The Second Higgs at the Lifetime Frontier

The second Higgs at the lifetime frontier

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As Published https://dx.doi.org/10.1007/JHEP07(2020)029

Publisher Springer Berlin Heidelberg

Version Final published version

Citable link https://hdl.handle.net/1721.1/126471

Detailed Terms https://creativecommons.org/licenses/by/4.0/ JHEP07(2020)029 Springer July 6, 2020 June 3, 2020 : : , February 20, 2020 and : a Published Accepted Received Seth Koren [email protected] c , Published for SISSA by https://doi.org/10.1007/JHEP07(2020)029 Stefania Gori, a [email protected] [email protected] , , Nathaniel Craig, . a,b 3 1812.09315 d,e The Authors. c Beyond Standard Model, Higgs Physics

We assess the current coverage and the future discovery potential of LHC , [email protected] E-mail: [email protected] High Street, Santa Cruz, CARaymond 95064, and U.S.A. Beverly SacklerTel-Aviv School University, of Tel-Aviv Physics 69978, and Israel Astronomy, School of Natural Sciences, InstituteEinstein for Drive, Advanced Princeton, Study, NJ 08540, U.S.A. Department of Physics, UniversitySanta of Barbara, California, CA Santa 93106, Barbara, U.S.A. Center for Theoretical Physics, MassachusettsMemorial Institute Drive, of Cambridge, Technology, MA 02142,Santa U.S.A. Cruz Institute for Particle Physics, University of California, Santa Cruz, b c e d a Open Access Article funded by SCOAP Higgs at the lifetime frontier. Keywords: ArXiv ePrint: searches typically provide the leadingdiscovery sensitivity potential in in current future data LHCinto and runs. the exhibit parameter We the further space strongest translate ofare the various a Twin impact promising Higgs of models, these avenuepropose demonstrating for searches a that discovering variety LLP of a searches additional Twin search Higgs channels that with would displaced improve decays. coverage of Finally, the second we are generic in darksubsequently sectors mix where with a the heavyanalyses scalar provide Standard broad decays Model coverage into Higgs. ofmeters, pairs LLP and of decay We explore lighter lengths show the states ranging complementaritystates that which from between in a millimeters searches several to for handful simplified tens displaced models. of of and For existing prompt both final heavy singlet and heavy doublet scalars, LLP Abstract: searches for heavy Higgsmarily bosons on decaying the into production long-lived of particles pairs (LLPs), of focusing LLPs pri- with hadronic final states. These signatures Diego Redigolo The second Higgs at the lifetime frontier Samuel Alipour-Fard, JHEP07(2020)029 ], the search for additional 2 , 1 19 27 23 30 25 4 23 13 9 – 1 – 16 23 27 21 8 15 5 1 20 There is now an extensive suite of LHC searches for additional Higgs bosons, covering B.2 CMS InnerB.3 Tracker analysis at CMS 8 TeV InnerB.4 Tracker analysis at CMS 13 TeV 13 TeV ‘beampipe’ analysis B.1 ATLAS muon regions of interest analyses 5.1 Displaced decays5.2 of a Twin New Higgs displaced signals from Twin supersymmetry 2.1 Status at2.2 13 TeV Projections at HL-LHC electroweak hierarchy problem such as supersymmetry.motivations, Even the apart diversity from of specific spin-half ultraviolet naturally and suggests spin-one searching states for observed similar in the diversity in Standard the Model spin-zeroessentially sector. all conventional decays of additional Higgs bosons to promising Standard Model 1 Introduction With the discovery of aHiggs Standard bosons Model-like Higgs has in becomeCollider 2012 (LHC). a [ The key existence of component such additionalapproaches of Higgs to states the is physics physics strongly motivated program beyond by many at the the Standard Large Model, Hadron including proposed solutions to the D Final states and rates in the Twin Higgs C The dark sector of the Fraternal Twin Higgs A Displaced searches at 8 TeV B Reinterpretation of LHC searches 5 Neutral naturalness 6 Conclusion 3 Displaced decays of a4 singlet Higgs Displaced decays of a doublet Higgs Contents 1 Introduction 2 Direct searches for a scalar resonance JHEP07(2020)029 ]. 10 – 8 ]. For a recent 17 , 4 , 3 ] for a survey of possible exotic ]). Diverse approaches to 7 15 – 11 = 8 TeV), decays of additional heavy s √ – 2 – ]. For a summary of past, present, and future experimental 18 Exotic decays can arise within an extended Higgs sector ] arise readily in an extended Higgs sector [ decays of additional Higgs bosons, in which the final states 16 1 exotic ]. For interpretations and forecasts of LHC searches for 125 GeV Higgs decays to 19 ]. ] for select examples and previous studies. Of course, exotic decay modes are also far from 6 23 – – The exotic decay products of additional Higgs bosons may be rendered long-lived 3 20 2 In pursuing a search program for heavy Higgs bosons decaying into LLPs, a natural The lifetime of new states produced in exotic decays of additional Higgs bosons can Despite their novelty, such exotic decay modes are far from exceptional in motivated See e.g. [ Such Hidden Valley signatures [ 2 1 exceptional in the Standard Modeldecay Higgs modes sector itself. of the For that 125 GeV matter, see Higgs. [ summary of theory motivation forsearches LLPs, for see LLPs, [ see [ LLPs, see [ Higgs to LLPs mayof be LHC difficult to searches discover forHiggs due Higgs bosons to decays can trigger into be thresholds LLPs much (a at more notable spectacular. limitation consideration is the complementarity between Higgs decays into LLPs and direct decays small mass splittings, smallcombinations decay thereof. couplings, Once off-shell produced, decays, thetive approximate signatures that symmetries, of they or LLPs may be aremaking often identified by them sufficiently analyses distinc- a with promising little channeltional or for Higgses no discovering provide Standard a additional Model promising Higgs production backgrounds, bosons. mode for Likewise, LLPs. addi- While decays of the 125 GeV range from prompt to stable,most giving distinctive rise to signatures a are rangethe those detector of volume experimental of set signatures. long-lived them qualitatively Among particlesparticles. apart the from (LLPs), promptly-decaying whose or detector-stable decaysby within any of the properties that lead to long-lived particles in the Standard Model, such as dark matter, baryogenesis, andprimarily the through hierarchy the problem Higgsexclusive entail rich property portal hidden of to sectors isolated additionaltheories coupled that models, Higgs-like extend scalars. such more exotic than Far just decay the from modes Higgs being are sector an of a the generic Standard feature Model. of bosons, but the exotic decaysHiggses may and provide the the new main states discoveryModel alike. channels predict For for example, a both supersymmetric the whole extensions(most heavy host of notably the of Standard the partner electroweakinos) particlessupersymmetric may of Higgs be Standard bosons predominantly Model (for produced fields, recent by studies some decays see of of e.g. which heavy [ extensions of the Higgsitself, sector. due to theMore broadly, presence very often of the multiplenew same scalars frameworks degrees that with of extend diverse the freedomHiggs Higgs masses charged decays. sector and under also couplings introduce the Not [ Standard only Model, do which these may new then states appear give in rise to exotic decays of heavy Higgs been devoted to potential are quite unlike those expectedModel from particles. the direct This couplingsfor provides of additional a new Higgs natural Higgs bosons, avenue states aof for to necessary extended the Standard step Higgs for further sectors ensuring at development complete the of experimental LHC. searches coverage final states (including the 125 GeV Higgs itself). However, considerably less attention has JHEP07(2020)029 ], 30 controlling the distribution ] such as the Twin Higgs [ β 29 -parity violation, giving rise to LLP R – 3 – , and the strength of the coupling to LLPs. While W W/ZZ relative to , we develop a model-independent parameterization of a second scalar 2 hh ] in which the couplings of the 125 GeV Higgs are exactly Standard Model- 28 – 24 In this work we initiate a systematic study of a second Higgs boson at the lifetime These simplified models can be mapped on to diverse extensions of the Standard Model Perhaps the two simplest frameworks for exploring heavy Higgs decays into LLPs are Standard Model. As wesome will of see, the searches strongest constraints for on heavy (and Higgs greatest decays discoveryfrontier. into potential LLPs In for) may section these provide theories. resonance and use it to illustrate the impact of existing LLP searches at the LHC and their hierarchy problem. Incan supersymmetric become theories, a for long-lived example,production particle the in in lightest heavy the supersymmetric electroweakino presenceeven Higgs of more prominent decays. role in Heavy theorieswhere Higgs of neutral decays the naturalness to [ additional LLPs Higgsinto play bosons hidden an sector required bound to states stabilize that the travel weak macroscopic scale distances generically before decay returning to the of simple frameworks forbounds jointly on interpreting heavy bounds Higgscoupling on measurements decays of heavy to the Higgs Standard 125 GeV decays Model Higgs. into states, LLPs, andthat involve constraints heavy coming Higgs decays from to LLPs, including proposed solutions to the electroweak of vacuum expectation valuesthey between possess the a doublets. varietyoption of As is possible for for decay them the modes,the to LLPs branching for decay themselves, ratios singlet via while of scalar mixingand a LLPs with proper Standard the the lifetime Model most as SM-like Higgs free natural Higgs. of parameters. the In Taken same this together, mass, these case leaving considerations they the define inherit LLP a mass pair limit [ like; this guarantees consistencydictates with that Standard the additional Model CP-even Higgs HiggsIn scalar coupling couples this only measurements case to and Standard thethe Model free strength fermions. of parameters the are couplings to the LLPs, masses and the of parameter the tan additional physical Higgs scalars, mixing between the singletsinglet scalar coupling and to the Standardthere Model-like are Higgs, more free the parameters strength inassuming the of one scalar the Higgs doublet doublet model, couples these to mayto be all the further Standard LLPs. reduced Model by fermions An while additional the other motivated couples simplification is to work in the so-called alignment reach in prompt and displaced final states can beextensions of compared. the Higgs sector byrespectively. a singlet scalar In or each an additional case,particles. electroweak doublet the scalar, The additional signatures scalar ofnumber can the of couple singlet free in scalar parameters, turn model namely to are the pairs determined mass by of of a long-lived the relatively additional small physical Higgs scalar, the couplings that induce directeither Standard intrinsically Model (if decay additionalbers) modes, Higgs or and through multiplets such mixing carry couplingssinglets). with can Standard the arise A Model Standard robust Model-like quantumsensitive Higgs program num- to (if of these they searches are direct for Standard decays, heavy Model making Higgses it in valuable conventional to final develop states a is framework in which the into Standard Model final states. Appreciable production of heavy Higgses typically implies JHEP07(2020)029 5 BR. · φ σ bosons with . In section X 4 . Hadronic final W of the dark sector boson may possess m 2 X X m & X , and a heavy Higgs arising m 3 could have nonzero branching φ , which we assume to be lighter than X – 4 – , and reserve both the details of our reinterpretation into SM states (henceforth assuming, for simplicity, and its signal strength in a given decay channel 6 X φ . m φ m X m quarks. b ] for a summary of the different cross sections at different masses and center 31 quarks, as is to be expected from LLPs that inherit Standard Model couplings b decays exclusively into the SM). These parameters determine the average decay X Another two parameters of central importance are the mass The two most relevant parameters to describe the phenomenology of this simplified states in these channels wouldLLP lead decays to into bounds qualitatively similar to those obtained from state and its totalthat decay width Γ lifetimes ranging from nearlya prompt variety to of detector-stable. decay Whilepairs products, the of in whatby follows mixing we with will the considerfavor Higgs. electroweak decays gauge predominantly Of bosons into course, and in eventually top such quarks a for scenario the LLP decays would begin to modes will typically bemass less (see than [ or equalof to mass that of energies). aattention Standard Among on Model all visible Higgs the of decaysleading the possible into constraints same visible di-boson in and and heavycouplings displaced di-higgs Higgs to channels, final specific scenarios we states flavors in focus of — the quarks our which absence and provide of leptons the parametrically — and enhanced on decays into model are the mass of theWhile scalar there are athe variety of most possible part) production assumeDepending modes that on for gluon the such fusion details a of is resonance, the the we model, dominant will the production (for relative mode contribution at of associated the production LHC. ratios directly into StandardThe Model latter decays states can as leadLHC. well to While invisible as and/or the into displaced dark new signatureswe sector of states consider a might in decays heavy contain into a scalar a athe at “dark” scalar great single the sector. resonance: dark diversity of sector state new states, for simplicity We begin by exploringexotic the decays phenomenology in of a aof relatively second a model-independent Higgs-like CP-even fashion. scalar neutralelectroweak with We scalar, multiplet. potentially focus which In primarily general, may such on be a the an scalar case resonance isolated state or a component of a larger this setting. We conclude inprocedure section for LHC LLPTwin searches Higgs and boson a for summary a of trio key of properties appendices. of the heavy fraternal 2 Direct searches for a scalar resonance two simple models tofrom facilitate an additional the singlet interpretation scalar,from of which an we these additional present limits: electroweak in doubletwe section a scalar, explore which heavy a we Higgs UV presentTwin arising in completion Higgs, section and of illustrate the the singlet-like prospects Higgs of LLP model searches in as the a leading form discovery of channel the in fraternal complementarity with searches for prompt decays of a heavy Higgs. We then construct JHEP07(2020)029 = = we s X (2.1) (2.2) (2.3) 2 √ search m ], which 40 ZZ ] and iii) CMS 35 lifetimes ranging ] and the ATLAS X 36 . X ], is an update of the previ- Γ 32 / channels [ q ]. We show that the combination = 1 34 X + 2 X φ . l m m 2 X φ · , cτ m m 4 X X and 2 -RoI trigger [ . The mass ratio between the mother particle µ cτ ' ν X – 5 – ' jj for two different choices of daughter mass , m ]. Similar bounds can be obtained from analogous + 2 R X l 37 ∆ [ LAB BR cτ b · cτ , 2 l φ has also non-trivial consequences for the shape of the final ]. We also include the invisible search at CMS [ , σ X ] searching for displaced hadronic jets appearing in the muon φ 39 , 41 m is proportional to its boost in the lab frame, 38 X . . For direct decays we show limits coming from the CMS 1 is the proper lifetime of A − we set the lifetime to three different representative values, in figure X -RoI trigger), to centimeters (IT trigger) and millimeters (BP trigger). 1 Γ µ / further decaying into 4 ] ii) CMS search using the inner tracker (IT) trigger at 13 TeV [ we present a set of relevant limits on the cross section times branching ratio, = 1 and the daughter lifetime hh 32 1 φ X τ The ATLAS 13 TeV searchous using 8 TeV the analysis [ m As for displaced searches at 13 TeV, we show representative limits from the following 300 GeV (upper and lower panels, respectively). The details of these three searches and • BR, coming from existing ATLAS and CMS searches in diverse final states at , -RoI) [ and the daughter particle · µ mass 50 our corresponding reinterpretations are as follows: search using the beamof pipe these (BP) three trigger searchesfrom at provide 13 meters TeV good [ ( coverageWhile for in different figure values of show the sensitivity of the three displaced searches as a function of the heavy resonance Model Higgs of the samesimple mass. models. As we will see, this assumption maythree be reinterpretations: readily i) violated ATLAS in 13( TeV search using the muon Region of Interest trigger 13 TeV with 36 fb based on asearch combination in of theATLAS/CMS 4 searches [ assumes that the ratio of associated production to gluon fusion is comparable to a Standard projections for HL-LHC. For completeness8 TeV we in present appendix our results on displaced searches2.1 at Status atIn 13 TeV figure σ products of the LLPindependent to characterization be of resolved. a All heavy in Higgs all, at the the lifetime most frontier relevant parameters are for a model- In what follows we review the status of 13 TeV searches on this parameter space, and present the daughter particle This impacts the sensitivity of LLP searches given that many of them require the decay where φ event. This is mainly related to the fact that the angular opening of the decay products of length in the lab frame, which is of the form JHEP07(2020)029 . ] is 1 3.0 42 - XX -RoI (2.4) B.1 : 16 cm µ → 13 TeV 300 GeV φ = 20 m [ IT ), and it 2.5 X m 1 . 13 TeV , 36 fb dark orange . For cτ dark red-dashed ], ]). Our reinter- hh in the lab-frame 2.0 panels correspond ] . , 33 43 X ) → is the ATLAS to pass the stringent BP: 2.5 mm X GeV φ 5 m [ cm [ . right φ ϕ 1.5 RoI: 2.5 m , cτ ∼ for m - m μ X X and 1 Orange can increase the sensitivity cτ , m φ φ 1.0 left : 16 cm m m ( light blue inv 8 TeV IT ) is summarized in appendix · hh X 0.5 1 ZZ inv., projected with 13 TeV luminosity. The − , cτ → X

