northwestern University, High Energy Physics Group, Blackett Laboratory, Imperial College, b c e d a f Open Access Article funded by SCOAP Large Hadron Collider. Thesystematic proposed broadening models of the and displaced searches dark provide matterKeywords: a search first programme. step towardsments), a Lifetime, Supersymmetry ArXiv ePrint: by, and mapped onto, complete modelsof such as neutral gauge-mediated naturalness. SUSY breakingsimplified and We models models also to outline incorporate how displacedlived signatures this charged and approach particles. to may characterise Displaced searches bebackground vertices for are free, used long- a and to striking thus extend signature provide other which an is excellent often virtually target for the high-luminosity run of the signatures through a minimalto extend set the of well-established dark displaced The matter dark simplified matter models to simplifiedA include models displaced displaced secondary are vertices. vertex, usedlifetime, characterised to is by added the describe for mass the the of displaced primary signature. the production long-lived We show particle vertex. how and these its models can be motivated Abstract: Oliver Buchmueller, Pedro Schwaller, Simplified models for displaced dark matter signatures JHEP09(2017)076 7 9 7 22 18 simplified models 9 12 T 14 / E 3 signatures using simplified models 11 T 12 / E searches – 1 – T 6 / E 3 5 19 5 1 21 3.3.1 The role of angular correlations 2.2.1 Decay2.2.2 EFT Decay simplified models ]). These particles can be produced in collider experiments and can propagate 3 – 1 While common reconstruction algorithms assume prompt decays of particles at the 4.1 Gauge mediated4.2 supersymmetry breaking Higgs portal4.3 hidden sectors/Twin Higgs Mapping into dark matter parameter space 3.1 Characterisation of3.2 long-lived plus Minimal set3.3 of long lived Hands-on plus simulation of long-lived plus 2.1 Production from2.2 simplified DM models Displaced decay models e.g. [ large distances in the detector before they decay. production vertex, long-lived particles caning lead on to the a particle variety nature of and unique signatures. its lifetime, Depend- these signatures can include displaced vertices, The nature of dark matteris (DM) a remains new, a beyond mystery.of the One a Standard explanation single Model is weakly interacting that (SM)to massive dark particle. particle the matter (WIMP) The SM. with most weakstructure, However, popular scale there mass paradigm replete and is is with coupling that alsomany additional the extensions particles, possibility of that the some the SM of predict dark which the sector existence may possesses of be a new richer long-lived. particles with long Indeed, lifetimes (see 1 Introduction 5 Avenues for extensions 6 Conclusions A Event simulation of displaced simplified models 4 Mapping onto UV-complete models 3 Experimental signatures and benchmark scenarios Contents 1 Introduction 2 Simplified model framework JHEP09(2017)076 , ]. T ]), / 41 E 26 35 – – 4 , 1 27 , 6 searches is to re- T / E analyses. T / E ]. In our approach, we extend these 62 – ] that are interpreted in the framework 56 37 , , 56 36 [ – – 2 – ], the recasting of these searches in the context T 43 / 40 E analyses, which are mainly used to search for SUSY production T / E signature is assumed to originate from prompt decays. The traditional ] that are motivated by long-lived chargino production in context of T / E 39 , 38 ), for instance. The most prominent examples of such analyses are the searches T / E The use of simplified models has become one of the main vehicles to characterise collider Although the current LHC experiments presently set strong limits on models of Super- searches are therefore typically far from being optimal for long-lived scenarios. Fur- ], which are based on previous work [ T / vertex of the interactiondisplaced is vertex described arising using from standard theis simplified decay parameterised of DM the in model, long-lived terms themodel particle secondary of has could its a involve light own handful model, “decay(EFT) of mediator” which vertex. basic particles, This or parameters modular simply and approach an interactions. facilitates Effective event Field The simulation, Theory which decay is an important searches for new particle production atand the DM LHC. production Today, in the majoritythis collision of data work searches we are for will benchmarked SUSY focus using42 this on bottom-up the approach. recently establishedmodels In simplified to models include for DM collider searches signatures [ of long-lived neutral particles. While the primary of long-lived signatures isreconstruction nontrivial in and the requires individualstrategy experiments. a for detailed Motivated the by understanding these systematic ofthat challenges, study the is we of based object outline various on a long-lived simplifiedthat models, neutral predict without particle such the collider topologies need signatures or to revert to to recasting the canonical more complex models in proton-proton collisions. Whilea the large SUSY variety search of programmetopologies, different at the final the states, LHCE spans including across multi-jet, multi-lepton/photon and thermore, as for example outlined in [ the Anomaly-Mediated Supersymmetry Breakinglenges (AMSB) in model. improving the One coveragethe of of relevant the long-lived parameter signatures main space is chal- are and related corresponding currently to collider explored. the means signaturesinterpret At by of the which present, long-lived canonical particles the main option for long-lived combine long-lived signatures withenergy topologies ( that includefor significant displaced missing photons transverse withof significant Gauge Mediated Supersymmetrying Breaking tracks (GMSB), [ and the searches for disappear- Collider (LHC). Itdark is sectors. therefore timely to develop a broadsymmetry programme (SUSY) that to can search predictdisplaced for new signatures rich long-lived for particles other (see,all. models for The example, are ATLAS [ either and CMS only experiments partially have covered executed or only not a covered few at dedicated analyses that dows, and the production of collimatedEach of jets these of signatures leptons, requires amongst the othertechniques development possibilities to of [ dedicated ensure reconstruction and theirthese selection efficient exotic inclusion signatures in are high-levelgrounds, produced and physics from make analysis. relatively for unique an Furthermore, processes, excellent target distinct for from the back- high-luminosity run of the Large Hadron disappearing tracks, massive particle tracks, jet production outside of collision event win- JHEP09(2017)076 - s 4 . We ], there 6 70 – ] in which all 67 , 66 – , the mass of the 62 , ]. χ we first outline the 63 m , 53 , and the coupling of 42 , , χ g 2.2 48 47 41 , – 46 46 gives an overview of the different 1 and section 2.1 – 3 – and end with our conclusions in section 5 ) is assumed to be either a Dirac fermion, Majorana χ ] for further details). 