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JHEP02(2018)048 Springer February 8, 2018 January 22, 2018 : December 29, 2017 : November 15, 2017 : : Revised Published Accepted Received Published for SISSA by https://doi.org/10.1007/JHEP02(2018)048 . 3 1711.03107 The Authors. c Beyond , Higgs

Twin Higgs models are the prime illustration of neutral , where the , [email protected] Johannes Gutenberg University, Mainz, 55099Laboratoire de Germany Physique Th´eorique,CNRS, Universit´eParis-Sud 11, Orsay Cedex, F-91405 France E-mail: Faculty of Physics, UniversityPasteura of 5, Warsaw, Warsaw, 02-093 Poland PRISMA Cluster of Excellence & Mainz Institute for Theoretical Physics, Open Access Article funded by SCOAP ArXiv ePrint: , which have interesting signatures involvingobservable displaced at vertices the and . are potentially Keywords: breaking, including explicit softis and employed. hard breaking The terms direct in andspace the indirect scalar of searches potential, Twin at the Higgsdecays LHC models of are used through the to mixing heavy probestudy Higgs of the the to the parameter production the heavy and SM Higgs decays states. of with twin Moreover, the for SM and the bottomonium Higgs Fraternal states and Twin to Higgs, the SM we light Abstract: new of thethe twin little sector, hierarchy gauge problem.the singlets heavy of In Higgs the this of Standard work,troweak the Model symmetry we Mirror breaking (SM), analyse Twin is ameliorate phenomenological Higgs linearly realized. implications and Fraternal of The Twin most Higgs general models, structure of when twin elec- Higgs Aqeel Ahmed Heavy Higgs of the Twin Higgs models JHEP02(2018)048 problem 4 15 8 27 9 naturalness/hierarchy 18 22 7 25 – 1 – is one such class of models, where the top-partners are not charged ] is the prime and first example of neutral naturalness, which is 4 – 1 1 25 Neutral Naturalness 4.1 Fraternal Twin4.2 production and Fraternal decays Twin4.3 hadron phenomenology Heavy Twin Higgs phenomenology 2.1 Physical basis2.2 for Twin Higgs Electroweak models precision constraints in Twin Higgs models under the SM gaugeHiggs symmetry, (TH) so model they are [ designed very to hard resolve to thenutshell, produce little TH at models hierarchy the have problem two colliders. and core make ingredients: Twin the (i) the top-partners SM-like elusive. Higgs is In a a Goldstone in the last fewsupersymmetry, decades composite constructing Higgs, BSM and(top scenarios. extra partners) dimensions Most just predict of above someHiggs the the sort . BSM electroweak of However, models scale the new absence to including physics hierarchy” of (fine-tuning) cancel such problem. the new Hence, physics there signatures correctionsscenarios is at a which to the need can LHC to the explain pose construct and the a analyse “little elusiveness new of BSM the top-partners and solve the SM puzzles. interactions, however, it is not a completepuzzles theory which of go since there beyondrelatively are light many SM the unanswered Higgs has Standard highlighted the Modelmore need than to (BSM). ever address before, In i.e. therecorrections particular, should to the be the some discovery mechanism Higgs which of mass. cancels a the SM Motivated radiative by naturalness, enormous work has been done 1 Introduction The discovery of a scalar bosonits with mass properties 125 show GeV that at the itThe Large is Hadron SM consistent with (LHC) of and the Higgs physics boson is of the the Standard most Model accurate (SM). theory of elementary particles and their A Twin Higgs Feynman rules and partial decay widths 5 Conclusions 3 Heavy Higgs phenomenology in4 Mirror Twin Higgs Heavy Higgs phenomenology in Fraternal Twin Higgs Contents 1 Introduction 2 Electroweak in Twin Higgs models JHEP02(2018)048 – ], 5 ++ hat 19 twin ]. of the 1 ++ 6 Goldstone ] states [ b ˆ 7 b ˆ ]. twin . ]. These features of 5 11 – ++ 6 ] and bottomonium [ , can be much larger than that of ] employs an SU(4) global symme- ˆ g ], composite/holographic TH [ 1 g ]. In most of the TH models, it is qcd 18 ˆ Λ – 35 – 12 25 c SU(2) of SU(4) global symmetry is gauged, symmetry. × 2 – 2 – Z ]. Moreover, among the fraternal twin hadrons, the 5 This mixing to exotic decays of the fraternal 0 SU(3) coset are “eaten” by the weak gauge of the SM / 1 ) sectors. The remaining one serves as the SM ˆ Z , ]. In order to solve the little , the FTH model 5  ], however, in the FTH case the stable twin hadronic states are the . Hence, the fraternal twin hadrons (/bottomoniums) can be ˆ ]. Note that the twin hadrons are colorless under the SM QCD. The 2 W 5 c SU(2) represent the SM and twin weak gauge groups, respectively ( qcd α twin hadrons are also present in the MTH model, however, given the usual spectroscopy of ++ ), but the fraternal twin hadrons are glueball [ˆ ) and twin ( ˆ c ) the fraternal twin QCD confinement scale, ˆ s, ii ,Z glueball and bottomonium states have the correct quantum numbers to mix with the There are many variants of TH models which offer UV complete description of the However, in order to manifest the features of the twin , one does not The simplest realization of twin Higgs mechanism [ ˆ The 0  d, ” denotes twin sector). After TH electroweak symmetry breaking (EWSB), 1 ], and some more recent TH constructions [ ) unlike the MTH model, there are no fraternal twin hadrons with light flavors b ++ i u, W assumed that the radial modeheavier. of Hence TH the EWSB radial is mode of is the integrated order out of and symmetrymirror low-energy breaking twin effective scale hadrons, theory or thesehadrons). contains states Hence, have phenomenologically low