1 2 3 4 1

L - - - - X

σ 1 fb φ

cτ ϕ .

in order to ensure the decay products remain

lifetimes and

10 10 10 10

] [ · pb BR , m 36 for X φ X · m m ]. For comparison, we also show in 1 ( – 6 – 3.0 - 34 1 m) and sub-TeV masses (see figure 083 fb the reach of this search is independent of the mass of . 50 GeV ∼ are fixed. The residual dependence at the boundaries = mm [ dark green X 2.5 RoI: 1 m cτ is the CMS IT exclusion with , - m X μ ∼ cτ 13 TeV , 36 fb ] with the same m X ZZ 35 BR = 0 cτ → · 2.0 , but uses updated information about the trigger and vertex ] and φ ) accounts for the detector acceptance and efficiency for the dark red A BP: 1 mm X cτ ], TeV for [ = 300 GeV, respectively. In the plot we select three representative values 13 TeV φ ϕ 32 1.5 , cτ σ X m X with different values of the m [ m relative to the actual integrated luminosity used in the search. Our , once ∼ , m φ jj L φ 1.0 X , in a large region of Dark blue → m : 1 cm 2 cτ . ( . The CMS BP search is effective for sufficiently high : 1 cm 1 inv X X 13 TeV − 8 TeV IT IT m hh 0.5 . Summary of the cross section times branching ratio probed by 13 TeV searches with ZZ = 50 GeV and

deteriorates for longer and shorterof figure displacements. As wethe can singlet, see from thecan left be panel easily explained by consideringcoming the from extra boost the factor decay of of the an heavier singlet. Heavier where signal and, for convenience, weluminosity include a possible luminosity scalingsimulation by procedure an integrated for obtaining The exclusion power offor this optimal search displacements is ( comparable to the ones from visible decays reconstruction efficiency appropriate tolimit the is 13 TeV given search. by The 95% C.L. exclusion chamber. The muondesigned Region is tailored of to Interest tagwhere displaced (RoI) the decays muon trigger with reconstruction decay around algorithm lengthpretation is which 0 procedure fully this efficient is (see search qualitatively ref.present is [ similar in to appendix the 8 TeV reinterpretation which we 2 3 4 1

= 36 fb - - - -

σ X ϕ requirement, which then necessitates larger

10 10 10 10

m ] [ · pb BR T now the CMS IT exclusiondiﬀerent data at selection 8 TeV requirementswith [ of light the 8 TeVH IT search makesresolved. it more sensitive to scenarios we consider to for these lifetime regimes whichexclusion maximize with the reach ofthe a CMS given search. beam pipe search with Figure 1 L JHEP07(2020)029 . ] ]. X 3.0 35 35 m (2.5) 4 - 10 · 3 we plot 50 GeV 3 2.5 2.5 300 GeV - = ] = ] 10 X 1 = 300 GeV X m 3 m - X TeV 10 ) for the three TeV · [ [ 3 X m ϕ 2 ϕ 3 - 2.0 - 3 m 10 - 10 m 2.0 cτ . 10 2 · 2 , together with a - - 3 2 ) φ 10 - 10 · 3 10 · 1 X - 3 m 1 - B.3 10 1.5 10 – , cτ ] updates the previous 1.5 = 50 GeV/ X

3 4 3 4 1 2 1 2

1 33

------τ τ B.2

, m 10 10 10 10 10 10 10 10

] [ ] [ x x m m m c c φ CMS IT search at 13 TeV [ m ( 3.0 3.0 · 2 - 1 10 − 50 GeV 3 2.5 Center: 2.5 - = 1 X 10 · ] 3 m and the angular separation between the L ] ] 9 fb BR in pb in the plane ( 3 32 . · 0.3 - 2.0 10 X φ 2.0 , and the daughter resonance mass, TeV TeV 35 σ [ [ φ 1m. By comparing the sensitivity at 13 TeV · 0.1 ϕ ϕ m m m 1.5 & 0.03 1.5 – 7 – ) we can see how a LLP search at the LHC can 0.01 X ]. 300 GeV A 1.0 = cτ X 34 1.0 1156 fb m .

1 2 3 1 2 3

1 1 0.5

------) is summarized in appendix τ τ

X 10 10 10 10 10 10

] [ ] [ x x m c m c BR = 0 , cτ · X 3.0 3.0 -RoI search at 13 TeV [ µ , m 1 ] for displaced dijet pairs appearing in the inner tracker. Both at φ 2.5 13 TeV φ 2.5 m 35 0.3 σ 1 ( ] ] we see that the exclusion power strongly depends on the hierarchy , which controls the boost of 0.1 2.0 ATLAS φ 0.3 1 2.0 TeV TeV [ [ m 1m and decrease it for ϕ ϕ = 50 GeV the exclusion powers depends strongly on the mass of the mother 0.03 0.1 m 1.5 . m Left: 1.5 X 0.03 X 0.1 50 GeV m = 1.0 cτ X 0.3 . Contours of the excluded signal strength 300 GeV m = 1.0 X CMS beam pipe search at 13 TeV [ m between the mother resonanceFor mass, resonance jet pairs. It is interestingallows to for notice that a the larger selection efficiency criteria at of large the 8 boost TeV analysis factor. [ For this reason, in figure validation of our recasting. The 95% C.L. exclusion limit is given by From figure trigger performance comparable to the 8 TeV analysis. The CMS 13 TeV search8 TeV using analysis the [ Inner8 TeV Tracker and trigger at [ 13 TeV thisfor search obtaining is nearly background free. Our simulation procedure for with the 8 TeV onebe (see zero-background: appendix the 13 TeV muon RoI analysis remains background-free with