42 , . A minimal width is also often assumed. For the latter, as φ 41 g , the coupling of the mediator to the DM particles, φ and demonstrate the utility of this modular approach with some sample event we discuss the relevant experimental signatures and provide recommendations m 3 A The current simplified models used to interpret DM searches at the LHC typically The paper is structured as follows: in section -channel and the interaction structure of the mediator is chosen to be either a Vector, t fermion, or a realor or complex Scalar.Axial-Vector, The Scalar or mediator Pseudoscalar exchange interaction. canbuilding Table either blocks take that place formsearches in simplified at DM colliders models (see that [ are currently used to interpret DM contain four independent parameters:mediator, the mass ofthe the mediator DM to particle, quarks, a simplifying assumption, theequal strength. mediator is The assumed DM to particle ( couple to all quark flavours with additional light particles, suchphenomenology as is a required. light mediator,plified As then model a an paradigm result, alternative that description effortseffort includes of have amongst additional the shifted both mediators. towards theoristsprogramme an and This to alternative experimentalists characterise has sim- DM at led searches the to using LHC an simplified to extensive models establish [ a systematic tations of the resultsthe in possible effective the operators framework allowedered. of by However, symmetry an as and EFT pointed dimensional approach outare analyses [ by are some several consid- drawbacks independent to groupsconsiders [ this the approach. SM and In dark matter particular, particles by as design light the degrees EFT of approach freedom, only thus if there are 2 Simplified model framework 2.1 Production from simplifiedThe DM programme models of general DM searches at the LHC and Tevatron began with interpre- other long-lived signatures inalso section provide a hands-onappendix description of thedistributions model generated implementation in this in way. event generators in extension of simplified DMIn section models to includeon a how variety to of applywe these long-lived motivate simplified particle models this signatures. in approachmodels experimental by and data showing theories. analysis, how while We these then in models discuss section possible can extensions be to mapped our onto approach complete to also include simplified models for long-lived particlecan signatures, be we motivated show by and examples mapped ofbreaking onto how and UV-complete these models, models models such of as neutralthe gauge-mediated SUSY naturalness. foundation of Finally, although these simplifiedthis extensions DM strategy for models can neutral be form long-lived extended particles, to we other will physics scenarios also (e.g. argue long-lived that charged particles). requirement for the application of models in experimental analyses. Furthermore, using the JHEP09(2017)076 and 2 χ X production encoded 2 1 χ 2 χ ) of the excited state χ 2 m 2 X 1 χ Scalar Vector χ Interaction X Axial-Vector → Pseudoscalar 2 1 ) χ b ) and mass ( χ ( τ is a schematic for the – 4 – Decay of 1 Dirac Majorana Scalar-real X DM candidate Scalar-complex Simplified DM models 1 Displaced signature extension 2 2 χ 1 φ φ χ m χ g g m , m τ Variables 2 χ produced at each vertex. In both cases the DM will typically carry away , which are required to add the displaced signature to the standard simplified X X X produced at each vertex. (b) A pair of displaced vertices is observed with a ) 1 1 a χ χ X ( → 2 . Collider signatures of displaced DM. (a) A pair of displaced vertices is observed with χ . Overview of the different building blocks that form simplified DM models. The lower part , then the central red dot in figure 2 On this latter point, although the simplified model approach has proven to be very use- The approach advocated here is to employ these same simplified models to capture χ known limitations to this framework that willstudied also here. apply In to the particular, displaced comparingthere vertices simplified framework are models any with signatures more present UV-complete instates, models, the such if complete as model cascade as decaysmiss a in signatures result SUSY of that scenarios, the turn then richer out the spectrum to simplified of models be strategy the may most constraining. As a result we would advocate way as for the mono-X signaturesmodels required for of long-lived DM searches. neutralwhen In particles applied this will approach, to share the dark simplified the matter same production. strengths and shortcomingsful as to perform a systematic and characterisation of DM searches at colliders, there are well- the phenomenology of long-livedas neutral particles. Referringby to the these dark long-lived matter particles economically simplified enables models. the Importantly inclusion of for initial triggering state considerations, radiation this in also event generation in the same Figure 1 a single state collection of states missing transverse energy, which is a smoking gun for displaced DM production. DM models. Table 1 of this table listsits the decay kinematic variables, lifetime ( JHEP09(2017)076 . 2 χ , to (2.1) (2.2) 12 g Λ, which & . We have now E 1 . 12 and the EFT scale Λ, O 1 . We will now describe is the Lorentz invariant 2 1

m ) χ f } , and in which the coupling f 2 is a SM object, which could p χ LIPS X d , → { a 2 − m and ( +1 d 2 2 12 M . Here, g

m f X a 1 ) 1 χ m d is the only additional degree of freedom which LIPS – 5 – 2 → d depends on the masses of the particles involved 1 − Λ 2 χ 2 2 Z χ χ m 2 ( 1 m ∼ 2 , is now identified as an excited dark sector state, χ Γ = Γ = , which describes the lifetime of the excited state, or its width τ 1 − τ depends on the specific form of the operator ) is the dimension of the operator. Such an operator schematically may be modeled through explicit simplified decay models or through a d 2 χ is the matrix element, proportional to where (4 + , we must also describe its decays. To this end we must add at least one new 2 M χ 12 The EFT description of the displaced decays described above is typically valid for The lifetime of the excited state Let us consider the scenario where O may be absorbed. However, in terms of model inputs Λ can be traded instead for the and SM states to allow the decay d − 2 12 gives us where the exponent the following reasons. We will always consider mass splittings, and hence visible energy where phase space.Λ We can parameterise the operator, and therefore the matrix element as more physical parameter Γ, as follows. and their couplings, and is given by χ either be individual or multipleintroduced particles. two additional This parameters: setup thewhich is mass dresses depicted of the in the figure specific DMg interaction state enabling the decay of manifests itself through unitarityarbitrary operators violation of in a scatteringscale. larger amplitudes dimension giving or, a equivalently, comparable by contribution at thisis energy added to the DM simplified model. We must introduce an additional coupling, 2.2.1 Decay EFT By construction, any effectivebelow theory some includes cutoff scale, the Λ, degrees andof allows of for the freedom all local considered theory. operators relevant economy. consistent with Often the This symmetries a effective single theory class will of break operators down is at considered scattering in energies a specific process for degree of freedom, althoughcandidate it in may simplified be models, Therefore, desirable we to must add addhow to more. the the decays model As of the noted,an true the EFT stable framework, usual DM starting DM state with the latter. not as a comprehensive substitute. 