they production have less multiplicity impact and than are the unstable fraternal (similar 0 to SM 0 scalar sector of thehadrons model. back into thethe SM FTH light model are and similar to at those the of colliders theTH [ ‘hidden mechanism; valley’ models including [ 24 supersymmetric TH [ relatively heavier [ lightest stable twin hadrons in thematter MTH candidates model [ are the mirrorlightest glueball/bottomonium which states could [ be dark 0 ( (ˆ and ( the MTH model, whichQCD is couplings due ˆ to fewer twin quark flavors and faster running of the twin to the SM Higgs mass.Higgs’ This (FTH) possibility model was first [ requires discussed only in the the third so-called generationtwin ‘Fraternal of sector. Twin quarks and Another leptons, striking and differencespectroscopy the of in weak the the gauge FTH two bosons model models. in to In the the particular, MTH the case FTH is model twin has hadron two interesting features: Higgs. The originalcopy incarnation of of the SM this particle idea, content, where is referred the as twinneed ‘Mirror sector to Twin has Higgs’ have an (MTH) anminimal model exact exact number [ mirror of copy states of are the necessary SM to ensure particle the content cancellation in of the radiative corrections twin sector, but rather a try which is spontaneously brokenbosons to SU(3) and a at radial a mode. highwhere energy A SU(2) scale subgroup Λ and SU(2) and gives “ Goldstone bosons of SU(4) ( tected, and (ii) the twinwhich top explains partners their are elusiveness neutralof (“colorless”) at radiative under the corrections the LHC. to SM thewhich In gauge are SM group, twin related Higgs Higgs to mass mechanism the are the SM due by cancellations to a the discrete exchange of new twin states which emerges due to spontaneous breaking of a global symmetry, hence its mass is pro- JHEP02(2018)048 ]. 16 ] for the 38 , 37 = 125 GeV and its h m ]. Moreover, see [ 36 , 16 , 5 , 2 in fact, is favored by the electroweak breaking parameter. In this work, we 2 2 Z ). Note that the TH symmetry breaking can 2.2 – 3 – = 246 GeV, we are left with three free parameters; the v hadrons through heavy twin Higgs are about the same order as ++ ]. In this work, we aim to investigate the phenomenological aspects of 42 – 39 , 33 – . We consider the most general form of TH scalar potential with soft and hard b H 25 , 5 In the case of FTH, the phenomenological study of the twin hadrons (twin glueball and To analyse phenomenological aspects of the scalar sector of the MTH and FTH models, Twin Higgs scalar sector provides a portal between the visible (SM) and invisible A possibility of twin Higgs radial mode is also discussed in [ discrete and SU(4) global symmetry breaking terms. The effective TH scalar potential and 2 2 twin QCD confinement/hadronization. However,estimates for of our the purposes, twinrates we hadron make for production conservative the through twin the 0 heavy twin Higgs. The production phenomenology of the radial mode in composite Higgs model. of-mass energy. Moreover, indirect searchesmeasurements at and the its LHC, invisible via decaysector the width, of SM provide the Higgs a TH signal-strength complementary models. probe to the scalar bottomonium states) is much more involved, mainly due to the lack of proper knowledge of It turns out that dominantSM decay weak channels gauge of heavy bosons,with twin and Higgs equal twin are branching weak pairs fractions. ofgauge gauge the bosons bosons This SM and (if Higgs, makes the kinematicallycolliders. the SM allowed), We heavy Higgs roughly perform Higgs as a detailed the decays analysis prime to of channels the these to channels SM at discover massive the the LHC TH with models 14 TeV at center- the explore the parameter spacethe spanned LHC. by Note these that three relativelyto free small discover number parameters the of of free twin the parameters Higgs TH offers mechanism models a at unique at the opportunity current and/orwe future calculate the colliders. branching fractions of the heavy Higgs to the SM and dark (twin) states. H Z has five parameters, however,vacuum after expectation fixing value the (vev) SM-likeheavy Higgs twin mass Higgs mass, its vev, and the hard phenomenological analysis of the scalar sectorwork of done TH models. on Recently, different theree.g. has aspects [ been of some the THthe scalar scalar sector sector of involving MTHthe only and fundamental FTH the scalar of models SM SU(4), focusing Higgs, which on breaks see heavy the twin global Higgs. symmetry, by We two parametrize Higgs doublets considering any specific perturbativescalar UV sector complete of scenario. the Inthe TH radial this mechanism mode. work, with we The a twin explorehence focus radial we the mode on refer is the it heavier as phenomenological than ‘heavy’ the implications twin SM-like of Higgs Higgs. of mass(twin) 125 sectors. GeV, Hence, the discovery potential of twin Higgs mechanism needs a detailed realized then, in principle, the radialscale mode and can be can much lighter be thanprecisions present the tests symmetry in (EWPT) breaking (see the below, low-energy section be theory, linearly realized in a perturbativeHowever, UV we complete work TH in model, an e.g. effective supersymmetric field TH theory [ (EFT) framework of the TH models without only the Goldstone bosons. However, if the TH spontaneous symmetry breaking is linearly JHEP02(2018)048 b b b b ¯ ¯ , is 2 0 (2.1) (2.2) (2.3) (2.4) λf = 2 + + 0 0 0 ˆ 2 h production via ˆ ˆ G G m + 0 hadrons (glueball ˆ G ˆ h . ++ 0 , is a radial Higgs which H at the LHC and decays to > 0 ˆ h t t H f = H twin hadrons decays are either