1 1 1 0.5

1 - 1 τ

τ • 10

10 10

] [ ] [ x x m c m c Right: Figure 2 LLP searches discussed inrespectively. the text. The upper/lower rows refer to JHEP07(2020)029 , ] = 2 34 X (2.6) m ]. Indeed 32 requirement, T ] and precision H . 47 ) X , cτ X 1 boost can only be seen at , m requirement is satisfied, this φ X T m ( H · 1. The same rescaling is applied to 1 . ] and the 13 TeV dataset [ − 0 41 ' L 91. More details about this comparison 5 fb . . 0 38 . When the ' · 1 TeV due to the substantial . This is due to the requirement that both 2 – 8 – X HL-LHC & φ m /L 13 TeV m 078 fb . now /L L p . Comparing the upper and lower middle panels of figure 8 TeV BR = 0 A L · , displaced searches at the HL-LHC have an unprecedented dis- 3 . For the visible searches we use the rescaling procedure already 13 TeV φ 1 σ . The 95% C.L. exclusion limit is given by − B.4 = 3 ab ]. Since the parton luminosities controlling the background do not change . φ mm. 46 – , we show the extrapolated reach for the high-luminosity phase of the LHC m ]) are likely to keep pace. ' 44 3 48 X HL-LHC drops rapidly once the averagethe separation of size the of decay productsupper the is and jet boosted lower right to radius. panels within search of covers figure This the behavior regioncτ of appears very very short clearly displacement by with efficiencies comparing maximized the for This analysis is only effectiveand for is mostlydisplaced sensitive vertices to be associated heavy with a resolved jet pair, so that the search efficiency high The CMS 13 TeV search lookingprovides for a two straightforward displaced generator-level recipe vertices in fortations obtaining the that limits beampipe is on (BP) faithful new [ for interpre- in signal appendix benchmarks with high acceptance, which we discuss other 13 TeV searches: will be given in appendix we can see300 that GeV. the Also largesearch the dependence is difference on reduced. between the the mother A efficiency mass slight of is degradation the reduced due 8 TeV for to and the the 13 TeV the expected reach of the 8 TeV search rescaled linearly with the luminosity of the L Let us finally comment on the main result of this model-independent parameterization. As far as displaced searches are concerned, we rescale the bounds linearly with the • additional hardware and triggertiming improvements [ (such as track triggers [ As one can see from figure covery potential for new heavy SM-like resonances. This is due to the very low backgrounds gressive extrapolation is to some extentof already the supported muon by RoI the search scaling betweenwith of the very the few 8 TeV background changes dataset in [ theevents actual search at from 13 8 TeV TeV to isOf 13 TeV, consistent course the number a with of variety background zero ofare while new expected the challenges to to luminosity arise the increases at background high by characterization luminosity, a of making factor LLP this searches extrapolation of optimistic. 2. That said, drastically between 13 TeV and 14 TeV, theroot rescaling of is essentially the controlled ratio by thethe of squared invisible luminosities searches at 13 TeV. luminosity, assuming their background to remain constant at higher luminosity. This ag- 2.2 Projections atIn HL-LHC figure with used in [ JHEP07(2020)029 for 3.0 1 - dark is the : 16 cm lifetimes 13 TeV 300 GeV = IT 2.5 X X m 14 TeV , 3 ab Dark blue 2.0 ] ]), to centimeters )), and is generic, -RoI exclusion with µ 34 BP: 2.5 mm 2.2 GeV dark red-dashed [ ], H 1.5 RoI: 2.5 m - m 33 μ ]. cm [ 1.0 34 ∼ : 16 cm ZZ = 300 GeV. For these channels, we . These channels are rescaled by inv X 8 TeV is the ATLAS IT X ] which indeed is likely to give the cτ hh mm [ 0.5 m hh with different values of the ∼ 41 , → jj

X decays. 3 4 5 6 1 2 1

32 ------Orange φ σ projected with 13 TeV luminosity, and

cτ

→ .

10 10 10 10 10 10

) ( · pb BR SM X for X cτ 13 TeV – 9 – 3.0 1 ]), to meters (as in the ATLAS muon chamber - = 50 GeV and /L 35 X 50 GeV m = light blue X 2.5 RoI: 1 m - m μ HL-LHC 14 TeV , 3 ab we consider L inv., , that couples to the Standard Model via the Higgs portal. ] with the same 2.0 ] XX S → 35 with → φ 1 BP: 2.5 mm GeV [ φ H 1.5 is the CMS IT exclusions at 13 TeV for m . For panels correspond to 1.0 ]). : 1 cm ZZ dark red : 1 cm inv 13 TeV 41 right , ], 13 TeV 8 TeV dark green IT IT /L 32 32 0.5 . Projected reach in cross sections times branching ratio at HL-LHC. hh , and is the CMS beam pipe search at 13 TeV with m [

ZZ 6 1 2 3 4 5

1 ------σ An interesting observation is the degradation of most of the displaced search strategies left ∼ HL-LHC

10 10 10 10 10 10

→

L ) ( · pb BR SM X While the model-independent boundsguide to presented the in relative the strengthcomparison previous of is only section prompt possible and provide in displacedof a the the searches context useful Higgs. for of a Here models we secondfrom that present Higgs, relate a the a the real first production true of CP-even two and scalar, such decays models, in which the second Higgs arises searches to heavier resonance masses wouldthe be collimated to tracks use coming jet-substructure from techniques to the resolve boosted 3 Displaced decays of a singlet Higgs for higher masses ofmainly the due mother to the resonance, collimation for ofas relatively the far daughter light as decay daughter products we particles. (seeexception expect eq. is This the ( the is dark ATLAS sector muonbest states chamber reach to analysis for be [ heavier lighter resonances. than the The second natural Higgs. next A step notable to extend the coverage of other far as the lifetimeon coverage different is detector concerned, components iting can is from be the clear sensitive sub-centimeter that to level(as different a (as in search wide in the strategies range the CMS based CMS ofanalysis inner beam-pipe displacements [ tracker rang- analysis analysis [ [ of these searches compared to thebeyond-the-Standard usual search Model strategies based scenarios, on the visiblefor decays. reach the In of explicit reduced these signal searches rates can of often these compensate exotic decays compared to the visible channels. As p and rescale the results incτ figure CMS IT exclusion atorange 8 TeV [ Figure 3 φ JHEP07(2020)029 ) ' 2 φ 3.1 (3.6) (3.7) (3.3) (3.4) (3.5) (3.1) (3.2) m . 4 S S symmetry under 4 ]). From eq. ( λ 2 φ , 53 Z − – ). Parametrically, we + 3 S H f 51 , S . 3 = a ) → 46 , hh − H 2 → . In what follows we will often 30 | φ S H | -invariant potential. Then ,S 2 2 ] for a discussion of explicit models BR S Z . , ! 49 − , ) h 2 v f + φ + 2 v HS √ (1 · = 246 GeV is the electroweak vacuum π v 2 φ (see refs. [ ]. λ m ( v

HS m v S f h 50 − HS a ¯ λ σ f,V V = λ 2 f ∼ · | ' γ , → γ γ ' H h γ | 2 – 10 – 2 γ S and HS ,H = sin = BR = cos a ) HS ¯ ¯ φ f f f − ) and the SM Higgs even ( λ σ 2 is the VEV of the singlet S ¯ HS ' f,V V S -breaking is the explicit breaking due to the singlet trilinear f f λ 2 S 2 S 2 φ SM hV V,f hV V,f → g g Z λ + m → − φ m 1 2 S HS BR − a ) ( v S µ -breaking is spontaneous, and the mixing with the SM Higgs is approx- ' ∂ 2 ( Z γ 1 2 and can be summarized as follows: -symmetry is exact, the singlet can only be pair produced at colliders and = 2 γ Z , the is the physical mass of the singlet, 2 f φ S visible , as m λ γ L a minimal scenario for EW baryogenesis [ and can be made arbitrarilywhere small. this We scaling refer to is [ realized. the Higgs couplings are modifiedscenario” only which at presents loop interesting level. phenomenological This challenges is and the could so-called provide “nightmare coupling with the SM Higgs. In this case the mixing goes as 3 imated by If the The primary source of The singlet takes a VEV at the minimum of a In what follows we will focus mainly on the first scenario. This is explicitly realized in The above formula shows how the mixing between the singlet and the SM Higgs is We introduce the effective lagrangian of a CP-even scalar up to dimension four: 3. 2. 1. Twin Higgs scenarios where the phenomenology of themixing singlet angle and the SM-like Higgs is completely controlled by the abuse terminology and referHiggs”, to though the of mass course eigenstates they are as ultimately the (modest) “singlet admixtures. controlled Higgs” by and the “SM-like spontaneouswhich and/or the explicit singlet breaking is of oddcan a distinguish ( three discrete scenarios: angle, where expectation value (VEV), and After electroweak symmetry breaking,ponent the of singlet the mixes Higgs withparameter doublet. the is uneaten larger In CP-even the than com- limit the that Higgs the doublet mixing mass is parameter, small we and can the express singlet the mass mixing JHEP07(2020)029 ) ) 3.5 3.1 (3.8) , leading ] or other γ 2 18 we assume 5 TeV. How- . , the only way 4 1 φ . From eq. ( & m φ φ ; (2) the branching π m HS 8 m λ is itself a portal to a ' S visible . In figure . 2 visible ]). In addition, we also show / ; (3) an additional branching 56 invisible . Finally, the branching ratios of WW γ 2 → φ displaced BR . The primary weakness of the displaced φ ' m can decay abundantly to a pair of dark states , where the muon RoI search loses sensitivity. as well. In the minimal scenario of eq. ( = 0, for simplicity. ) are rescaled by a common factor depending ZZ S cτ → – 11 – X 3.7 φ rescaled by sin φ BR invisible m ' refer to the couplings of the SM-like Higgs to Standard hh ¯ , and large f . The latter is in principle model dependent, however, for ) has triggered intense phenomenological studies with the → φ the relative strength of existing and future di-boson and di- X SM hf hh 3.1 4 8 and BR m /g / BR ¯ f ) is that of a Standard Model Higgs of mass φ hf = 1 g , low m φ ( ZZ h m σ → and φ ]. BR SM hV V the potential has an approximate SO(4) symmetry which implies 55 ' /g – W ) shows that the production cross section of the heavy singlet is the one of the 52 m hV V , g 3.6 The situation becomes drastically different when the singlet Having constructed an explicit model for the heavy singlet Higgs, it is worth briefly The interplay of searches for visible decays, displaced decays, and Higgs coupling de- The lagrangian in eq. ( We summarize in figure 46 displaced φ price of a large suppressionof of suppressing the the signal decay rate.Higgs. width Indeed of since Γ the singlet itself is to suppressgeneric dark its sector. mixing In with this the case SM the singlet searches is at high Optimal coverage of this region couldproposed in experiments. principle be provided by MATHUSLA [ exploring an explicit modelone for might the naively LLP conclude that having a displaced signature would always come at the absence of singlet Higgs decaysis into LLPs, unlikely the to sensitivity of surpassever, direct limits searches for at from singlet the Higgs Higgses HL-LHC searches coupling decaying for measurements partly displaced for into decays LLPs,pling makes the measurement a potentially to direct much considerable search higher program reach values competitive of of with Higgs cou- ratio into long-lived orratio “displaced” into final detector-stable states,BR or BR “invisible” final states, BR viations highlights a notable feature of future LHC sensitivity to a singlet Higgs. In the higgs searches at the LHC,of as Higgs well couplings as (taking constraintsthe for coming possible definiteness from reach the the of precisiondistinct values measurement LHC in branching [ displaced ratios searches. that(1) the determine In branching the principle ratio relative there into contribution are prompt of or three displaced “visible” qualitatively searches: final states, BR aim of comparing the reachwith of direct the searches sensitivity for a fromers singlet Higgs [ decaying coupling promptly to measurements SM at states, the LHC and at future collid- corresponding Higgs boson atthe mass singlet into SMon gauge bosons the in branching eq. ratiom ( into Model vectors and fermions,The respectively, cross normalized section towe the see Standard that Model the couplings prediction. to of a the reduced SM-like Higgs productionEq. to cross SM ( states section are in reduced every by cos channel but unchanged branching ratios. Here JHEP07(2020)029 3.0 grey with

(3.9) HL

]). If @ γ ϕ 0, and m / = 8 TeV h

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o: m RoI:1 - = blue line 36 fb . Parameter space of the singlet Higgs as a function of 0.5 > and = 1 m while on the right panel the exclusion region for visible 13 TeV displaced 3.1 region is excluded by the combination of ATLAS and CMS Higgs coupling measurements = 1 mm on the left panel and left = 7 & 8 TeV, while the S L S X X 2 3 4 1