2.2 Displaced decay modelsWhile the DM simplifiedstate models economically describe the production of the long-lived the simplified models approach as complementary to the study of complete models, but JHEP09(2017)076 SM + SM), → will always be ( n D . As depicted in 1 φ Λ] ] are completely SM m / + ) µν µν µν 2 1 1 − χ G Z F χ 2 ) ) m 1 1 µν ll h tt bb m φ φ 1 1 1 → − 1 G . Since the energy flowing ν ν for fermionic (middle column) S φ φ φ and φ 2 2 1 ∂ ∂ 2 2 2 2  was the only new light degree O 2 2 Tr[ χ 1 φ φ X φ φ m m φ φ 1 1 1 1 1 Λ χ 1 Λ Λ D Λ µ µ φ χ χ ), the matrix element will never − ∂ ∂ 2 1 m ( ( 2 φ 2 2 → 1 1 m 2 Λ Λ 1 m 2 Λ − χ 2  ] m µν ( , of mass G µν µν O 1 D 1 1 Z F µν χ φ χ 1 1 χ h 2 2 G 2 1 χ χ – 6 – F χ χ χ χ µν µν O 2 ll Tr[ tt bb . σ σ 2 2 χ 2 1 1 1 2 1 2 Λ Λ 2 Λ χ χ χ 2 1 1 Λ Λ χ (10s GeV) and particle masses accessible at the LHC 3 1 Λ ), implies that Λ O there is a new light field below the cutoff Λ that participates 2.2 & 1 χ 1 m ∗ ), for fermionic (scalar) DM, respectively. A complete treatment h ll tt Z bb jj − SM γ/γ 2 m × O Final state X 1 1. Therefore, it will always be a good approximation to employ only the . φ − 2 . The addition of models with light decay mediators is phenomenologically φ W ( D + φ |M| ∼ decays then it must also be added to the theory. Let us call this field the “decay which, through eq. ( SM 2 . List of example effective operators for the decay , in this instance the decay process will be two-step, 2 χ TeVs. By comparing these two energy scales, one sees that a displaced decay requires 2 m ff, W × O Let us consider a light decay mediator Since we are considering the scenario in which both 1 . → χ  2 2 ∗ in the mediator” motivated as they may have distinctive signatures. figure provide a sample of operators in table 2.2.2 Decay simplified modelsThe previous discussion on EFT consideredof the freedom. case where If in addition to of all effective operators couplingtreatment pairs of that, neutral states for toAlternatively example, the some SM preferred ensures would choice require that of arelated operator detailed a to basis could complete the be theory basis motivatedthis in by of work. considerations the Instead, operators UV. we is will Both characterise of considered. the these decays options by the are SM beyond object the in intended the scope final of state. We lowest dimension operator.smaller In than addition, the higher leading orders order pieces. in [( gauge neutral, the relevantat operators colliders. are similar Theχ to displaced those vertices considered will previously thus for be DM characterised by additional operators, in LHC detectors, m Γ through the effective operator inapproach this decay is X (left column). Notefinal that states. this is Furthermore, not the anγ scalar exhaustive charge list. radius For operator example, one gives could decays also only have to diboson off-shell photons, deposits, from the displaced decays that are large enough to give an observable signature Table 2 and scalar (right column) DM particles. Each of these operators corresponds to different final state JHEP09(2017)076 . D φ , and the EFT operators, q 5 and make the replacement 2 q q γ ) through a light mediator 5 µ µ φ X qγ qγ qγ qq D µ D µ D D φ φ φ φ q q q q g g g g SM X − − − − O 2 2 2 2 signatures using simplified models + χ 1 χ χ χ 5 5 1 µ ], we present a list of possible decay medi- χ T γ γ decayed to boosted muon pairs then each γ χ 1 DM 1 µ X / D E D χ γ 42 χ D O φ , 1 give rise to smoking gun collider signatures φ D φ µ D and SM particles ( χ 12 φ φ 2 41 – 7 – g µ D 1 12 12 φ χ − g ig 12 − − g into − 2 2 . Similarly, for decay simplified models, we may take 2 χ χ χ can be boosted, leading to a new class of displaced objects: 1 χ D φ ff → 2 Final state , including the mediator interactions with the SM fields. χ D . Note that these decay mediator models have no limit that captures φ 3 → φ and decays promptly. 2 . Topology for the decay of χ . A small sample list of example vector, axial-vector, scalar, and pseudo-scalar decay D 1 φ χ Following the models discussed in ref. [ To construct models of decay mediators one may again take inspiration from the DM → 2 Figure 2 The simplified models proposedthat in directly section connect withprogramme dark by combining sector the physics.the signatures discovery into They of a also events setused establish exhibiting of to a displaced reference characterise systematic vertices, the analyses. search these discovery using In simplified different the models low-level event can hypotheses, of which also in be turn may possibilities. 3 Experimental signatures and3.1 benchmark scenarios Characterisation of long-lived plus ator models in table the mono-boson decays of theby first construction, three EFT have operators no in limitThus, table that together both captures classes the of phenomenology models of encompass a light complementary decay set mediators. of phenomenological displaced vertex would feature highly collimated muons. simplified models. Formake EFT the models replacement ofthe decays DM we simplified could models takeχ coupling the DM DM pairs EFT to a vertices mediator and mediator couplings for fermionic DM particles. Similar models may also be constructed for bosons. where boosted pairs of SM fields. For example, if Table 3 JHEP09(2017)076 symmetry that 2 Z ]. 23 , it is reasonable to start T / E production, in fact this possibility , the SM final state particles 2 2 χ χ 1 χ . This is an important characteristic searches and to extend the comprehensive T / E decays is sufficiently small to suppress the width, which – 8 – 2 , X 1 1 χ → 1 metre, searches with single LLPs might nevertheless be more . This connects to the underlying 2 χ  cτ decay products since they are necessarily soft. . In the event that the visible decay products are too soft X ] in the context of inelastic dark matter models, with accompanied concrete . By design these models lead to the appearance of displaced ver- 22 searches to also cover long-lived signatures. T . This is typical in DM searches and reveals the escape of neutral DM candidates / E T / dark sector couplings. point back towards the interactionsource vertex of or evidence beam for pipe, DM. providing a complementary Initial state radiation for triggering, mono-X ISRtandem signatures with typical the in other DM searches signatures, may for also event be characterisation used, and in determination of significantly reduces backgrounds. Non-pointing events/large impactfeature, parameter used to reveal additional evidenceof for DM vanishing in MET the the final state. visible Even final in states the event in each displaced vertex typically will not Displaced vertices tices in colliders.neutral. The Furthermore, the observed observed objects objects may may be beDisplaced highly any vertices boosted SM are and collimated. final paired enforces state pair that production is of dark gauge sector states. The requirement of coincident pairs tracker region then no trackssufficiently from delayed, the the energy decay deposits daughters can willoutside be be discarded