t twin glueball ) , , . 2 H ++ 2 . An illustration of a benchmark pro- (      ++ 2  H  2 0 0 0 V H d 2 0 / 2 2 f 0      d f −  . The 0 − 0 2 Π g g Figure 1 cess of 0 heavy twin Higgs the SM bottom quarksHiggs. through an off-shell SM 1 f i H H †  , λ H and – 4 – 1 4 A exp λ Goldstone bosons and con- 2 . The 5 1 ) = 7 , √ ) = 2 H ( H = ( = 0 V V H 0 f = 0. Note that mass of the radial mode can be much lower than H

) H . Twin Higgs potential for the EWSB is λ > ( H 0 d f dV Goldstone bosons. For the TH symmetry breaking we employ a scalar 0 and 7 ), we get a quartic potential for the radial Higgs , respectively. Section > hHi ≡ 4 2.1 2 0 f and 3 The paper is organized as follows. Twin which belongs to fundamental representation of SU(4) and parametrize as, The above conditions insure thatpositive for mass squared of the radial fluctuation, where using ( In order to have a global minimum of the above potential we require, where Π is aacquires a matrix vev containing the H 2 Electroweak symmetry breakingWe in consider Twin the Higgs TH models modelsSU(3) providing where an SU(4) global symmetry is spontaneously broken to tains the summary andlect conclusions. supplementary We col- material inwhich includes appendix Feynman rules and partialcay de- widths of the heavy twinand Higgs twin to sector the SM states. Higgs symmetry breaking details,of the physical choice basis, andTH EWPT models constraints on are presentedphenomenological in analysis section of theof twin the Higgs MTH and FTH modelssections are presented in and/or bottomonium states) decayHiggs back mixing, to see the a SM prototypeprompt process light or in quarks displaced figure and depending leptonsa on through unique their discovery the kinematics. potential Especially, for the the displaced FTH signals model offer at the colliders. those of the SM Higgs and massive gauge bosons. These twin 0 JHEP02(2018)048 2 Z (2.5) (2.6) discrete 2 Z . , 4 | ]. ! 3 H 16 | ˆ h 2 ρ i , in order to not Goldstone bosons ˆ h λ i + + 7 2 0 ≤ + | ˆ h ) 1 H | ˆ h + 2 0 1, we recover a non-linear ˆ v 0, this terms is the source of σf

κ, σ, ρ  2 > − 1 λ 2 discrete , as a result √  0 4 f | 2 SU(4) symmetries and it helps to ≡ Z b / H are degenerate in the absence of | 2 b H v Z + 4 symmetry, however, breaks SU(4) global | SU(4) explicit symmetry breaking terms 2 and ˆ H , / Z | in a linear sigma model framework, i.e. v 2 ), which is phenomenologically not a viable ) sectors. Hence, in the unitary gauge, we ]. ! κ Z κ ˆ 3 Z H 1. Whereas for 16 , + 2 + – 5 – ih  λ 2 ih + ˆ Goldstone bosons are “eaten” by the weak gauge λ <  W (2 0 + 2 0 6 h 2 p f 1 . As noted above, for for / 0, the vevs h + b discrete and SU(4) global symmetry breaking terms can 0 0 H − f v f 2 2 |

Z ↔ = κ > b H 2 | v 1 H √ . + = ˆ ) and twin ( 0 2 ≡ ˆ h v | ,Z H  |  W ], λ SU(4) breaking terms are important in the above potential to generate are doublets under the SM and twin SU(2) weak groups, respectively, are their respective vevs. The most general TH effective scalar potential / ,H 16 2 , b v ) = ! H 5 Z b b H H H -term ‘softly’ breaks both SU(4) global and -term is invariant under SU(4) global symmetry as well as respects -term captures ‘hard’ breaking effects of -term is invariant under the discrete