- - - - m γ cτ displaced cτ √

10 10 10 10

. A simple example is to add an extra dark singlet scalar daughter sin displaced 2 tivated by a class ofsector Hidden communicates Valley with models the whereboth a Standard rich Model and via approximatelyfor stable a hidden Higgs portalΓ (see refs. [ in eq. ( This type of setup arises naturally in Twin Higgs constructions [ by the visible search.background and The same orange lifetimes. lines are the projected reaches forwithout the suppressing the HL-LHC signal assuming rate. zero these Depending states on can the be speciﬁc approximately long structureS lived of and the lead dark to sector, displaced or invisible signatures for lifetimes. The for projected reaches for the HL-LHC assumingregion zero on background and the same lifetimes. leftfor The panel indicates the exclusion of the ATLAS muon RoI search at HL-LHC. The two the mass of theBR singlet Higgs ( tracker (IT) search at right panel, the for the same lifetimes. The coupling measurements of thein Standard the Model-like Higgsthe at combination 125 GeV. of We currentwhile choose the searches for decaysshaded in the at Figure 4 and projected constraints from direct searches, as well as current and projected indirect limits from JHEP07(2020)029 . . . 3 ], φ is 1 2. β 2 φ 2 X as b 58 √ m m 2 X γS 2 (4.1) (4.2) (4.3) sin 2 · S − β/ , 2 ' S SH SX λ λ cos symmetry and 2 A ∼ v 2 1 . m S +h.c.) Z S , with hyper- : . 2 1 3 ) i ≡ 1 S H ! we will see how H ) visible H 1 3 h Γ 5 ) is a function which H / iS , ( β 2 5 ( 2 combination. + 2 + λ √ F 2 H π/ − S = 0: β/ ( + displaced i 2 H β 1 1 H √ -breaking parameters and can sin 2 − φ v

h , which suppresses the rate of Z bH α . , = b and the new scalar by 2 +( i ≡ 2 H 2 √ | , H Φ γS h 2 v/ displaced H 2 A 1 + = m 1 λv H | S · i 4 v ) λ ∼ φ β h ( + h – 13 – , F 2 is the mass of the pseudoscalar | ' ! H A ) | 0 γ 2 m | 1 iG will get a VEV: H with a vector or a fermion. This upper bound is easily | + 1 3 1 λ + X H S G + 4 + | and 1 v ( H gives an upper bound on Γ 2 | H 1 1 √ , we can write the mixing angle between these two ﬁelds λ X b

dependence, and + = 2 , the SM Higgs is given by | β b v 1 2 v Φ H i | into SM states is instead proportional to the 2 1 λ 2 2: µ v / ). is the SM Higgs doublet, and where we have imposed a discrete i X is a typical size of the quartic couplings of the potential, = λ 3.5 H λ For Generically, both It is worth noticing that in this simple model, avoiding a fine-tuning of the mass of In the standard 2HDM language, this angle corresponds to the 2hdm 3 visible V This scale controls the scale of the two heavyThis Higgses mixing up leads to to EW thein corrections. suppression eq. of ( the SM Higgs coupling to massive gauge bosons as where encodes the tan where only one Higgs doublet gets a VEV: In the limit where that is only softly broken by the terms proportionalAfter to EWSB, it is convenient to write the Lagrangian in the so-called Higgs basis [ Another simple scenario thatwhen gives the rise Standard to Model thedoublet Higgs decays scalar. sector of is a extendedcharge second We by +1 Higgs introduce the into addition the LLPs of potential arises a of new electroweak a new Higgs doublet, dimensional transmutation in the darkbecause sector, of and the the decay rich oflightest structure the dark of singlet state. the is hidden unsuppressed sector where heavier states decay4 down to the Displaced decays of a doublet Higgs checked replacing the singlet circumvented if a cascadeif of decays the of UV multiplethe states contribution Twin occurs to Higgs in gives the the anidentified explicit hidden daughter with realization the sector mass of lightest and/or glueball. this is simplified The absent. model mass of where the the In glueball singlet is section naturally lighter because of be arbitrarily suppressed. the scalar daughter decays into dark states comparedThis to feature the does one not into depend SM ones: on the Γ spin of the hidden sector state, as can be explicitly width of JHEP07(2020)029 . S A m (4.8) (4.4) (4.5) (4.6) (4.7) . After EWSB, 2 X 2 ), having a displaced | 1 4.1 H | λ , cτ , − hh , . . In this same limit, the heavy , ) → ) ) β 2 S 2 production cross sections (either A γ γ Γ ( ( S m , , O ( O ) . 2 + VS + γ , or because of the reduction of the , X ( ) without reducing the production cross γ γ A O , invisible VBF h h m Γ β hh + σ ( 2 , · + sin β γ γ ggS with the dark sector that is independent on its ) parametric dependence of the Higgs couplings , tan β and 2 – 14 – β sin ffS S h tan 1 σ tan displaced ZZ = sin = Γ − mixing with = 1 + = VS β, ggS , , S ffS S SM SM hff hff hff Sff tan VBF S σ g g g g σ , γ, ) the corresponding cross sections of a SM Higgs with mass S A m m ( ggS , ffS , 0, the couplings of the observed 125 GeV Higgs are exactly as predicted by the . This adds an additional (tan VS with a generic (displaced) dark sector of the type 1 , is the life time of the dark sector particle ≈ 1 H γ H VBF h cτ σ There are ultimately several key differences between the singlet and doublet models. In conclusion, for the purposes of our study, the dark sector-enriched 2HDM can be Similarly to the singlet case, in the minimal setup presented in ( The cross sections of the different production mechanisms of the second Higgs will Contrary to the singlet case, we can write explicit Yukawa terms for the second Higgs signature generically implies a reduction of the several section of the newHiggs coupling states. measurements changes Moreover,model, significantly. the In complementarity the alignment betweenStandard limit direct Model, of searches while the and the doublet Model heavy fermions Higgs whose states strength depends retain on nonvanishing the couplings value of to tan Standard where In the former casefixed, the whereas relative in ratio the latter ofof case heavy powerful they Higgs searches are couplings for allowed to to decays vary, fermions potentially into and lessening vectors the is impact states; and invisible final states. parametrized by seven free parameters: couplings with fermions).of This the tension is againthese easily interactions generate solved a by coupling addingmixing of with new the interactions SM Higgstotality and of on decays its couplings of with the fermions. doublet As might in involve the prompt/visible singlet final model, states; the displaced final with Correspondingly, the scaling of thesive several gauge branching ratios bosons will and differentiate fermions. between mas- S because of the reduction of the scale in different ways. In a Type-I: doublet, to SM fermions and gaugethe bosons. Higgs Particularly, couplings if to we fermions focus are on a Type-I Yukawa structure, JHEP07(2020)029 ¯ t = t 3.0 X → . m 300 GeV S overlaid = X H 2.5 m β 0 m = γ = Gray contours S . m HL 2.0 @ and tan 4 we include all SM

BP:1mm ]

BP:1mm S 250 GeV (550 GeV) for m TeV [ & can arise from the mea- S 1.5 visible 5 transition leads to a bound HL @ m :1cm :1cm 6 pb IT13 TeV - H HL 10

@ 13 TeV sγ IT m (2 displaced). For a matter RoI:1m - → μ 1.0 b panel we show results for are as in ﬁgure XX :1cm 8 TeV IT RoI:1m - μ → 0.5 γ , under the assumption -5 pb s 10 4 → - pb = 0, where in Γ

10 b

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6 – HL - @ 10 TeV [

BP:1mm 4 59 S = 0 (for which prompt di-boson and di-Higgs searches are ineﬀectual). , 1.5 displaced ¯ tS, S m t BP:1mm γ and light charged Higgs masses in Type-I 2HDMs: 11 β boson.

HL pb ]. See the blue region in ﬁgure :1cm @ 5 IT13 TeV - , we show the reach of the several LHC displaced searches performed so far in 1.0

10 S 66 HL

@ 5 -RoI:1m = 300 GeV. The :1cm μ 5) [ 8 TeV :1cm . IT RoI:1m - X 13 TeV μ IT . Parameter space of the doublet Higgs scenario as a function of 0.5 = 0, the branching ratio into invisible equal to 0 and equal branching ratios into displaced /m γ s

4 of the Standard Model. - pb → γ

= 2 (1 b 10 a hidden sector with a QCD-like gauge group whose conﬁnement scale is close to that

In ﬁgure associated production as the dominant production modes, and the challenging β Additional (relatively weak) constraints on the parameter space of ﬁgure β 4