a if found. time the If window decay daughters thefactors coinciding arrive decay tend with is to the induce LHC missing bunch energy crossing. in Such addition experimental to the DM candidates. E from the detector.may only Depending be partially on measuredconstraints the due in to lifetime limitations the of of event the reconstruction. detector instrumentation If or the displaced decay happens beyond the In the limit of long lifetimes, Events with a single displaced vertex are possible through • • • • • 2 1 simplified models. However, inlarge, the context otherwise of the the decays, modelsexception which proposed occurs proceed here if through this the production thee.g. phase rate same happens space cannot operator, in for be the would too is case not very of be difficult pure displaced. to Wino/pure observe The Higgsino the dark only matter insensitive, the since MSSM. only one In decay those is cases required however to it happen in the detector volume [ contains only a fewwith long-lived a rather searches small requiring set significant prompt of new displaced plus was already explored in [ All of these signatures provide useful handlesDM to frontier. search for The displaced challenge topologies is arisingthat at to can the combine cover most these of individual the signatures relevant into topologies. a set Since of the analyses existing experimental programme signatures include: suggest new searches required to reveal the underlying nature of the discovery. The relevant JHEP09(2017)076 ]. 74 – 71 topolo- ]. These . Follow- T ) for DM T 42 / E / E γ 2.2.1 package [ γ . γ dMET system in the decay of − τ shows a list of the basic X + 4 DMsimp τ -pair τ searches, which in both cases is potential long-lived particle sig- dMET . A list of basic operators that would -based T simplified models γ systems, the dMETs can be combined all / E − T µ X system / + E systems, the dMETs can be combined µ X system could consist of any SM particles, -pair X µ X searches dMET FeynRules T – 9 – . searches (dMETs) that cover the basic displaced / E 2 − T e + / E e plus displaced -pair ’s. These final states would cover most of the relevant e T γ / E dMET jj -pair . All other displaced final states are either not combined with a . However, in the interest of keeping the initial set of benchmarks ¯ γ f , the neutral displaced jet dMET f 2 for some examples). 5 and . A complementary example of a decay EFT (cf. section X as well as by the nature of displaced vertices, which can either be a single or dMETs X Z, h, γ 2.2.2 kinematic compatibility or heavy quark tagging. Table + . Minimal set of dMETs searches for neutral displaced SM particles. To facilitate the 1 h χ The minimal set of dMETs also demonstrates that using simplified models as a vehicle While this minimal set of dMETs does not cover requirement or have to be recasted from prompt → and T 2 / include displaced signatures in practice.of dark Here, matter we production focus that onmodels were the developed are s-channel in simplified the publicly LHC models DarkUsing available Matter these through Forum [ models, the wein construct a section concrete simplified decay model of the type discussed can serve as thesearch basic (see signature section hypothesis to develop and benchmark3.3 the corresponding Hands-on simulationIn of long-lived this plus section, we demonstrate how traditional simplified models can be extended to GMSB inspired dMET E often not optimal. to motivate, develop, andapproach benchmark to explore new opportunities long-lived in searches the provides long-lived particle a sector straightforward more systematically and with a ISR signature such as an additional hardnatures jet that or can additional arise hard insignificantly dark beyond sector the physics, establishing currentgies. these experimental analyses At programme would present, for already the go long-lived only plus search that is consistently performed by the experiments is the Z dMETs that are categorised byχ the SM particles thata define pair the of displaced SMdisplaced particles. topology Furthermore, to searches, facilitate especially the trigger for acceptance soft for these ing the logic of table including manageable, we focus the referenceand analyses leptons on as signatures well involvingneutral displaced as displaced pairs displaced signatures of and jets can be extended to add more dedicated requirements like give rise to such topologies is shown in table 3.2 Minimal setWe of propose long a minimal lived set plus ofSM displaced particles — quarks, leptons and photons — in combination with significant Table 4 trigger acceptance for these topologies,with an especially ISR for signature, soft such as an additional hard jet or hard JHEP09(2017)076 1 χ (3.1) (3.2) (3.3) (3.4) (3.5) , add 2 decays models. χ from 0 Y T 1 , where the / E χ FeynRules , V,A 0 1 → , represent stable Y Y 2 µ 1 DMsimp ) are provided at  , and a new scalar χ χ j Y 1  u χ ) j 5 u γ ) 5 ij γ P u ij ig A u . g . The appendix also contains model the + DisplacedDM models that describe the pro- + A ij in the spin-1 model as S u ij g χ V u + h.c. ( g ), and introduce models. These models describe the into SM particles. The model that produces displaced verticies ( 2 0 1 u i,j µ Y 0 χ √ y γ 1 Y i DMsimp i χ mediator with the SM and DM sectors u u as DMsimp ) 1 5 + ¯ χ + ¯ γ Y j j ) mediators with the SM and DM sectors: P χ d DMsimp d ) P ) ig 5 5 . γ γ – 10 – DisplacedDM + µ 1 ij ij S χ P d A d g , we redefine the g . χY ( ig ) 0 2 5 + + χ γ , via a vector or axial-vector mediator, χY ij A χ ij ) V d ¯ 2.2.2 = ¯ χ S d g 5 g g χ ( γ ( 0 ] for this model (henceforth, + µ P χ can decay. The required particles and interactions are in fact Y DM 2 γ 0 d i,j V i indicate the spin of the mediator. χ 75 ig ¯ model is implemented as the union of the two [ √ χ y L g d i (  Y ¯ + T d µ  / ) and pseudoscalar ( S χ E i,j g X χγ S ( UFO i,j ) with: X χ = = ¯ = = ¯ 1 3.4 1 Y SM Y DM 0 0 L L Y SM Y DM from the spin-0 model (redefining L L χ , into which the 0 Y . A representative diagram from the shows a representative diagram from our model that manifests both . The subscripts on and ]. 3 T 0 / 76 E We begin by considering the class of spin-1 Y Figure production and displaced vertices from theand decay a of corresponding ref. [ Our new displaced plus Following the notation ofthe section by replacing eq. ( interactions of scalar ( To accommodate displaced decays, we introduceparticle, a new stable fermion, already contained in a second class of spin-0 superscript denotes the typedark of matter interaction. particles. In the Theare interactions given as: of the a more generalintroduce outline displaced of decays the inSUSY proposed and DM simulation other simplified strategy. BSM models models. The can techniques also we beduction of use extended Dirac to to fermion pairs, simplified Figure 3 plus production in a GMSB-like model is considered in appendix JHEP09(2017)076 , V 1 Y ] files model ]. We 79 particles 78 DMsimp is used to 2 χ observable. As DMsimp = 13 TeV using T / Pythia E s decays are displaced √ . S 0 observables. However, Y particles are determined coupling values and xy 2 χ d g χ decays are performed using internal decay chain syntax. ¯ f f and shows the difermion mass peak and MC@NLO 1 distributions are unchanged with a χ 4 T S 0 / xy E . Y is produced at d → , A 2 V S MG5 1 ¯ 0 χ Y MadGraph Y and 2 replacement for the spin-1 1 χ χ T coupling values. The / E S χ → → – 11 – g 2 option in mediator. decay chain with a program that incorporates spin V 1 model. Simulation proceeds in two stages. First, χ Y S 0 MadSpin . Following this approach, we produce LHE [ Y shows the distribution of the transverse impact param- → ] section of the LHE header. Spin correlations are not 4 → parents. The upper-right panel shows distributions of the , and kinematic features such as final state resonances for flight are decayed isotropically. In short, the spin-1 T ]) or to use the 2 Pythia 82 (10) on the particular computing cluster used in our studies pp / , χ E S 83 ] at leading order with the NNPDF3.0 PDF set [ 0 of [ O 81 . As expected, the inclusion of spin correlations significantly Y 77 4 MC@NLO models, the shapes of these distributions depend strongly on the DisplacedDM Pythia , and the resulting a to study the relationship between the predicted kinematics and time and decays for a range of 2 3.3 χ v2.4.2 [ − and the original simplified production model can remain unchanged. We MadSpin µ ]. The masses and widths of the particles in the model are communicated MG5 UFO mediator. The bottom panel in figure system, which is a good generator-level proxy for the + DMsimp 80 µ [ V 1 1 ¯ χ Y via the SLHA [ masses. The partial widths of the 1 → χ S χ Pythia 0 . As such, spin/angular correlations between the displaced decay products and Y MC@NLO a Thus the extended simplified models enable the efficient modeling of collider signa- The upper-left panel of figure For convenience, the subsequent We use the of the , and Pythia S 0 T correlations (e.g. We have performed the described in section respect to those oflengthened figure — by a factor of Pythia amongst the displaced andfinal DM state particles angular are distributionsdiscrimination not are relative included. not to expected Forfor the a to searches much generic that provide more dMET seek asimply powerful search, to significant modified incorporate to gain angular replace in the distributions, signal our general procedure can be transverse impact parameter, light decay mediators. 3.3.1 The roleOur of default angular procedure correlations combines long-lived signatures with DM simplified models using mass of the from the resonant decays a 20 GeV tures and include thebenchmarking relevant of kinematic dMETs. information In necessary particular, for we the have optimisation illustrated and relevant features such as the eter for due to the long lifetimep of the in the original included thus the model has been extendedefficiently perform with the new associated particlesadded decays. to and Alternatively, the interactions, new while particledemonstrate content this could alternative be approach in appendix automatically in containing unweighted events for theare production included process. using The the lifetimes of the Pythia8.205 to parameter space of the the vector-mediated process MG5 assume flavor universal vectorY couplings and scan a range of JHEP09(2017)076 � , S χ V 1 �� g µν Y ] F ��� ��� ��� ��� ��� 1 ] for a )[ χ � � Pythia ( 84 � µν σ 2 -SM coupling. χ � S ] 0 , which can be �� )) for various Y h 1 1 ¯ ) for a range of ��� χ φ )[ 1 xy 2 � χ χ d φ ( � χ T ( p � � �� � � ��� ��� decays ( ���� ���� ��� ��� ��� ��� � � �� � ) = � � � �� ( µµ - � ��� ��� �� = = = � � → χ χ χ � � � � S 0 ��

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� � In GMSB, the supersymmetryreview) breaking and is the LSP mediated issector by typically gauge particles. the interactions gravitino, In that (seepure may this [ be Bino section very we NLSP weakly coupled willproposed and to demonstrate here. a visible that In gravitino GMSB GMSB LSP the with mediation maps an of directly approximately SUSY onto breaking is one via of the the gauge interactions simplified of models well motivated models. Thefound first in example GMSB, is while forfound the the in second fermion Higgs example dipole portal is operator scenarios for such the as scalar certain4.1 operator Twin Higgs models. Gauge mediated supersymmetry breaking hadronisation, and to include spin correlations only when necessary. 4 Mapping onto UV-completeTo models demonstrate the utilityexamples of that this map displaced the vertices simplified framework, model we interactions provide described two concrete in the previous section to Other parameters in the in all panels are unit-normalised. — the runtime of the MCto generation exercise process. the default For most dMET searches we therefore advise Figure 4 coupling values. Top right: themediator transverse masses. momentum of the Bottom: DM the system ( dimuon mass spectrum for several values of the JHEP09(2017)076 , M (4.7) (4.4) (4.6) (4.1) (4.2) (4.3) as , and the scale 0 X F , and if kinematically . An appealing prop- 2 e G is the hypercharge field = 1. The gauge coupling , the messenger mass γ M . 5 µρ Y N 4 → N F   e 2 2 Z B e B F at the GUT scale. The mass of M M e 5 B S − M α + h.c. (4.5) 1 . F 2 M W  ∼ j F p µρ θ ) Y , and represents the mass splitting inside 2 t W Φ 2 πF θ ( M π W F θ e 3 X Y GF F 2 α 16 + i cos 12 α √ ¯ µρ Φ 2 5 ∼ k k M ij is a measure of the amount of SUSY breaking. e λ Bσ Y – 13 – = = tan = 2 , the messenger index α ) = F e GeV is the reduced Planck mass. The constant B ˜ ) = i = t ) G 3 ) the gravitino will typically be the LSP. ( √ ˜ √ ˜ / ˜ 18 G M G X e 4 G m B P h W 10 + k + F/M F + M M γ γ × Z = → 4 → . → L → 2 e M e B e B B ' Γ( Γ( Γ( 2 , demonstrating that the effective phenomenology of the decay is acquires a vev along the scalar and auxiliary components, / 1 2 − X ) , with widths given by N e G Z πG → , are defined such that 5 , the supersymmetry breaking Bino mass is r 2 e = (8 B α is the ratio between the fundamental scale of SUSY breaking, is the messenger scale while . is the longitudinal component of the gravitino and M p 0 β e M G M  F/F From this effective operator two decay channels arise In GMSB the interactions of the Bino and the gravitino are described by the effective In the leading-log approximation, assuming a single SUSY-breaking superfield satisfy- F ≡ where strength. Thus the interactionoperator allowing listed Bino in to table gravitinocaptured decays by is the described simplified model. by the first accessible, operator where k of SUSY breaking felt by the messengerthe particles, supermultiplet. This ratio isapproaches traditionally the set equal Planck to scale unity. Unless the messenger scale where we have chosen theconstants, number of SU(5) messengersthe to gravitino be is and tan ing where For most realistic cases,erty it of is GMSB appropriate models tosupersymmetry-breaking is scale assume Λ that that = the entire supersymmetric spectrum is determined by the The chiral superfield chiral messenger superfields, Φ, interacting with the goldstino superfield JHEP09(2017)076 (4.9) (4.8) = 15. In this model, . β  p ], which describes the set of M " " 3 85 2Λ G G γ γ √ -channel squark exchange, which t ) vs. Λ into our simplified models = 2Λ, tan − 1 0 ) χ t 4 , which can be found in Higgs portal (˜ M ( ) 1 h τ 2 α -channel scalar mediator DM simplified 2 Z,γ 2 φ s π ]. Here, they present their results in terms 1 F 5 = 1, M φ e 3 12 B can be varied independently, demonstrating 36 −  " " M B F e 2 B B mess – 14 – N M = Λ ]) and can be converted into the simplified models ( can be written ˜ G 37 ∼ ˜ , G m -channel model of the DM simplified models paradigm τ t ). ! 