and ˆ ρ λ σ κ and H, ( v = eff H H reduce the fine-tuning in TH models [ symmetry explicitly. For breaking term, i.e. option. a misalignment of the two vevs is generated. symmetry under which spontaneous breaking of SU(4) globalplus symmetry a to radial SU(3) mode giving V The The The The We impose unitary gauge where Before moving forward, we would like to discuss the role/significance of each term in In this work, we parametrize the scalar 4. 3. 2. 1. sence of such terms.to Moreover, these be explicit smaller symmetry than breakingproduce the parameters large are symmetry radiative expected preserving corrections parameter, to the i.e. SM-like ( Higgs mass. bosons of the SM ( Note that the mass of the SM-like , which would have been a pure Goldstone boson in the ab- of effective potential can arise from a particular UVthe complete above model, effective e.g. potential. [ Note that one canin rewrite the all form other of above possible any potential specific parameters. UV As complete mentioned description above, of we TH do models, not rather aim we to assume consider that the above form where whereas including explicit soft and hard be written as [ sigma model version of the twin Higgs models where the radial mode is decoupled. the TH symmetry breaking scale JHEP02(2018)048 and (2.7) (2.8) (2.9) 2 (2.14) (2.10) (2.11) (2.12) (2.13) v . , ,  . ) is,  0 ! 2 2 ) ˆ h v α f α , are admixture of  λ , 2 ˆ h 0 , one needs a tuning ρ λρ h 2 sin cos 1 + ∆ + 2 α . . f + . κ 2  ) + ( α  f  ! 2 2 cos σ α 2 κ 2 . This result implies that 0 ) κ λ 0 2 . v f κ ˆ h κ sin + v ˆ h  cos 0 ! ) + λ + − + ) + O λ as κ ˆ v (2

λ and α 1 + 2 1 or κ ˆ v + +

+ R = λ  measures the amount of fine-tuning + (  κ 2 2 0 λ  sin λv ρ ) ( 1 ( f 2 2 R 0 √ ρ 2 σ 2 ξ h ξ v ρ v + 2 + 2ˆ = = = and heavy twin Higgs λ ) 2 2  = b H ρ ˆ 2 h 2 ]. h ˆ 2 h (2 with for fixed v f σ + 2 16 ρ , ˆ v κ 5 − – 6 – λρ doublets as, , 1 + , f ) ) results in the following values of vevs,  + λv , α, can be written as, σ )  2 ! b λ H , m σ λ  ! 0 2.5 ) 2 (  ) + ˆ 2 h h ξ 2 sin 0 λ v ∆ 0 λ λκ 0 m + 2 + ( 2 κ ˆ h + ]. ρ − 2 h κ v