30 20 10 50 40

(1) Tan ¯ tS surement of flavor transitions.at low For values example of thetan tan measurement of the wide variety of compelling scenariosnotable for among physics these beyond scenarios theNaturalness, Standard are which Model. provide approaches a to Particularly motivatedaddressing the target the hierarchy for hierarchy problem LLP problem such searches in at these as the models Neutral LHC. requires: Successfully decays of the 5 Neutral naturalness The simplified models presented in the previous sections capture the salient features of a additional Higgs states. the alignment limit The several dashed contours correspondbe to the looked cross for section at forof the a simplicity LHC new we signature in fix that Γ the could coming years: Higgses do not couplet directly to Standard Modeldecay as vectors, the leaving only primarythe gluon prompt recent decay fusion studies mode and [ (for the prospects for this decay mode see e.g. limit objects and visible50 final GeV states (mainly represent the rate for plots is the region probed by the measurement of Figure 5 with current and projected constraints from direct searches. For the plot, we assume the alignment JHEP07(2020)029 ], ]. 30 17 , charged un- A H ] with the lightest ]). Here we present 57 22 , 21 – 16 – ], however, there are not necessarily light quarks in 57 across the full range of possible lifetimes will be difficult 5 − –10 4 . − C 10 ∼ ], where a heavy singlet-like hyperbolic Higgs can decay into pairs of scalar top ], to which we refer the reader for further details. In what follows, we will focus 67 and couple to states in the hidden sector. 68 one or more additional Higgs bosons that mix with the Standard Model Higgs doublet The essential properties of Twin Higgs models and their variants are summarized in Long-lived particles arising in incarnations of neutral naturalness are produced in de- (2) 5.1 Displaced decays ofIn a Twin Twin Higgs Higgs modelsproximate the global SM-like SU(4) Higgs symmetrylightness is spontaneously of a broken the pseudo-Goldstone down Higgssymmetry boson with to arises (PGB) respect SU(3), from of the to explaining potential an the the of ap- scale the of two Higgs new doublets, physics. a doublet, The approximate SU(4) Twin Higgs, exclusively considering the Fraternalglueball Twin being Higgs scenario the [ lightest darkorder particle to (LDP) make as the a paper benchmarkare for self given displaced contained, in signatures. more appendix details In about the structure of the dark sector and/or annihilation into glueballs orin aggregate. bottomonia, leads to a large rate ofe.g. LLP production [ on the features of Twin Higgs models that are most relevant to the decays of the heavy branching ratio of at the LHC due toa limitations potentially from more trigger promising thresholdsheavy Higgs strategy (see decays, refs. which for [ is which triggeringthe to is heavy less look Higgs of for a to limitation. thethe hidden totality While production sector of the of heavy partial glueballs Higgs widths LLPs or decay for from bottomonia modes into may the not hidden individually sector, followed be by large, cascade decays these top partners into hiddenfraternal sector Twin glueballs Higgs. lead to signatures analogous to thatcays of of the both the heavyLLPs Higgs(ses) in and exotic the decays SM-like of Higgs the at SM-like 125 Higgs GeV. is While a production motivated of target, reaching the irreducible then typically decay back to the StandardHiggs, Model giving on rise collider to length classic scales displaced bySimilar signatures mixing with typical signatures the of a arise Higgs in portalHiggs Hidden related [ Valley [ avatars ofpartners neutral charged naturalness under such a as QCD-like hidden the sector Hyperbolic gauge group. The subsequent decays of the hidden sector or,sufficiently if slowly such so decays assuch are to as unavailable, be the decay fraternal effectively backthe Twin detector-stable. hidden to sector, Higgs the and In [ the StandardBound variants lightest Model states hidden of sector with the bound the Twin states same are Higgs spin glueballs and or angular bottomonia. momentum quantum numbers as the Higgs These ingredients automatically leadnotably to decays exotic to decays boundlong-lived of on states collider additional of scales Higgs thethe varies bosons, lightest hidden from hidden most sector. model sector to bound Whether model. states the are In decay typically the pions products mirror that are Twin decay Higgs to [ lighter states in JHEP07(2020)029 . 5 , , . B 4 0 | r (5.6) (5.4) (5.5) (5.1) (5.2) (5.3) A B ↔ . τ H l | B A λ τ ρ B + , H 2 τ | ) A θ δy H | + mirror symmetry 2 ] and will be used cos r A 2 µ τ ]. In the Fraternal φ Z 70 l A + ˜ ) and the Twin Higgs 57 τ + breaking terms. A A ) θ 4 θ | 2 H H B Z , sin 2. For the ease of notation sin 2 2 τ H h | ˜ √ f µ y φ limit. In the same limit, after / − + + ( symmetry under which + ≈ . λ 4 2 | θ φ 2 A,B . 2 r B preserves the 2 are the f v Z A b − ˜ µ v f m κ m ρ l B λ H cos = | b Bµ ≈ ≈ h , charged under a mirror copy thereof. i B ≡ ( W θ κ B . and µ H , are related to the masses of the corre- =0 κ, ρ, σ b + A,B H + B B µ sin − µ δy h,φ V H f/v , σ | W 2 h W | 2 + V , B V µ λ B r A 2 2 h m W m + b – 17 – ∂ H l A | φ λf = ≈ b W 2 gM ∂ + A B 2 B W V + 2 ≈ ≡ v H | m 2 φ A + gM b Bµ m φhh H y 2 A Z | + v A + µ B , by µ 2 Z ≡ Z V r B m B µ 2 t ]. Formulas at all orders can be found in [ Z Z f l B − t Z M 70 2 , B , but breaks SU(4), and ˜ M W 2 H g | 69 B c W 2 B + 0) are the SU(4) preserving terms, g c 3 [ r A ↔ H 2 / t | > ( l A A + 2 t + 5–1 A = 2 m | / H 1 A L H t & | and y λ = λ κ/λ ) doublets is given by In the mirror Twin Higgs, the fermion content and Yukawa couplings are mirror copies The tree-level interactions of the two Higgs bosons with the SM and Twin gauge We can parametrize the Higgs VEVs as = B Yuk V L H free parameters leads toTwin Higgs, the the more relevant Yukawa minimal interactionsleptons are Fraternal those Twin of Higgs the third [ generation quarks and where the masses ofsponding the SM gauge twin bosons, gauge bosons, of the Standard Model.bilization of However, the the weak majority scale, of and these treating states the are masses inessential and to couplings the of sta- irrelevant states as cially in supersymmetric UVand completions of Twinin Higgs the models plots where that typically follow. bosons are In addition, the trilinear coupling of the Twin Higgs to two SM-like Higgses is given by In general, there can be substantial deviations from these approximate expressions, espe- where the approximated expressions holdEWSB, in the the mass of the twin Higgs and the mixing angle are given by where that exchanges we define The two copies of theThe Standard most Model general are renormalizable related Higgs( by potential a for the visible ( der the Standard Model and a second doublet, JHEP07(2020)029 b δy ZZ Solid = 1 m 1. The . = 1 mm. cτ = 0 cτ = 1 cm. For ρ 3.0 cτ light blue dashed

blue shaded horizontal

= λ 2.5

HL for details on the calculation @ correspond to constant values of LHC8 BP:1mm D region on the lower left corner of the

0.1 -

LHC = - 10 2.0 ] HL the extrapolation of the 8 TeV search. The (see text for details). We assume that 100% of TeV region cannot produce EWSB for [ cτ blue shaded ϕ dashed black lines – 18 – m 1.5

LHC are projections of the displaced searches to HL-LHC under BP:1mm 3 dashed red line

- gray shaded

- HL

@ , while the shows the projections at HL-LHC. The

10 HL @ γ

RoI:1m 2 - hh HL

IT:1cm μ :1cm . The λ

8 TeV = 1 since naturalness requires the top and twin-top Yukawa

IT 1.0

0.1 t blue line =

:1cm δy is probed by 8 TeV Higgs coupling measurements, while the indicates the exclusion for the CMS IT search at 13 TeV with pairs from the decays of the Twin Higgs eventually decay into glueballs.

IT 13 TeV f

region shows the exclusion from the CMS BP search at 13 TeV for oEWSB no RoI:1m B - hh Z overlaid with current and projected constraints from direct searches. We vary 13 TeV

μ , we show the status of a representative slicing of parameter space of the Fra- B f

0.5 region indicates the exclusion from the 13 TeV ATLAS muon RoI search for

2 1 5 4 3

6 Z

] [ TeV f red shaded indicate the value of sin . Parameter space of the Fraternal Twin Higgs model as a function of the Twin Higgs , and and φ in order to fix the lightest glueball mass to 50 GeV across the entire parameter space and B ¯ t m at low values of orange, red and dark orange lines B In figure shows the corresponding extrapolation to the HL-LHC. δg t ternal Twin Higgs model.of We refer the the Twin reader Higgs to ratesthe appendix into Twin visible and Higgs displaced into finalshowering glueballs states. to are capture While quite correctly, the we complex cascade takeLLP and decays the pair-production require of glueball a simplified final states detailed model to treatment for be of the well-described dark by purposes our of illustrating the potential reach where we havecouplings fixed to be essentially identical closephenomenology to the of cutoff. the These Twin couplings Higgs. define the dominant The the assumption of zerofigure background. indicates the The exclusion small searches from in resonance this di-Higgs case. production,band The which is strongerline than the the SU(4)-symmetric quartic, orange shaded for the lightest glueball.text. The assumptions The about thethe glueball same production modes decay are length,dark detailed we orange in show shaded the as a Figure 6 mass, and simultaneously single out representative valuesthe of blue lines JHEP07(2020)029 . 4 = 0. ρ 5 TeV, . 2 1 for this . ∼ = 0 ρ Higgs portal to the for the lightest glue- to fix the mass of the cτ becomes a more appro- δg 4 CP-odd and is enhanced compared to the b hh δy This has several novel implications. → 5 φ itself against sensitivity to much higher f – 19 – ] are particularly compelling, as they automatically 72 – 69 (blue shaded region in the figure). In some sense this gives the b 4 ], the MSSM-like Higgses can be lighter than the Twin Higgs, in → 70 hh 5 TeV, at least for the representative parameters chosen here. Suitable . 1 → ∼ φ associated production can become more significant, providing a new handle ¯ t t = 0, so that limits from prompt decays in current data and HL-LHC projections ρ and As discussed in [ b ¯ The two Higgs doublet model introduced in SUSY completions of the Twin Higgs is necessarily of Type b 5 doublet charged under the Standardhidden Model. sector, corresponding This to opens new adecay dimension-5 new of and CP-odd dimension-6 bound operators that states. allow In the particular, upon integrating outII, the for heavy which radial the mode, scaling of fermion couplings differs relative to the doublet model presented in section First, the relative branching ratios ofand the Standard heavy Higgses Model into fermions LLPs, changes Standardening significantly Model bounds from vectors, in the prompt singlet decay case, modes.as potentially weak- Second, fermionic associated productionfor modes LLP such searches. Third, there is a new massive CP-odd Higgs arising from the additional Higgs-doublet models, significantly increasing thebranching number ratios of Higgses into with LLPs. potentially large which case the doublet Higgs simplifiedpriate model characterization presented of in the section relevant phenomenology. scales. This necessarily entailsthe the “big” UV hierarchy problem completion such of as supersymmetrycompletions Twin or of Higgs compositeness. the models Supersymmetric Twin into UV explain solutions Higgs the to [ approximate SU(4) symmetry of thewith Higgs precision potential electroweak and constraint. are in Such betterextension UV agreement completions of necessarily both predict the the further Standard Model Higgs sector and the Twin Higgs sector into two- 5.2 New displaced signalsUltimately, from the Twin Twin supersymmetry Higgsproblem, and insofar its as they relatives do are not stabilize only the a scale solution to the “little” hierarchy searches at the HL-LHCsignificantly could exceeding potentially the extend reach of coverageOf searches to course, for masses prompt we of decay emphasize order productsparameter that of space we the to Twin have Higgs. shown illustratedisplaced only the searches a is value particular quite of sensitive slicing LLP to of searches, varying the the and Twin lightest the Higgs glueball coverage mass and of lifetime. direct and are driven by strongest possible projection fortiveness the of reach LLP searches of all visibleCMS the searches, IT more making and apparent. the BP Thedata searches potential 13 TeV have at effec- ATLAS the muon 13 TeV RoI potential suggest search, tomasses that the provide up LLP broad to searches coverage with of current the 13 TeV parameter LHC space for Twin Higgs lightest glueball to 50 GeV, andball also that to highlight the single sensitivity outfigure, of specific which various values leads LLP of to searches. a broader WeOne have parameter consequence chosen space with of successful this EWSBcase choice compared of to is that the rate for of LLP searches. For each point in the figure, we choose JHEP07(2020)029 (5.7) , and both A ... + B b 5 γ B b ¯ A d h Λ A u . The latter is typically the lightest h + bb ud − 0 c χ + B G · – 20 – B ˜ G A d 2 h Λ A u h gg ud c = , but this nonetheless opens up a rich variety of new long-lived 4 A /m 4 h A-portal MSSM m L glueball and the CP-odd bottomonium + − These simplified models can be mapped on to well motivated extensions of the SM. In this paper, we have initiated the systematic study of a second Higgs boson at So far, the LHC has focused on searches for new Higgs bosons decaying to Standard Twin Higgs models and their supersymmetriction completions of offer these a two particularly scenarios. cleanto realiza- hidden In sector Twin bound Higgs statesobservable models, (e.g. lifetimes. the glueballs) The additional that sensitivity decay Higgs of into bosons SM current can particles and decay with projected potentially searches for displaced decays analyzed the impact ofor these an limits additional on electroweakset doublet simplified of scalar models parameters coupled containing that to alimited, fully a new offering pair characterize singlet an the of scalar interesting phenomenology longsearches opportunity lived of for the particles. these to new models study The scalarand is the (decaying LHC either relatively complementarity in Higgs of conventional coupling ways LHC measurements or direct in to probing long lived the particles) parameter space. decay of the additional Higgses, theseat long-lived the particles can LHC. lead to spectacular signatures “the lifetime frontier”. Wedisplaced reinterpreted decays a at variety of 8 LHC and searches 13 for TeV both in prompt the and framework of a heavy Higgs scalar. We then Considerably less attention has beenbosons devoted into to new possible particles exotic thatinvisible) decays final undergo states. of further additional These decay exotic Higgs decays intothe may Standard provide heavy the Model Higgses main (or discovery and channels potentially fornew the both states new in states question alike. are long-lived. In When many produced well-motivated at BSM relatively scenarios, high the energies from the electroweak symmetry breaking —Standard potentially Model, motivated or by merely resolutionsparticles. another to instance puzzles of of plenitude the in the spectrum ofModel fundamental (SM) particles, as obtained in many minimal beyond-the-Standard Model theories. 6 Conclusion The search for additionalthe Higgs Large bosons Hadron Collider. is While aobserved the crucial 125 Higgs GeV component sector Higgs of of Nature boson, the may there physics trivially contain could program only readily at the be a variety of states associated with Higgs. The lifetimes of thesestates, CP-odd since states the are partial necessarily widths longera for than relative that their factor of decays the of into CP-even thechannels Standard connecting Model the are Standard suppressed Model by and the dark sector. which lead, among otherthe things, 0 to mixing betweenof the the pseudoscalar bottomonia Higgs, states, which might otherwise be detector-stable in the fraternal Twin the theory contains effective interactions of the form JHEP07(2020)029 ], which 73 ]. We thank Can ]. Since both these 74 35 , we will explicitly com- for the 13 TeV analysis. 2.1 2.1 ) plane. The contours of the ]. We thank an anonymous X 73 cτ , φ m – 21 – 9. The reason behind this simple rescaling is that . 0 ' 13 TeV /L 8 TeV L While this work was under preparation, we became aware of [ = 8 TeV: the ATLAS search based on the muon Region of Interest trig- , we show the excluded regions in the ( associated production of heavy Higgses with decays to LLPs, and the devel- s ¯ t 7 t √ ] and the CMS search based on the Inner Tracker trigger [ 41 The contours of the CMS IT search at 8 TeV are also qualitatively similar to the 13 TeV In figure -RoI search looks very similar to the ones obtained in section Indeed, the 13 TeV exclusionwith can the be luminosity roughly obtainedvery by little rescaling changed the in 8 the TeV data one selection linearly from theones, 8 TeV but to the the actual 13 TeV value search. of the signal efficiency deviates significantly form the 13 TeV ger [ searches have an updated version atpare 13 them TeV with discussed their in updates section efficiency at for 13 TeV. the Our 8 simulation TeV procedure searches for is obtaining summarized the in signal theµ next appendix. A Displaced searches atWe 8 TeV present representativesearches limits at obtained from the reinterpretation of two displaced The research of SGcollaboration is supported of in NC part andFoundation by (BSF) DR the Grant is NSF No. CAREER supportedPhysics 2014230. grant in for PHY-1654502. We part hospitality The also by duringsupport thank the from the the Israeli-U.S. the Kavli completion Binational National Institute Science of Science of Foundation parts under Theoretical Grant of No. this NSF PHY-1748958. work, and corresponding reinterpretation procedure for theKilic 8 and TeV CMS Chris LLP Verhaarenreferee for search for correspondence used a in regarding thoughtfulby [ report. [ the U.S. Thethe Department research Cottrell of of Scholar SAF, Program Energy through NC, under the and Research the Corporation SK for Early is Science Career supported Advancement. Award in DE-SC0014129 part and in a specific search for long-lived particles. Acknowledgments We thank Simon Knapen, Tedfor Kolberg, helpful Zhen conversations. Liu, We Simone thank Pagan Eric Griso, Kuflik and and Brian Oren Shuve Slone for discussions about the opment of boosted strategies tothe access larger LLP mass — differences that betweenpotential. the could heavy be Higgs and adopted by the LHCNote collaborations added. to maximizeinvestigates the the discovery prospects for discovering the radial mode of the fraternal Twin Higgs model these theories. Thislived can hidden be sector achieved bound ininto states spite di-bosons. are of typically Finally, the subdominant we factHiggs have compared investigated that to bosons the branching branching at prospects ratios ratios for thesearches into probing for HL-LHC, long- or highlighting discovering a new few new search strategies — most notably demonstrates that they can provide the strongest constraint on the parameter space of JHEP07(2020)029 . ] a X 3.0