36 q − 6 1 0 and ˜ χ the value of 1 0 m e χ B ≡ M (figure ¯ q q m m ∆ ) vs. ∆ 1 0 χ (˜ τ . Bino production through t-channel squarks, which maps to the t-channel mediators of ). In summary, the production and decay of a pure Bino NLSP is captured by the 5 Therefore, we can translate the constraints on Analyses searching for the displaced decay signature of two displaced photons plus The production of a pure Bino neutralino is through 4.2 Higgs portalOur hidden second sectors/Twin example Higgs isscenarios. for the The scalar Higgs operator portalmodel, model where maps the to scalarenough the to mediator cover greater is parameter the space by SM considering more Higgs general boson, scalar mediators and than in fact would be general parameters diphotons and missing transverse momentum [ of the Snowmass Points andminimal Slopes GMSB parameter set models 8 in (SPS8)gravitino, which [ and the the NLSP other isthe parameters the mass are difference lightest between neutralino ˜ and the LSP is the set of simplified models proposedonto here, well-motivated demonstrating BSM that models these for simplified displaced models vertices. do map missing energy already exist (e.g.frame [ work. The ATLAS collaboration has performed a search for non-pointing and delayed where for a fixedthat value of the lifetime and mass may be taken asmaps independent directly parameters. to the colored(figure scalar The total lifetime thus scales as Figure 5 the simplified DM models. JHEP09(2017)076 (4.10) symmetries 2 Z through the Higgs 2 φ decay are mediated by . The ATLAS search was 2 m ... φ ��� symmetry to the diagonal, + ... 2 2 | ��� �� + = H τ | 2 × Z ��� hv ATLAS 2 φ 2 1 respect independent φ χ Z 1 φ and the pair production of the lighter 2 φ ˜ �������� ����� G 12 λ 2 → ) �������� ����� ��� � 12 λ - � ] φ g m e - B 1 1 λ φ ( + − φ τ m → ��� and m + [ 2 e ��� �� ���� �� B | Y 1 � = = ��� → → → m Δ λ production and the H hv �� �� 2 | e e ˜ q ) B πα B – 15 – � � breaks the ) 2 = √ 2 2 4 ∫ ∫ 2 2 M m 4 m φ φ √ φ m 2 12 k F 2 ��� λ λ Dirac fermion ∆ λ � ���� � ���� e = = + B + � � 2 1 2 1 φ ��� φ 1 , and Bino-gravitino mass splitting ∆ 1

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The first five rows characterise Figure 6 model variables of Bino lifetime, presented in terms of SPS8 (see text for details). in the broken EWacting vacuum. on The couplings implying that portal displaced decays isportal the (figure pair production of the heavier state where the ellipses denote terms irrelevant for the phenomenology and the second line is displaced vertices simplified model. the Higgs boson alone.displaced One distinguishing dark feature matter of is thethe that Higgs same both portal particle. simplified the This model is for given by Table 5 the DM simplified model while the last two rows are the additional parameters required by the JHEP09(2017)076 × W (4.12) (4.11) 2 2 φ φ q q ∗ 1, the associated h .  ) c ) ( 2 1 W W 12 m λ + , which is a free parameter, 2 2 12 m . q q λ ( 2 2 h  2 m 2 ∗ 2 f 2 φ 1 2 − − g φ 2 φ 2 h/h | ) 2 1 T ∗ 12 h m H λ | − t ) + 2 2 b . t t – 16 – 2 ( 1 | m φ pair production can only be detected through the H interaction. The emitted Higgs can be on- or off-shell | ). For small enough t 1 + (  12 and 2 φ 8 4 h 2 λ λ φ 2 through the Higgs portal alone, emitting an on-shell or m g g φ = 1 q φ 3 2 V 2 2 2 v φ φ πm 2 12 λ 16 through the the decay mediator. This scenario maps onto the Twin Higgs mod- 2 ∗ decays to These models are a class of pseudo-Nambu-Goldstone boson (pNGB) φ Γ = through the top-loop higgs production, while diagram (c) is through the VBF h ) 2 2 a 3 and φ ( φ t t t ], which are a class of “neutral naturalness” models that have received a recent g g also proceed through the Higgs portal. However, for . Decay of . Various productions modes for the Higgs-portal modes. Diagrams (a) and (b) show the ]. 1 are subgroups. As any quadratic corrections are equal for both doublets, they also 87 , 88 φ Y Importantly, 86 Another class of neutral naturalness models which give rise to displaced vertices are models of folded 3 This scalar potential respectsU(1) an SU(4) symmetry, ofrespect which the the SU(4) two copies symmetry. of SU(2) In theSUSY vacuum, [ this symmetry is spontaneously broken, to the cutoff inthe both SM sectors and is Twin identical. Higgs In doublets addition, there is a scalar potential involving Essentially, in the context ofduction mediator the proposed simplifiedels models, [ the Higgs bosonrevival is in interest. the pro- Higgs models that contain two exact copies of the SM, such that the quadratic sensitivity off-shell Higgs in thethis process decay (figure can be displaced. The on-shell decay width is given by state production is very suppressed,standard and MET searches, and therefore are not relevant to our purposes. Figure 8 depending on the mass difference of Figure 7 pair production of higgs production. JHEP09(2017)076 , 0 → m 4 . ++ (4.13) (4.14) 2 1 ), when G ∼ notation), 2 4.12 m PC are SM gauge J T τ ) is the only interaction , with mass ]. , 4.12 ++ 95 2 T – t G 92 T t (using standard ,  T ++ t T µν 2 0 ]. In this case, the lightest objects h G m G 2 5 89 T µν − G 1 Tr  T h f t – 17 – v f m T 3 π + 6 α tt and so tests of the Twin Higgs scenario rely crucially h 4 t λ L ⊃ − = Int L . This glueball can be pair produced in Higgs decays and subse- can decay into further Twin sector states, such as pairs of Twin g m ++ . In this case the decays would be invisible as the 0 T G τ 2, and the SM Higgs emerges as a light pNGB. If the SU(4) symmetry T τ √ f/ → ]. = is the Twin QCD field strength. As a result, Twin gluons may be produced in ++ 91 , 0 i T T G 90 G H h If the lightest glueball decays predominantly into invisible states then it may still be The lightest Twin glueball state is the scalar In the most minimal scenario, the Twin sector only contains the third generation For phenomenology, the most important aspect is that eq. ( If the new physics at the cutoff couples to both sectorsIn then additional fact, couplings the are Twin introduced, however leptons are compelling dark matter candidates [ 4 5 hidden sector states. For example,is the metastable next and lightest its glueball dominant decay mode is through radiative Higgsthis production aspect is very model-dependent. that states such as leptons neutral and would escape the detector unobserved. possible to uncover evidence for the hidden sector from the production and decay of excited to long-lived glueball states, which mayportal decay [ back to SM particles back through the Higgs whose mass we denote quently decay back into SMmode states it through can the Higgs lead portal. to observable If rare this Higgs is decays the at dominant the decay LHC. However, it is also possible where rare Higgs decays. fermions, the so-calledcarrying “Fraternal Twin Twin colour Higgs” are the [ Twin gluons themselves. These Twin gluons may hadronise just as a looptop of quarks top will quarks couple the couples SM the Higgs Higgs to boson Twin to gluons gluons, as similarly a loop of Twin where the specific form of the interaction arises due to the imposed