], and also [ + ( 0 + 2 κ 1 − , the 16 m

κ ( κ 43 2 λ . Roughly speaking, 2 = λ σ α 2 2

κ 2 + 1 f √ +  ) + 4( ) = v/f , such that ρ σ cos M λ  κ ρ κ 0 = R κλ ≡ 2 2 ' + h 2 + v f and twin Higgs ξ 2 2 H 0 κ λ = ξ κ f ( and M by an orthogonal rotational matrix H ρ 1 h 1 + σ + ( − 2 = 2 λ M 2 In a limit − v ρ v ≡ R 3 , = 2 ) are the two scalar mass-eigenstates (without the subscript ‘0’) with = 1 v 2 diag 2 h ˆ h , and are defined as 2 0 m ). The two physical scalars, SM Higgs + ˆ h, ˆ M h ˆ 2 h ∆ 2 v Moving on, the mass-squared matrix for the scalar fluctuations ( , m We do not discuss in detail, issues related to the fine-tuning in TH models but refer the interested and ≡ 2 h 3 2 0 m where readers to a dedicated recent paper [ The corresponding mass eigenvalues are, where ( ( h We diagonalize large hard breaking effects couldsee potentially lower also the a amount similar of fine-tuning discussion in in TH [ models, In order to have smallin fine-tuning the in the parameters model, i.e. We define a parameter in our model. Minimization of the scalarf potential ( write the SM Higgs JHEP02(2018)048 v and ), but (2.18) (2.19) (2.20) (2.15) (2.16) (2.17) 2.9 is crucial = 14 TeV , the SM 1. At the 2 s ]. However, v = 246 GeV.  , λ, κ, σ √ ˆ hhh . v 44 0 g . 2 ) f , and twin vev ˆ i  v , 5, [ /f κλ . i ]. Furthermore, in α 2 0  v 2 λ 16 α + 2 2 + = | ∼ sin 2 . κ κ 2 κ 1 and fixed ( sin ξ sm hhh 2 , SM vev κ v ˆ h κ/λ + 3  /g 2 + ) m , λ 2 2 λ − . Therefore, the hard breaking ξ ξ hhh  ρ α ) 2 g 4 4 α λ v f − − cos + 1  2 sin | v ξ κ = 125 GeV and its vev ˆ v O ( is a very crucial indirect probe of new + ˆ , which are given as 2 − , h − + ) + (1 f 2 h  1 m 2  2 α 2 v ˆ hhh hhh ξ m α p v g ) f 2 g 3 = 2 ξ 2 similar to composite Higgs model. 2 2 ) ˆ 2 h = 2 ρ/λ κ – 7 – and ) cos ) contains five real parameters, 2 ) cos ρ /f λ + ρ 2 sm hhh 2.6 λ + v g hhh (2 + ( + , heavy twin Higgs mass g κ ' h κ − = , m α m ) (1 α + ( 2 + 3( 2 κλ λ λ 1, the mixing angle can be written as, ) = λ sin α α  α + 2 + to get the SM Higgs mass correct, see also [ 2 2 sin cos ξ κ κ κ ( v v 2 h h tan(2 v 2 = 2 = 6 ). We fix the SM Higgs mass + , in order to reduce the fine-tuning as mentioned above in eq. ( f 2 ρ ˆ hhh hhh , it is expected to achieve sensitivity of ρv g g 1 would be severely constrained by the SM Higgs mass. However, it is possible − ρ = 2 2 h m Before going ahead, we would like to comment on the most relevant scalar sector . For phenomenological analysis, it is more convenient to choose a basis where these Twin Higgs effective scalarρ potential ( parameters can be expressedTH in models more are physical the SM . Higgs(or Physical mass observables equivalently for linear as we see in theis following very sections, in mildly most constraining. offor TH the On parameter decay the space of other trilinear heavy Higgs hand, twin Higgs the to triple2.1 a Higgs pair coupling of Physical SM basis Higgs. for Twin Higgs models physics at the current and future colliders. Any deviation from its corresponding SM value, would be a signal of newwith physics. 3000 fb At the high-luminosity LHC (HL-LHC), i.e. Trilinear Higgs coupling of the SM-like Higgs which shows a dependence of sin couplings, the triple Higgs couplings parameter to have sizable at the price of reducing the same approximation The above expressions manifestlyHiggs mass show is that directly in related to the hard limit breaking parameter For more intuition ofleading the order above in results, this we approximation, expand we get in the the mass limit eigenvalues as, The mixing angle is given by JHEP02(2018)048 as ρ (2.25) (2.22) (2.26) (2.27) (2.21) (2.23) (2.24) ), where 2 h . Since we , ρ /m , )) 2 2 0 . ξ > 2 h − 2 ]. In the linear TH 0 m ) ln(Λ f ˆ 2 2 h (1 45 2 a m b ∆ 4 ρξ − , ) 2 − )) ) . 2 ρξ 2 = 246 GeV. If any (or more and (1 + ˜ ξ , . ξ ˜ } ρ 2 v 1 − ξ , −  ˆ h (1 + ˜ 2 . − (1 ξ (1 | 2 2 ) 1 2 λ, ˜ ρ , m 2 | ξ , we require the following conditions ρξ ξ h −  p {z as 2 ξ 4 1 | ≤ ˜ − ρ 2 ρ ρ 2 b | f ∆ ) κ (1 + ˜ (1 4 2 h , and hard breaking parameter ) plane and constraint the parameter space and κ 2 TH physical basis − f receive infrared contributions — due to the v, f,| m ξ m − 3 , 2 + ˆ h  T − − f/v ) λ – 8 – ˜ ρξ λ, such that 1 2 ˆ 2 h m − λ ⇐⇒ ξ m 2 p ˆ h } and | ≤ ξ λ m 2 − κ ) and the cutoff scale Λ is the heavy twin Higgs mass, | S + ( )) f = 125 GeV and its vev = 2 2 4 (1 ) ξ h ˜ 16 ρ 2 h ρ/λ, {z + m − − m ) ≡ 2 2 λ, , λ, κ, σ, ρ )) (1 ˜ + ρ ξ 0 ξ 2 2 , σ TH gauge basis 2 f | 2 ξ ˆ 2 h  ρ | ≤ ρξ 2 − − m σ ξ | (see figure 4( (1 (1 2 + ˜ −  ˜ 2 ρ α (1 + ˜ 1   q 2 ρξ 2 h 2 h f κ λ ≡ m m 4 π, and Λ is the scale associated with the heavy states [ 4 = cos b + + ∆ (1 + ˜ h 1 + ≤ , therefore, it is instructive to define ˜ ˆ ˆ 2 h 2 h 2 g λ SM f hV V r m m 4 = f ≤ /g < λ a ρ = = = 0 0 κ λ hV V f g ≡ the electroweak oblique parameters mixing of the SM-like HiggsHiggs with the to heavy the states and SMa the gauge reduced coupling bosons of —models, the SM-like which are proportional to (1 2.2 Electroweak precision constraintsIn in this Twin subsection, Higgselectroweak models we precision briefly data commentrelatively when on light the the radial TH constraints mode symmetry (twin in Higgs) breaking the is is TH present models linearly in the realized from effective and the theory. a In particular, along with the SMthan Higgs one) mass of the“unphysical”. above conditions is not met then the parameter space would be called where In our phenomenological analysison in potential sections parameters in order to satisfy unitarity and perturbativity constraints, Advantage of the above parametrizationa is free that parameter, it which leaves the givesparameters hard us have breaking a the parameter handle following on ˜ values hard in breaking the effects physical in basis: the model. Potential at the LHC. The trade of potential parameters in the ‘physical TH basis’ is as, require In the following sections wethrough work direct in searches of ( the heavy twin Higgs and indirect limits from the SM Higgs data This leaves us with three free parameters JHEP02(2018)048 , ) ii 321 (3.1) (3.2) L light- (2.28) 13 with . , the TH 0 ). Notable  gauge group f/v 2.6 4 . Y 09 ! . ˆ 2 h 2 h ) and 95% ( m m U(1) = 0 ,