75 0.3 + MET 300 GeV = j 50 GeV 2.5 X 2.5 =

X 0.1 ] for a heavy ] a m ] CMS IT search ] 3 41 41 - 2.0 10 2.0 ) plane for the two TeV TeV [

3 [ X 0.03 - Right: ϕ 1 10 ϕ cτ · ] 3 0.3 m , m 1.5 41 φ 1.5 m

2 0.01 - = 300 GeV, respectively. 10 1.0 X 1.0 that the 8 TeV data selection is m

1 1 1 2 3 4 1 2 3 4

1 1 0.5 BR in the ( 2.1

------τ τ · 10 10

10 10 10 10 10 10 10 10

σ ] [ ] [ x x m c m c = 50 GeV/ -RoI search at 8 TeV [ µ X m – 22 – 3.0 3.0 3 ATLAS = 50 GeV. ] and the ATLAS RoI trigger search [ 1 X 50 GeV 35 2.5 m Left: 2.5 = X 0.3 1 m ] ] 0.1 2.0 0.3 2.0 TeV TeV [ [ ϕ ϕ 0.03 0.1 m 1.5 m 1.5 0.1 0.04 0.3 1.0 1 300 GeV = ]. The upper/lower panels refer to 1.0 = 8 TeV. X 35 s . Contours of the excluded signal strength m

1 1 √ 0.5 1

1 - 1 τ τ

In addition to these two searches, we note that in the ATLAS ref. [

10 10

] [ ] [ x x m c m c jets at trigger is used todifferent tag search strategy shorter is displacements put forward incalorimeter. for the particles We decaying inner checked to that jets tracker. in boththe the Moreover, these CMS ATLAS in hadronic analyses inner ref. are tracker less [ resonance analysis decaying sensitive into than a [ pair a of combination displaced daughter of particles further decaying into hadronic Indeed, while the 8 TeV andthere are 13 TeV at analyses most have two aleast “prompt qualitatively tracks”, one similar the “displaced requirement 8 track”. TeV that analysisto This does the feature not one makes require of the that the there coverage 13 is of TeV at one the for 8 TeV search superior Figure 7 LLP searches discussed in theat text: 8 TeV [ analysis. In particular, wemore efficient already in showed selecting in the section signal coming from a highly boosted daughter resonance, JHEP07(2020)029 T 30 60 k . . . 8 5 which . 2 5 are given . ]. Instead of < 2 | 74 η branching ratio | < 5. For our active | . < × 2 η | 0 with an efficiency . 0 . < 1 < | ) signal events at each 60. No change is made η . b < ¯ 0 | . | bb ¯ 60 efficiency, independent η < b . | 5 m, 1 . 0 . → 13 ( 5 m, 1 65 efficiency for activating the . ], as can be seen in figure 0 m, . . selection with the following mod- 7 12 41 XX i 0 m, 1 , . 15 GeV flowing into the HCAL from xy < z < ]. Particle decays, hadronization, and 32 → 12 L 7 ns. We give each barrel vertex a 0 > . h 77 φ ] to define signal models for our analyses < r < [ < z < 5 m . 76 → [ 0 m 5 with efficiency of 0 < z < . . 0 m pp 2 . ], and detector effects are taken into account ’ assignment of tracks as jet constituents (but 0 are given a 0 – 23 – . 0 m < 78 . 1 [ | 0 and 5 1 GeV to be considered). For the purpose of veto- . η | 1 < ] reports a tracker-based search for displaced dijets, MadGraph 5 > | < < FeynRules η T 35 | Delphes 0 | p . 0 and 6 ] do not differ greatly. We therefore implement similar . η | 1 32 Pythia 8 < 0 m, . | 0 m, 1 7 0 m, . η . | 8 12 5 and use . 5 m, . < r < 6 = 0 ]. < r < < z < R 79 [ 5 m . 5 m 0 m ) signal point. . . < r < ] and at 13 TeV [ X 41 0 m , cτ . φ Delphes ] for the 7 TeV muon RoI analysis. For the reinterpretation of the 8 TeV search, , m 30 and 6 For the reinterpretation of the 13 TeV search, we modify our trigger efficiencies to 0 We validate this reinterpretation by comparing our cross section For both searches, we use a reinterpretation strategy inspired by the approach taken 60 efficiency. An event passes the trigger if it contains at least one LLP decay which . 80 . X m ifications, some of which areassociating modeled tracks off to the jets reinterpretation basedalgorithm performed on in angular with [ separation, we reconstructstill jets impose using that an anti- theing tracks jets have with ‘prompt tracks’ we define prompt tracks as those whose vertices are located limits to benchmarks given in the ATLAS analysesB.2 [ CMS InnerThe Tracker analysis CMS at IT 8 TeV analysisand at we mirror 13 TeV their [ event reconstruction and high within 4 vertex reconstruction volumes we nowof take 0 4 to the time delay or isolation requirements. occurred at a maximum delayefficiency from light for speed being of 0 reconstructedof the and triggering each requirement. endcapvetoing We vertex events furthermore with a LLP approximate 0 decay athe products n barrel. of isolation energy requirement by occurring at 3 Muon RoI Cluster Triggera and 0 decays inactivates 6 the trigger. Wethe then regions require 3 the reconstruction of two displaced vertices within For these reinterpretations we generate( 5 k in [ we define ‘barrel’ and ‘endcap’ trigger regions with flat, non-zero efficiencies. LLP decays B.1 ATLAS muon regionsAs of discussed interest in analyses theat previous 8 TeV section, [ theanalysis procedures pipelines for for the thereconstruction two ATLAS searches, searches efficiencies, which performed as differ informed primarily in by the auxiliary triggering material and made vertex available by ATLAS. For all our reinterpretations we use and generate the signal eventsshowering using are modeled with using B Reinterpretation of LHC searches JHEP07(2020)029 ] . . 5 32 xy L track xy where L 15 . N = 1 TeV, √ φ / m a comparison 1 50 GeV = ) Right: X m ( m X τ 0.50 c ATLAS 13 TeV Reinterpretation 1 TeV, = ϕ = 50 GeV. m differ by no more than 0 X 4 mm is considered a candidate . m ] and our reinterpretation as described 0.10 track xy 41 L , for an example mass point

9 TeV,

a comparison between the 95% sigma times

. ϕ→ →ϕ 1 σ 0.05

0.50 0.10 0.05 0.01

) ( ) ( ) ( % pb XX Br pp on Limit Upper 95 B.1 = 0 Left: φ 50 – 24 – m is the result given by the experimental collaboration and , is greater than 2 xy L 10 5 orange line 50 GeV = X ) m m ( X τ c ATLAS 8 TeV we ﬁnd the intersection of the track trajectory with the line passing Reinterpretation 1 .9 TeV, = , for an example mass point ϕ track xy 0.5 m L correspond to the result of our reinterpretation, where the error band are estimated B.1 5 mm of the primary vertex, rather than placing a requirement on their impact . In both panels the .