symmetries. Notably, between the SM and Twinon the sectors, collider phenomenology ofboth the Higgs Higgs Portal. bosons Ininherits obtain particular, couplings through vacuum to eq. expectation the ( Twin valuescomponent fields of they from the the will SM Twin mix, Higgs Higgs doublet boson. and is the For coupled example, SM to the neutral SM Higgs top quarks and Twin top quarks as were exact the SM Higgsdo would not be respect massless. the However,couplings the full that gauge SU(4) give and symmetry, rise Yukawa interactions which tologarithmically leads a sensitive to non-zero to Higgs one-loop physics mass.the at quartic quadratic the Importantly, scalar sensitivity these cutoff. potential of corrections the Thus, are Higgs these only mass models to successfully new remove physics at the cutoff. with JHEP09(2017)076 1 at χ 2 m (4.15) (4.16) ≈ is directly ] and have T constitutes which gives 1 96 1 χ χ 12 g ) on the mass of . : 2 2 / cτ χ 3  is part of the thermal ) 2 2 2 χ m ( 10 ∗ g  2 can be sufficiently long-lived to and is very feeble such that  then the Higgs is off-shell and the 12 ++ , are one or more SM particles. The g 2 χ h 2 2 1 G χ ]. The freeze-in mechanism works by m X ) m 2 2 decays where χ m Γ 99 1 0 m < m → ++ 200 GeV – 2 X → χ → 0 m m 1 g φ G 4 0 assuming that the total relic abundance of 97 g + 2 . ( m m  27 / 4 τ m 1 → 1 . 3 ? → − χ g χ 10 2 = 0 h = scalar → v q 2 1 – 18 – 3 = 1 πf g 2 m → = ˆ 3 6 α m m ++ ++ ˆ α 0 2 2 ∆ 2 2 ++ πM G h y 2 χ 100 GeV 3 G 1 G m χ  m is the DM, while Ω -channel, scalar mediator s 1 sec is given by a coupling χ 3 1 − χ 10 via 2 × and χ 7 . Map of fraternal Twin Higgs to simplified models 2 χ the parametric dependence on the decay length ( and the DM candidate = 7 9 2 2 χ τ 100 is the number of relativistic degrees of freedom at temperature ≈ ? . Map of twin glueball parameters to the simplified models. The first five rows characterise g , if the mass splitting permits. If ] for relevant expressions. h It is worth emphasising that although the Twin Higgs provides motivation for the Depending on the parameters of the model, the 90 ++ 0 all of the DM today, we in turn obtain a prediction for the lifetime of We show in figure both the NLSP where which the freeze-in receives its dominant contributions. By requiring that populating the abundance of DM,bath by in the earlyinteraction universe between and is thermally decoupled fromrise the to plasma. the It displacedrelated is vertex to precisely signatures the this at width feebleness colliders. of of The relic abundance of esting in its own right due to4.3 the simplicity of the Mapping setup. intoDisplaced dark vertices matter are parameter a generic space been feature studied of models in of much “Freeze-in” detail dark in matter [ the literature [ give displaced vertices at the LHC.matrix elements Rather and than the going details into ofto details the [ on lifetime the calculation various we transition will refer the interested reader topologies captured by the displaced Higgs portal model, the Higgs-portal model is inter- displaced vertices simplified model. G decay will proceed directly to SM fermions or to Twin fermion states. Table 6 the DM simplified model while the last two rows are the additional parameters required by the JHEP09(2017)076 1 ]. . ��� 103 = 0 ��� – 2 = � h � Ω 100

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As weestablished have dark demonstrated, this matter scenario simplified allows one modelsHowever, to models to port the models with well- of gauge new,with neutral displaced metastable, new vertices. neutral states Thus, particles. in form lineone only with can the a philosophy take of subset a our of simplifiedthat proposed models all covers programme, dMETs possible the as models full the range first of BSM step scenarios. to a more comprehensive programme 5 Avenues for extensions Throughout we have focusedgauge on neutral. models where This the was metastable and for stable good new reason, states as are the physics motivation was to search for within the detector, i.e. length scale of detectordetector, components a is fraction meters, evento for the Poissonian nature of the decay process. detector of DM is set by thisto freeze-in mechanism, give i.e. the Ω observedparticular, relic there are abundance regions can of span parameter over space a in which wide one range would of see decay displaced vertices lifetimes. In Figure 9 via the freeze-in mechanism. We set JHEP09(2017)076 ] for 109 , 108 ) is shown in 0 1 ˜ χ 1 0 1 1 in the final state, ˜ (b). Depending on χ χ χ T X X q qq q / E 10 . (see e.g. [ 1 that can possess a sig- ) is shown in a). In this χ T to be a neutral weakly → 2 2 0 1 2 / ˜ χ E χ χ 1 χ ˜ q 0 1 χ q ˜ and χ (˜ ) qq b ˜ ˜ X q q T ( ] for further discussion) that in / E → ˜ 107 q q – (˜ T 104 / E p p search programme at the LHC. T / , which is shown in figure E – 20 – X 0 0 e e χ χ q and q 0 1 , the arising final state could either consist of a neutral χ 2 χ is assumed to be prompt. In b) we show a potential extension of 0 1 . Since the corresponding prompt SUSY searches are already ) ˜ χ ˜ ˜ q q q a ( 3.3 , which may then decay to SM states 2 → χ q . For example, one simplified model diagram for the direct production → 1 0 1 χ χ p p would be replaced with a next-to-lightest state system, and may be accompanied with significant 0 1 χ ), in which case it may have a long lifetime. This opens up the possibility of ) may have a mass only slightly greater than that of the lightest supersymmetric X 1 2 . An example of a simplified SUSY model diagram showing the direct production of χ χ (a). However, it is well known (see e.g. [ as in the simplified DM models. In the example case provided here, the lightest 2 10 χ It should always be kept in mind with any simplified model programme that nature Furthermore, the simulation approach does not require Using the approach outlined in this paper, it would be straightforward to extend the As with the canonical simplified DM models, the vast majority of simplified SUSY simplified models that canopening benchmark the displaced possibility signatures for without in a general. systematic characterisation of the long-lived particle frontier may not abide by our desire for simplicity. For example, in many SUSY scenarios with dure described in section in place, adding thetheir scope, long-lived broadening signature the to long-lived these plus analyses seems ainteracting natural particle. extension Hence of in this vein it would be possible to also establish long-lived nificant lifetime and will decaythe to choice ˜ of SUSY particleor charged for recent work in thismodels direction). to Simulation include of long-lived the signatures extensions is of straightforward and the similarly usual follows simplified the SUSY proce- signatures from displaced vertices in the detector. simplified SUSY models to alsoticle include long-lived signatures bySUSY adding state the long-lived ˜ par- in our notation is of light flavour squarkfigure pairs decaying tomany SUSY two co-annihilation jets scenarios, the plus notation next-to-lightest supersymmetric particle (in our particle ( long-lived fermion ˜ models also assume a prompt decay to the weakly interacting stable particle state which Figure 10 light flavour squark pairsframework the decaying decay to of twothis ˜ jets simplified SUSY plus model to feature displaced signature. Here the neutralino is replaced with the JHEP09(2017)076 – 21 – The simplified models proposed here do not comprehensively cover the displaced fron- To bridge this gap, in this work we have proposed a first set of displaced vertex However, the experimental long-lived programme today is still rather sparse and does Further motivation for extending the displaced vertices searches at the LHC comes tier at the LHC, butmatter are rather hunt. a To first capture stepto a with be a greater view extended variety to and of connectingbe we signatures with used have the these outlined to collider simplified how broaden dark models the the will current scope need set of of the SUSY displaced simplified vertices simplified models models may significantly. in the hunt forimplementation dark of matter. the simplifiednew We models set have to of illustrated event genericFurthermore the we generation. dMET analysis have demonstrated (displaced+MET) chain how We these from searchessearches have simplified map the that also models onto practical proposed can and well corresponding motivated be a dMET theories. readily implemented. events for every BSMmotivates a scenario greater with breadth displacedrequires of efficient vertices. displaced event vertex simulation Thus searches, and modeling. yet the the theoretical experimental landscape landscape simplified models connecting these signatures with the dark sector, to cast a wider net not cover systematically all relevantsearch signatures and programme final in states. thecraft To new expand future, experimental this simply searches important as providingoptimising, signal and a event interpreting list simulation a plays new of a search. final critical On role states the in other is hand, defining, insufficient it is to not feasible to generate from the factscenarios that beyond long-lived the particles Standard Model,theories show from to up the generic dark readily hidden sectorswill in valleys. to require a SUSY Exploiting a to this similarly plethora strongly rich rich of coupled frontier experimental of programme. well-motivated discovery opportunities fully exploited. Inremain particular, to it discover is long-livedsome particles becoming cases from increasingly this characteristic clear will displaced thatand remain vertex low many signatures. true backgrounds opportunities throughout inherent In LHC inbecoming operation, displaced limited as vertex by the signatures systematic distinctive will uncertainties. signatures shield the searches from 6 Conclusions No stone should bethe left unturned LHC. in the Some search avenues for for physics discovery beyond are the well Standard established, Model however at others remain to be example, heavy gluinos. Presumably, ifthere the will number of always simplified be modelsby examples is simplified to of models. remain BSM finite, models Thusconsidered the whose as models, phenomenology complementary and cannot to, possible but be not extensions, captured replacing, proposed model-inspired here searches. should be metastable particles the dominant signatures could arise from cascade decays involving, for JHEP09(2017)076 ), their 1 χ MC@NLO MC@NLO MC@NLO a a a ) and interac- ParticleData 1 decay using the χ , X S MG5 MG5 MG5 1 0 χ Y Pythia → χ , which will result in an LHE . . For the simplified decay model to efficiently perform the decays. 1 χ decay. requires only that a finite width be X 1 MC@NLO χ Pythia a MC@NLO a → can compute the mediator’s partial widths and . Any additional new particles (e.g. χ – 22 – MG5 MC@NLO , which will perform the models. Event generation with MG5 a Pythia MG5 . The simulation procedure in this approach is to: MC@NLO Pythia χ a DMsimp in process process in ¯ χ ¯ χ χ )), this information and the new particle content can be input χ mass, width, and SM couplings in the MG5 → to achieve displaced decays. to achieve displaced decays. 2.2 → χ will then perform the pp . In this case, no modifications to the original simplified model are pp we considered the case in which new particles (e.g. +X events. Alternatively, if the widths are calculated by other means (e.g. ¯ χ 3.3 χ card.dat card.dat Pythia Pythia properties, and their decaytable. modes should be added to the param file that contains the necessary width information in the SLHA header. SLHA information. EFT operators, or interaction terms involving a mediator. param model, this is simply thethe new, mediating stable particle DM must particle also be included. Generate the Pass the resulting the LHE to Configure the Generate the Pass the resulting LHE to Add new interactions to the original model. TheseConfigure can either the be relevant single-parameter particle masses and couplings in the Add the new particle content to the original DM simplified model. For an EFT decay This approach is naturally suited to the use of simplified decay models, in which the 2. 3. 1. 4. 5. 2. 3. 1. directly to needed. Event generationassigned with to the formerly stable properties of the mediator andOnce its these couplings are to specified, the SM andgenerate DM the sectors are free parameters. analytically from eq. ( of the particle propertyThe information procedure needed for for simulating events in the embedding approach can be summarised as: A strength of the proposedels. methodology is In its section reuse oftions well-established DM are embedded simplified in mod- familiar proceeds in exactly the same way as with the original models. The output LHE contains all We would like to thankStephen James Mrenna, Beacham, Maurizio David Pierini, Curtin,tions. Brian Paddy Shuve, The Fox, and Kentarou work Daniel Marwatari, of Stolarski KH for and useful KS conversa- is supportedA by DOE Award Event DE-SC0015973. simulation of displaced simplified models Acknowledgments JHEP09(2017)076 � ) 1 ¯ 1 �� χ ¯ χ 1 ] 1 χ , �� �� ��� ��� ��� ��� ���� table, χ ��� ( [ χ T verticies � p γ 1 events using χ widths. Right: , ] ¯ χ χ � χ ) of (2007) 1 ��� �� xy )[ � d , χ production model of � 438 ParticleData χ ( � � masses. Other parameters chi χ observable. The ��� �� - T Pythia udcs / ]. E ]. ]. � � ��� � � �� Phys. Rept. �� = )= , � χ χ ( � Γ vertices for a range of SPIRE SPIRE SPIRE

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� � References distributions broaden as the Open Access. Attribution License ( any medium, provided the original author(s) and source are credited. Pythia for a range of Γ in eq. ( system, production model with andiscussed EFT in section decay. Thisref. is [ a concreteMG5 example of theconfigure GMSB its model mass, and specify a the transverse momentum ofin the the DM system GMSB ( unit-normalised. model are fixed as per the panel headings. The distributionsis in more both simply panels applied are with the latter. We demonstrate the approach for a t-channel Figure 11 JHEP09(2017)076 , , , , , , (2014) 088 (2010) 067 11 ]. ]. 10 , , (2015) 059 SPIRE JHEP SPIRE ]. , IN Data-driven JHEP IN 05 , (2016) 099902] ][ ]. ]. , ][ ]. ]. ]. ]. SPIRE Hidden Higgs decaying to lepton ]. IN JHEP D 93 SPIRE SPIRE ]. , SPIRE Lepton jets from radiating dark Lepton jets in (supersymmetric) ][ IN IN SPIRE Searches for long lived neutral SPIRE IN SPIRE ][ ][ IN ]. ]. 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