red f × T y ln L due to the SM-like Higgs ' W ˆ T f θ α , see also below. There are ˆ y gauge couplings, respectively, 2 , 2 α ) SU(2) Y 11 and and b . sin cos H × receive contribution proportional 0 S π , c 0 H,  ) for a fixed value of g ( 3 i 16 S, T eff ' 05 . V 0 :( ], and U(1) ˆ g ≈ − − 2 L 45 ] to construct 68% ( ˆ 1 is a mirror copy of the SM Lagrangian = 0 T , are smaller for lighter twin Higgs, and ( ˆ 2 5 ˆ 3 ˆ 1 is the corresponding twin sector Lagrangian. ∆ 46 ), respectively, for the color-coded values of ˆ 2 ˆ S L ˆ 3 ♦ ˆ 1 . It provides a vector portal between the SM and twin g, – 9 – . The left (right) plot considers hard breaking ˆ SU(2) ˆ 2 , L ? S, T + , ˆ 3 µν c ' × ˆ soft breaking term involving mixing of the SM hypercharge ˆ L B , , ) for the MTH model is given in eq. ( ˆ ). The contribution of a pure SM Higgs of mass 2 g 321 b µν Z ! H L = 0 case. This is mainly due to the fact that the ˆ h 2 h 2 εB 0) slightly worsens (improves) the electroweak precision = H, ρ m m ( , purple s = 125 GeV [

eff g , i.e. ρ < mth V ˆ Y ln h L ' 0 (˜ m s α ), 8 ( ˆ g 2 π denote the SU(3) ρ > 5) in the TH effective potential. Note that the presence of hard sin . 0 2500) GeV as (+ g , green 1 12 are the Yukawa couplings. This is required to cancel the quantum ≈ and = 0(0 1500 contours. Twin Higgs contributions to the oblique parameters are shown f , ), 5 ( S y ρ , g s ∆ T ]. represents full SM Lagrangian with SU(3) g – . Hence, the shifts of the oblique parameters , we employ Gfitter values for blue 47 ˆ h S 2 , this feature is similar to . In the following sections for 321 m = (750 for the SM Higgs 2 L and twin hypercharge U(1) ˆ h whereas corrections to the SM Higgs mass. and the twin sector particle content isTwin the sector same gauge as and that Yukawa couplings of are the almost SM. equal to that of the SM,where i.e. Gauge structure of twin Lagrangian /f = 3 ( U 2 = 125 GeV is shown as a black star Y m We have not included a renormalizable   ) C.L. v 4 h U(1) sectors, see [ where excluding the SM HiggsThe potential effective and scalar potential features of the MTH model are: 3 Heavy Higgs phenomenologyThe in most Mirror general Twin effective renormalizable Higgs Lagrangian for the MTH model is for a fixed twin Higgsto mass, the oblique parameters the phenomenological analysis, we implementC.L. the on electroweak precision the constraints TH at parameter 95% space. breaking contributions ˜ constraints as comparedhard to breaking the effects ˜ aretwo proportional interesting to features the wecontributions mixing observe to angle from the figure oblique parameters free red for f/v m contributions ˜ and heavy twin Higgs in the TH models are [ In figure i.e. Λ = JHEP02(2018)048 ]. S, T ). 48 (3.4) (3.3) , 32 , hat ) ♢♢ ×× XX = 0 (right). We ++ → ♢♢ ρ ×× ), respectively, for ˆ h ♢♢ ++ ×× ( ♦ ★★ , B × , scale universally w.r.t. ˆ f 2 ˆ hY Y C m ˆ h , f m = 0 (left) and ˜ = ρ m h ˆ v v m

). ) = h ˆ f → and fermions purple ˆ V ) C.L. contours of the oblique parameters YY m ( ), 8 ( , m 2500) GeV denoted as (+ , V SM – 10 – σ m green ˆ v v light-red to their respective SM values, which is a common 1500 , ) = = α ), 5 ( ˆ V XX m denotes the SM fermions (twin sector are with a blue = (750 ]. For different initial (production) and final (decay) states, = cos f → ˆ h ♢♢ 49 h ×× ) and 95% ( ˆ h m g ( = 3 ( ++ ♢♢ red ×× ·B ×× ) and ♢♢ ++ ★★ ) f/v ), where apart from tree-level vertices for the SM and twin-sector ˆ h ,Z . For computing heavy twin Higgs cross-sections, we adopt a strategy  A → A W YY = ( ( σ V ≡ . Magnified 68% ( (appendix . The SM Higgs coupling measurements at the LHC put severe constraints on the XX α they are irrelevant to our discussion. where We assume a mechanismHowever, for twin play almost no mass role generation in the exits, phenomenology see of e.g. TH [ scalar sector so Masses of the twin sectorthe gauge SM bosons counterparts as, 16 → We collect formulae for partial decay widths of heavy twin Higgs to the SM and twin YY ˆ h   σ states in appendix similar to the one outlined inthe [ cross-section of heavy twin Higgs is parametrized as: gauge bosons of theparticles two sectors. are suppressed Note by thatfeature the of SM-like BSM Higgs scenarios couplingsangle to where the the SM SM sector mixing Higgs angle mixes and exclude with some another of scalar the with parameter space a of mixing the MTH model. We collect the mostfigure relevant Feynman rulesmassive for the gauge scalar bosons sector and of fermions, the we MTH also model include in loop induced vertices for massless the color-coded values of Figure 2 showing contributions of the scalarconsider sector the of twin the Higgs TH mass models for ˜ JHEP02(2018)048 ˆ h gg m = (3.8) (3.5) (3.6) (3.7) = h m | ) YY , YY . ) is the twin ) is defined as, ) . For ) → XX XX h A , ˆ hY Y XX ( C XX ˆ h → → → m SM ˆ h h → ( = σ ( h h ( B B ) h ] and they provide strin- m ( | ) SM B 51 = 0. Notice the lower mass YY B 2 hY Y ρ = 125 GeV, the cross-section C YY as, → ) h 2 hY Y ˆ h α , h α . → ]. Above m C 2 2 XX h Γ( 50 ( → = → YY h increases. This is due to the fact that ) SM µ = sin = cos Γ YY ) ( 2 2