Then for each candidate secondary vertex in the event we further form clusters using To ﬁnd displaced vertices, rather than running an ‘adaptive vertex ﬁtter’, we identify 0.1

= 50 GeV.

blue dots

ϕ→ →ϕ σ are the number of events passing the cuts. 1 5

X 0.50 0.10 0.05

% ) ( ) ( ) ( pe ii on Limit Upper 95 pb XX Br pp To compute through the origin in the directionplane. of We the then dijet form a momentum, cluster assecondary of projected vertex maximal by onto track clustering the multiplicity together transverse from tracksWe tracks whose require associated that with this the cluster has at least one track from each jet in the dijet, that the cluster We assign to each groupgroup. a Any location, group which is whichdisplacement the contains from average tracks of the from the both beamline, secondary origins jets vertex. of in all the tracks pair in and the whose transverse the transverse displacement of the tracks in the cluster from the primary vertex, origins are within 1 mmorigins of are the within seed 1 mmstep track. iteratively of until the We no then origin furthertrack tracks add of can which to any be has tracks that added. not already groupWe We yet in then any repeat been randomly the tracks this assigned choose group, whose a process to and new a until seed repeat group all this and tracks begin in the the clustering pair process of anew. jets have been assigned to clusters. candidate secondary vertices usingassociated to a each depth-first possible ‘grouping’ pairingchosen of track algorithm jets as run in the the on ‘seed’pair event. of track the jets Beginning for tracks and with our create a algorithm, a single ‘group’ we of randomly- look tracks through consisting of all the other seed tracks tracks in and any the others whose and our reinterpretation asm described in appendix within 0 parameters. the from our montecarlo byN taking the variablebranching ratio we limits placed are by the plottingin 8 TeV and ATLAS appendix analysis multiplying [ itbetween the by 95% 2 cross section times branching ratio limits placed by the 13 TeV ATLAS analysis [ Figure 8 JHEP07(2020)029 ]. ]. 1, × in X 82 35 φ track xy L /m X m 1 event in the ) signal events ∼ b ¯ bb ¯ b 1 background event. ], an example of which → ( ∼ ] along with the following 35 ] towards signal parameters 33 XX 35 → φ ], but leads to an expected falloff in ]. However, we have found that jet → 35 35 pp ] is used to perform detailed analysis on 81 [ . In this regime, the decay products of the X – 25 – ] shows removes all but m typically forms jets containing significant numbers 35 . ROOT 9 and ] updates the previous CMS tracker-based search [ to cluster particles from different secondary vertices into φ 33 9 tracks, which the cluster track multiplicity distribution m Delphes < 4 GeV, and that the vector sum of momenta of tracks in the 5 at truth level. This has no impact on our reproduction of . > 0 Delphes 1. ≥ ) signal point. 8 GeV. If the event contains more than one secondary vertex which X R φ > , cτ T /m φ p X , m m X m At trigger level we apply a track reconstruction efficiency based on figure 12 of [ For this reinterpretation we generate 5 k This procedure faithfully reproduces the acceptance times efficiency for the heavy We mock up the event reconstruction andmodifications. selection described in [ We ignore tracks with probabilityof given track by reconstruction a as linear a approximation function to of the the fourth radial iteration distance from the beampipe at which a The CMS IT analysis atHowever, 13 the TeV [ 13 TeVcontains analysis tracks does from not bothsensitivity require of to the that the pair the of case reconstructedcollimated jets where and secondary identified cannot pair-produced be vertex as LLPs resolved, the but each dijet. requires decay more As to stringent background a a discrimination. result pair it of retains jets which are at each ( reconstruction-level events. Webranching validate ratio our limits to anlaysis benchmarks bycan given be comparing in seen the our in CMS cross the analysis left section [ panelB.3 of figure CMS Inner Tracker analysis at 13 TeV events passing cuts contain atangular least separation one secondary vertexthe whose efficiencies daughter partons for have the an efficiency benchmark as signal points in [ of a single secondary vertexsearch. would The fail tendency to for bethe resolved same and jet leads fall to outas an of unrealistically the the high acceptance acceptance jet for ofcompensate pair signal the for points passing this with inaccurate cuts aspect does of our not simulation, we genuinely additionally originate require that from signal one vertex. In order to clustering as implemented by of particles originating from differentextrapolating away secondary from vertices. the benchmark This signal parameterswith becomes in larger problematic [ separation when between particles become collimated, such that jets faithfully constructed from the decay products based on the value ofintegrated this luminosity discriminant considered. to give We anthe mock expected selected up background cluster of this contains discriminantgiven by in vetoing the events supplementary where data from [ scalar simplified model benchmarks presented in [ cluster satisfies contains clusters satisfying these requirements,track we multiplicity. select Finally, the the secondarytrack CMS vertex multiplicities of analysis of maximal forms the athe selected background cluster, vertex discriminant and and using the its signed the associated impact cluster, parameter the of RMS the of tracks in the vertex, and tunes a cut has an invariant mass of JHEP07(2020)029 1 where Right: 0.500 N ] and our √ / ]. We form 33 82 0.100 ) signal events b ¯ = 150 GeV. bb ¯ ) 0.050 = 100 GeV. Since no X b m ( CMS X m X τ 100 GeV c = m → ] and our reinterpretation ( Reinterpretation X m 35 0.010 XX 0.005 → = 1000 GeV, φ φ m s are pair-produced through a deriva- ]. We tune the precise values of both → X 0.001 82 4 - a comparison between the 95% cross section 10 0.010 0.005 0.001

× pp

5. ] is used to perform detailed analysis on Efficiency 81 3 mm, and require that tracks with transverse [ . Left: – 26 – for an example mass point 1 ROOT is the result given by the experimental collaboration and B.3 0, so we model a impact parameter uncertainty using . 0.500 and mock up the discriminant by requiring that the number orange line 5 mm comprise no more than 15% of the energy of the jet. 120 GeV for an example mass point, . = 0.100 ) track xy X m ( L m X B.2 τ ) signal point. c CMS 8 TeV 0.050 ] (see text for further details). X Reinterpretation 33 , cτ ], generating events in which the 1 TeV, φ = 33 ϕ m , m correspond to the result of our reinterpretation, where the error band are estimated X 0.010 m . In both panels the requirement. We also ignore the cut on the track in the vertex with second-highest 0.005 ]. We again use our depth-ﬁrst algorithm to search for secondary vertices, and ignore 2 For this reinterpretation we generate 5 k At the level of event selection, we go back to truth-level and then apply a track recon-

blue dots

82 ϕ→ →ϕ σ are the number of events passing the cuts.

0.001 0.005 0.002

% ) ( ) ( ) ( pe ii on Limit Upper 95 pb XX Br pp at each ( reconstruction-level events. Since no heavythe resonance collaboration, interpretation was we directlyCMS validate given analysis our by [ analysis by emulating the jet-jet model given in the rameter resolution, which we againclusters mock as above up using by approximatingof figure tracks 20 in of the [ when cluster rejecting is jets greater with too thanone many 5. track prompt with tracks: We 3D use we impact require slightly parameterimpact that below different parameter the 0 definitions below jet of 0 has no ‘prompt’ more than struction efficiency now based onof [ the final iteration ofthe track reconstruction from figuretransverse 12 impact parameter significance. The analysis also requires the 3D impact pa- reinterpretation above. Theparameter definition significance of larger ‘displaced than 5 a tracks’ piecewise requires linear a approximation transverseof to impact these figure 20 approximations ofdifferently. based [ on the validation data. Endcap tracks are not treated reinterpretation as described inheavy appendix resonance interpretation was directlythe given jet-jet by model the of collaboration [ we validate our analysis on given track begins. We use the same modified definition of ‘prompt tracks’ as for the 8 TeV the from our montecarlo byN taking the variabletimes we branching ratio are limits plottingas placed and by described the multiplying in CMS appendix ita IT by analysis comparison 2 at between 8 TeV the [ efficiency reported by the CMS IT analysis at 13 TeV [ Figure 9 JHEP07(2020)029 , B τ . By 1 mm 5 TeV . 9 ) signal & X algorithm 05 to each . T UV , cτ k φ not far from the and 0 , m equal to the SM B s b X ¯ ]. The logic of this . The spectrum of b g B 2 m g 57 QCD , and the dark tau, B b 8 to decay to . , are required and demanding nat- i B W . We assume a dark photon to not be requirement on the LLP decay products tB y signal events at each ( T H . – 27 – XX and the dark EW coupling b,τB y → B t 4 on the LLP decay products directly to mimic the y . φ 0 a branching ratio of 0 → X pp R > 4, and place the . boson. We compare the resulting efficiencies to benchmarks given ] reports a search for dijets displaced from the beamline by 0 , and the dark gauge bosons, Z B 34 t amount of states in the dark sector to preserve the naturalness of the 10%. We implement this recipe as instructed, with the caveat that we ]). Finally, a dark QCD is also required with a coupling . > ¯ u within 1% and 10% respectively. A dark bottom, 83 and the approximation we used to estimate the signal rate for displaced events. ¯ d, u UV 5 minimal ¯ s, d The Twin sector contains a copy of QCD whose coupling cannot be arbitrarily different The dark top, ¯ c, s c in the Fraternal Twin Higgsthe and phenomenology show the discussed portion in of this parameter paper. space which isfrom relevant for Standard Model QCD becausesectors. of This the approximate leads mirror to symmetry dark between confinement the at two a comparable scale to Λ ones at Λ are required for anomalydifferent cancellation from in the the dark SMpresent, sector, one as but as their its long coupling presence(see as can e.g. would be ref. introduce [ vastly anotherSM portal one. and Given these modify premises, the in phenomenology what follows we review the structure of the dark sector Twin Higgs construction. Notonly surprisingly, this a logic handful fixes of the darkcouple masses sector the and states most the which to couplings are the of the SM mirror Higgs. partners ofuralness the fixes SM the states which dark top yukawa Here we describe the naturein section of the dark sectorWe focus we on used the as Fraternal a Twinbottom benchmark Higgs up for proposal construction first our discussed discussion isonly in to ref. the [ introduce below a given UV threshold scale Λ point for this analysis, andof give C The dark sector of the Fraternal Twin Higgs avoid relying on thelar reconstruction separation of displaced requirement jet ∆ requirement objects. that We two instead jetswith impose are distance an reconstructed parameter angu- from 0 eachthemselves. decay We with generate the 5 k anti- B.4 CMS 13 TeVThe ‘beampipe’ CMS analysis analysis [ to 20 mm. Asimulated ‘recipe’ data is which was providednal tested for efficiency to the be reinterpretation accurate of to the 20% results for using a truth-level variety of models with sig- in the CMS analysis,tuning an our example implementation of of whichresolution, the can and track be the reconstruction seen discriminant probability,is we in the clear are the impact that able right parameter a to panel moreresponse achieve of faithful reasonable that figure reinterpretation agreement. we will do However require not it additional have details access on to. the detector tive coupling to the JHEP07(2020)029 ) B t m (C.4) (C.5) (C.6) (C.7) (C.8) (C.9) (C.1) (C.2) (C.3) ( state. B QCD Λ ++ > by lattice com- B b 0 , m M , 2 0 0 1 , b b 0 2 6 M M 2 s 54 8 . . g = 3 but at most 2 active 1 0 scale. If . c b b , is to use for the renormal- f = 1 = 1 N N + c (2) B QCD 1 + B QCD − 2 , . ++ 0 N G G 2 0 3 1 10 b , b 2 b , and its mass is related to the Twin B QCD δg. − − δy = 0 while, in the other limit, we use f 8Λ ++ · . flavor in the theory. We first define the 2 s f N by imposing a boundary condition at the g v f 1 1 0 N (Λ) + · π = 6 b b , A s b c 4 − g f / N 2 m c ++ 0 2 active – 28 – N ) G N 2 3 = 2 s B s -symmetry relating the Standard Model QCD and g m ) with g B 2 − 0 1 ( − b (Λ) = b Z 2 = c c 2 B s m C.1 ≡ 0 g N N − ,,,... m m = 1. 0 0 0 B s M 3 3 11 34 f 7 α M M M ]: N 4 5 7 quantum numbers 0 = = . . . exp 84 0 1 b b µ ] slightly differs with this definition in order to match with the standard PC ) in eq. ( = 1 = 1 = 1 57 J = B + − b 2 ) with − 0 + 1 ++ G m ] G G ( is then the one of a gauge theory with m C.1 QCD m m 85 Λ B s ]. , = 0 QCD [ , we can develop a more quantitative picture of the Twin spectrum. The α B QCD 84 , the mass of the lightest f 84 µ N B QCD ) in eq. ( is the SM bottom quark mass computed at the Λ B t b m m ( Given Λ A way to define the Twin QCD confinement scale, Λ First we identify the Twin QCD confinement scale. Recall that Notice that eq. (35) of [ The two lattice computations agree very well but for the presence of the extra excited 0 6 7 B QCD lattice definitions [ The masses of theputations additional on stable glueball states are set in terms of then we takeΛ Λ lightest glueball carries QCD scale as [ constant will run fastersuch in that the IR. We also allow the dark bottom Yukawa towhere be modified UV cut-off, Λ, whereits we counterpart expect to the be satisfied up to small deviations, The running of flavors, the Twin top and the Twin bottom. As a consequence, the Twin strong coupling ization scale, dark strong coupling constant where trum of the dark sector.scale In is the an Fraternal Twin SU(3) Higgs, gaugeconfined the field twin Twin sector theory, QCD with near being the at either confinement most the one glueballs flavor or and the the bottomonia. lightest states in the bound states arising from Twin QCD confinement depends sensitively on the fermion spec- JHEP07(2020)029 , 5 + − 0 χ

5 v 0 sector

m (C.10) (C.11)

f G 0 G

G . 4 <

bb 0 bb M

m m .