XX

f/v = ˆ h h SM g ) is subdominant in most of the parameter g ˆ h

XX → σ

m h = = = → ( vbf – 11 – h ) = ) h m ( SM ˆ h | ) 2 ˆ hV V 2 hV V h C XX ·B ·B C → ). The SM Higgs cross-sections ) ) = = → h h → final state, whereas, effective coupling YY h ( 2 → → ( ˆ hgg 2 hgg σ YY C C is the SM Higgs partial decay width evaluated at the heavy ( gg, V V ·B XX ˆ h ) is the twin Higgs decay width, see appendix ) YY YY SM ( ( m h = ( the lower twin Higgs masses do not reconcile with the SM Higgs σ ) the effective SM Higgs coupling is σ = h YY SM → ≡ m σ | YY → f/v ) ) is the SM-like Higgs production cross-section calculated at the heavy = 3 (left-panel) and 6 (right-panel), and ˜ ] incorporating the twin sector, where all the appropriate QCD and ≡ h ˆ h YY 2 ˆ hY Y gg, V V ( 52 YY C σ → f/v XX we show branching fractions (larger than a percent) of heavy twin Higgs = ( ≡ → → 3 YY h h YY µ code [ ( ( YY XX → , one finds the effective twin Higgs coupling, SM SM YY h σ σ ), whereas, the vector-boson fusion ( VV In figure For numerical analysis of the twin Higgs phenomenology, we employ a modified version f HDECAY gg for different final statesHiggs of mass the for SM andof the twin heavy (invisible) Higgs sector iswith as shifted the to a increase higher function in values of as the heavy of electroweak corrections are included inthe the MTH SM running as of wellthat twin as at gauge in the couplings the cutoff is twinare scale similar sector. exactly Λ, to equal. Note the those that SM Moreover, oftwin in the and states the heavy twin are SM. twin gauge invisible We Higgs coupling at also (and as the assume the well colliders. SM-like the Higgs) Yukawa couplings decays to the The SM Higgs signal-strength measurementsbeen in measured many with production unforeseeable and precision decaygent channels at constraints have the on LHC BSM run-1 models. [ It is convenient to define SM Higgs signal-strength times branching fractions are given as, where for which is a universal rescaling ofers. heavy Note twin that Higgs production the at main( the production LHC channel and for future thespace collid- heavy of twin Higgs TH is models. -gluon fusion Similarly, for the SM Higgs with where Γ Higgs mass and Γ( and twin Higgs mass for are obtained from Higgs Cross-sectionHiggs Working Group branching [ fraction to where JHEP02(2018)048 ) ˆ Z 2000 , (3.9)  (left- ˆ 3 W -term in , ρ the heavy ) 0 enhances ) are equal. ˆ 3 W ZZ ˆ W ρ > Λ=5 TeV , = 0 and Λ = 5 TeV. → ˆˆ ZZ ρ 1500 =0 ˆˆ ZZ ˆ h ˜ ρ ZZZZ [GeV] ( , and the twin vector , ˆ h B h m ¯ 1 2 =6 t = 0 we find, t ˆˆ WW ρ )). Hence, ˜ ' f/v ˆˆ WW 0 suppresses those rates. As ) WWWW ˆ Z hhhh , Higgs 2.16 ˆ Z SU(4) hard breaking ]. Notice for the case of positive MTH, ρ < / ,Z 2 16 → we plot the twin Higgs branching  1000 Z 7 and that in the invisible ( ˆ h 4 / W ( = 0, it is clear from figure 4 1 1 ρ .

01

0 . ∼

. As we are working in EFT framework

'B 0 ) XX → h ( B ˆ ) (right-panel), as compared to figure ρ/λ ρ ≡ – 12 – WW 2000 ρ → ˆ h ( ]. This gives a profound prediction for the TH models = 3 (left-panel) and 6 (right-panel) for ˜ B and vice versa (see also ( 1 2 36 ρ f/v ' 5, where ˜ ) sector would be . 1500 ) 0 Λ=5 TeV ¯¯ ˆˆ tt ), the above-mentioned universality among the interactions of ˆˆ tt , − ZZ , Z, h 2.6

=0 ¯t

t  ˜ ρ [GeV] → , ˆ h W 7, see also [ ˆ h / m 5 and ( =3 . 3 SU(4) hard breaking term, i.e. ˜ / 1000 f/v ∼ 2 'B = 0. The reason for this is the effects of explicit breaking on mixing angle = 0 Z ˆˆ ) , are the most dominant channels. Moreover, for ˜ ZZ hhhh ρ ρ ˆˆ ˆˆ ˆ ZZ WW Z MTH, hh , ˆˆ WW left-panel), there is a sharp increase of SM branching fractions, whereas this  . These plots show heavy twin Higgs branching ratios in the MTH to different final states → 4 ˆ W WWWW ZZZZ ˆ h 500 ( On the other hand, in the presence of explicit 1 1 B .