6 4

- - ) 3

10 10

Τ= Τ= m yb

c c

2 ∆

- B QCD .

Τ= B

c b + Λ 2 B B b ¯ 100100 GeV GeV b 1 m we ﬁx the Twin Higgs VEV to is not allowed to be heavier † A Τ=

c m 0 H ] 50 GeV A = M 0 Λ 86 1 Left: M = 2( H ), 25 GeV . bb H v , is the LDP, darker shading indicates 0 c 0 ++ 1 . As one can see, in the most natural 5 G χ G + . of 10 m 0.02 0.04 0.06 0.08 0.10 0.12 0.14 0.00

. B ------

g f v ∆ . cτ G · = 5 ++ 0 B χ f 5 G – 29 – m † m A 6 glueball, i.e. - . H 3 v

10 0 2 A =

−

Τ= f G 0 Λ ++

c + 1

H G χ 4

gg H ®

0 m

m c

4 bb - G

< = 10 bb

Τ=

c the Lightest Dark Particle (LDP) can be either the CP-odd −− 1 3 χ b

m yb m

2 ∆ δy

- H-portal SM

10 . L 100 GeV

Τ= There are two leading portals that connect the bound states of Twin

c + and − 0 2 χ

1 m δg m

Τ= we ﬁx the Twin Higgs VEV to

50 GeV

0 sector:

M . Summary of the structure of the dark sector in the Fraternal Twin Higgs. The light 1

25 GeV A

0 Right:

M . v 0.12 0.14 0.04 0.06 0.08 0.10 0.00 0.02

------

= 3 g ∆ These portal operators both allowbound the states SM-like and Higgs enable to the decaythe bound into Higgs. two states While or with there more appropriate are Twindimension quantum additional QCD numbers or portal to involve operators mix states beyond with neutral these, under they appear Twin at QCD. higher QCD confinement to theHiggs, Standard they Model. can be At writtenwith low in the terms energies, of below higher-dimensional the operators mass that mix of the the Twin region of the Twinthan Higgs roughly parameter 100 GeV. space (i.e. Dark hadronization and spectrum. Twin-SM portals. Depending on bottomonium or the CPas even highlighted glueball. by We the will spectrum focus presented here in figure in the case where the LDP. Blue dashed contoursf denote the average For the spectrum of the stable bottomonia, we take ref. [ Figure 10 pink shaded region showswhere where the decay the of 0 bottomonia into glueballs pairs is allowed. Red contours indicate the mass of JHEP07(2020)029 ]. (D.1) (C.12) (C.13) (C.14) 87 glueballs ) for the ++ D.10 , that can be 3 0 state via an off- κm ), the scalar lightest ++ = 3 0 C.11 F , . 2 = ) i 2 0 gg 0 m 3 0 G | → ) is the width of a Standard Model − 0 B κm glueballs is given by 2 h (Φ G m ( · m ..., h LO ++ 2 B v + Γ Λ G 3 Φ 2 3 ... | 2 c 0 m B π s 2 h + πf 8 α b – 30 – f 12 ) arise from the Twin bottom Yukawa coupling ) y 0 , we show in blue the lightest glueball proper life . Correspondingly, also the heavier 0 quantum numbers are either stable or quasi-stable, = = m 25), while Γ Φ) = . πv ( 10 C.13 2 0 h gg H bb H PC Λ Λ c c → J ), the resulting lifetimes are typically too long to give ' = 6 ∗ κ h gg ) = Γ ; the red curves represent the glueball mass in GeV. For the ( πf 0 ++ . The width of the 0 δg ) comes from integrating out the Twin tops in the infinite mass LO G 2 0 σ . In figure Λ Γ( 0 / → and 2 C.12 m b v δy ++ ) is the scalar width into gluons (and is given in eq. ( gg = 1 and Λ = 2 → 3 will be unstable and will decay back to the SM in a Higgs-like manner, with c we sketch the structure of the displaced processes of interest. Since the process (Φ ++ parametrizes the matrix element 11 LO κ The gluon fusion cross section for a scalar Φ can be written at leading order as The glueball states with other The Wilson coefficients of both operators have irreducible infrared contributions of where Γ Twin Higgs). This cross sectionon is the known to mass be of enhanced at the NLO scalar. by 60%–90%, depending For our numerical calculations, we take the state-of-the-art In figure is fairly complicated, it isseparately. useful to factorize it into different building blocks that we discuss appreciable decays inside the LHC detectors,In and instead its generically totality, lead the to pure missingback energy. glueball to spectrum the contains SM a with variety Higgs-like of branching states, ratios of and which withD two a decay macroscopic life-time [ Final states and rates in the Twin Higgs decay lengths. depending on the detailedEven spectrum when decay in modes theshell invariably Twin Higgs exist, sector boson such and (2 as the the available decay decay of modes. the 2 extracted from the lattice dataHiggs ( boson with mass time as a function of plots, we fix will have Higgs-like decays thanks to its mixing with the Higgs boson with macroscopic a width suppressed by where The contribution in eq. ( limit, while the contributionafter in mixing is eq. taken into ( account.glueball Thanks 0 to the first operator in ( the form JHEP07(2020)029 , (D.5) (D.6) (D.7) (D.8) (D.9) (D.2) (D.3) (D.4) )) (D.10) τ ( f , , ) τ ! ! − A B 4 φ 4 φ 4 V 4 V m m ) is the standard m ] which is due to the m τ ( 70 f (1 + (1 + 12 + 12 τ 3 2 A B 2 φ 2 φ 2 V ]. The Twin Higgs cross 2 V . 8 m ≡ ) m m m 31 s ) 4 4 τ √ ( , − − φ 1 1 m

( , , ,A 2 h 2 / 2 2 / 2

1 / → 1

, 3 , ! SM gg ! 2 ! 2 is the Twin gluon. Q A / φ Q B / 2 φ 2 φ φ 3 B θσ 2 V 2 φ 3 2 V 2 b m B m m 2 m ! m m m ! 4 g m m 4 m , B 4 2 f 2 φ 2 φ 4 2 t 4 2 m m m / − – 31 – m − A − A 1 4 1 4 1 1 ) = sin t,b ! ) and t,b −

− = 2 h 2 φ

= X 2 1 X 2 √ Q 2 1 Q θ m m

θ ,

4 φ W, Z 2 2 2 θ 2 θ sin θ m − cos θ cos ) has a factor of 1/2 with respect to B.29 of [ ( = ( A 1 φ B sin φ 2 V 3 φ cos sin 2 3 φ V D.9

→ cos 2 V m 2 2 3 φ φ m m f 2 b 3 φ φ 2 gg φ 2 f 2 πM 3 2 m B m πM σ 3 g πv m m m π g 2 f πv 2 π b 2 φhh 64 2 t πv πm 2 sA 64 16 ) for . 2 sB m A V 16 α m δy V 16 32 144 3 α s 2 W 3 3 144 s φhh c 2 A / ) = ) = ) = ) = ) = ) = ) = ) = A A A (1 B B B B g f hh , V will be given by t b g V A A A B . Cartoon of the production and decay of LLPs through heavy Twin Higgs states. B s B g B f t V → b g V √ = 1 φ → → → → → → V → Γ( φ φ φ s φ φ φ φ Γ( Γ( Γ( Γ( The partial widths of the Twin Higgs to dark sector particles are Γ( Γ( Notice that the width in eq. ( Γ( 8 Figure 11 different definition of where gluon fusion loop function. The LO decays into SM objects are NNLO+NNLL values for thesection at SM Higgs cross section from [ JHEP07(2020)029 (D.14) (D.15) (D.11) (D.12) (D.13) undergo B b ]. As expected, , , , 1 7 89 φ final states, while π 2 2 decays with respect 8 B v f λm b ¯ ) = B − b hh ZZ 6= 0 the mixing receives 1 ) = B → ρ W hh 2 h φ B m 2 → W ). NLO corrections can shift the − φ ρv BR( 2 2 φ π. Γ( 5.4 ≈ m ) . ≈ pairs. In both cases these in ( + ) λ B A,B b 2 A,B 2 W φhh v f ⇒ W A 2 A,B − A,B – 32 – W 1 1 . W . → 2 h φ ρ ]. These can be included following [ → φ λ m φ − 88 6= 0 also the trilinear coupling gets modified. 2 h 2 /m − still allows a large portion of the parameter space of the λ ρ Γ( BR( Γ m 2 φ 2 1 2 1 λ − m 50% [ 1 ≈ ≈ ) ) − ∼ 2 φ 2 2 (i.e. for large mass of the Twin Higgs) we recover the result from f v f m A,B A,B bosons decay (in part) to Z Z = ' Z θ , κ , ρ A,B A,B 2 2 φhh Z Z g A sin → → φ φ λ Γ( BR( The production of glueballs through decays of the heavy Twin Higgs proceeds through One important lesson we want to emphasize is that for ticles in the final stateenergy, while may providing reduce stronger the coverage sensitivitydisplaced from of searches vertices. some that LLP combine Detailed searches missingment study that energy of of veto dark with missing the showering and finalFor hadronization, states the which is necessarily sake beyond requires of the a illustration, scope of careful we the treat- estimate present work. the branching ratio into glueballs coming from tion of Twin bottoms leadsaccessible. to annihilation Likewise, decays pair-produced intopair-produced Twin Twin Twin tops glueballs when decay kinematically into subsequent annihilation decays intofrom Twin these processes glueballs. are rich Ofparticles complex, course, and with a widely the variety varying of final multiplicities. both states The long-lived presence resulting and detector-stable of additional detector-stable par- to Goldstone theorem limit. For a variety of channels. Whileis relatively the small. Twin Higgs A far hasstates larger direct which production decays undergo rate into subsequent arises Twin annihilations from gluons, and/or decays this decays. into rate heavier In dark particular, sector pair produc- This effect makes theregion for branching the ratio Twin into Higgs SM somehow Higgs weakening the pairs bounds dominant from in the light mass than 1 TeV while theexpression. trilinear Expanding coupling the full is expressions, always we well get approximated by its leading order The resulting upper boundComposite on Twin Higgs to be probed by LHC narrowimportant width corrections resonance (bigger searches. than 10%) in the region where the Twin Higgs is lighter where the branching ratioslimit in we the can different also channels estimate approach the the narrow same width constant. limit for In the this Twin Higgs resonance decay into Twin gluons by in the limit the Goldstone equivalence theorem where we have defined the triplet interaction JHEP07(2020)029 , , (2015) ]. 91 SPIRE at the LHC IN 1 ][ − fb (2012) 1 10 GeV with the CMS Phys. Rev. D 716 , to be 100%. The resulting . In (light) gray, we show the 3000 6 pb 125

- f 10 B 1 ]. Z - 10 B , and 2500 = 0). The blue shaded region at low Z φ arXiv:1207.7235 ρ SPIRE m 5 pb [

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