01

0 .

0 ) XX → h ( B (figure ˆ , which increases for positive ˜ ˜ ρ behavior is reversed for thepanel) case where of ˜ negativeα ˜ the rates of heavy twin Higgs to the SM sector, whereas ˜ the TH scalar potential ( heavy twin Higgs to thesee SM this Higgs/vector explicit bosons and symmetryfractions twin breaking vector for effects, bosons ˜ in would break. figure where the To sign and/or theso size of we explicit consider hard both braking sign term possibilities, is a see model-dependent for quantity instance [ sector would be that the decay rates ofSuch heavy Higgs an to observation the at SM thebetween Higgs and TH LHC vector and and/or bosons other future (say BSM colliders models. would provide a clear distinction which is alongitudinal clear modes manifestation of of massivethe the vector TH Goldstone bosons spontaneous boson symmetry andthe breaking. equivalence the Goldstone Since theorem. SM modes, the Higgs therefore, radialHiggs are Since one mode in would Goldstone the couples expect the modes universally that visible to of the ( all branching ratio of heavy twin Higgs branching fractions tobosons the SM vector bosons as a function of its mass. We take mass 125 GeV. Forof a these given production branching ratios modeabsence determine (e.g. of the gluon the fusion), relative rates the relative for magnitudes the various final states. In the Figure 3 JHEP02(2018)048 ]. ≡ hh ]. 2000 f 51 → gg ˆ h 55 ZZ – σ f ZZZZ WWWW → (dashed gg 5 (right). ˆ h = 0 and 53 . ˆˆ WW ˆˆ σ ZZ 0 ˆˆ ˆˆ ρ WW ZZ plane with for the HL- ZZ − f → gg h Λ=5 TeV ZZ ¯¯ ˆˆ tt ˆˆ tt f µ 1500 , f/v → 5 . gg ˆ h 0 − σ − ˆ h 79) at the LHC [ [GeV] = . ˜ m ρ 5 (left) and 0 ˆ h . , m ¯ t < t = 0 =3 . This estimate is adopted ) (solid green curves). The 1 ρ ZZ 1000 f/v − f hh → gg h µ → MTH, ˆ h hhhh ( ·B 1 1 ) .

01

0 .

ˆ h

0 ) XX → h ( B ˆ are as follows: . → 0 (see below). 6 ˆ h are for hard breaking parameter ˜ gg 5 ]. – 13 – ( ρ < 2000 and σ > m 36 ) is excluded at 95% C.L. by the combined ATLAS presents contours of heavy twin Higgs cross-section 5 ˆ h 6 ≡ ZZZZ 6 ˆˆ WW ˆˆ ZZ ) captures parameter spaces where heavy twin Higgs ˆˆ ˆˆ WW ZZ hh represents unphysical parameter space excluded by the ) shows projected 95% C.L. exclusion limit for cross- f and 6 → 6 6 gg ˆ h 5 σ 0 than for ˜ final state at the ALTAS experiment with 13 TeV [ 1500 ¯¯ ˆˆ tt Λ=5 TeV and ˆˆ tt and , 5 ) shows 95% C.L. exclusion by direct searches of heavy scalar 5 ) presents projected 95% C.L. exclusion limit for cross-section 5 ρ > . VV 5 but for explicit hard breaking parameter ˜ 5 =0 [GeV] 3 ˜ ) (solid blue curves), and SM Higgs signal-strength ρ ˆ h , m ¯t t ZZ =3 1000 → f/v we show parameter space of the MTH model in WWWW ˆ h ]. ( 5 36 MTH, ·B ) hhhh . Same as figure ˆ h 500 5, respectively. Similarly, figure LHC at 14 TeV with anfrom integrated [ luminosity of 3000 fb Green shaded areasection (figure times branching fraction ofat heavy the Higgs HL-LHC, to as a adopted pair from of [ SM Higgs bosons Purple area (figure decaying to the SM Blue region (figure times branching fraction of heavy twin Higgs to SM vector bosons Orange area (figures width is greater than its mass, Γ Red shaded region (figures and CMS analysis of the SM Higgs signal-strength ( Gray region of figures theoretical constraints as outlined in the previous section. . → In figure 1 1 . 01

• • • • • •

0 .

0

gg ) XX → h ( B = 0 ˆ ( ˜ description of shaded regions in figures σ red curves). The14 TeV. cross-section is The calculated leftρ at and the right LHC plotsto in with a figure the pair center-of-mass of energy SM Higgs bosons, a consequence, the LHCTH (and/or parameter future space colliders) with would ˜ be able tocontours probe of more heavy region twin of Higgs cross-sections to a pair of SM vector bosons i.e. Figure 4 JHEP02(2018)048 5 (right). Shaded regions . = 0 5 (right). Shaded regions read [fb] (solid green) and SM Higgs ρ . at the HL-LHC (light-blue), and hh f = 0 → ZZ gg ρ ˆ h [fb] (solid blue) and SM Higgs signal- σ → plane for the MTH model. The contours plane for the MTH model. The contours ZZ ˆ h f → gg ˆ h f/v f/v σ = 0 (left) and ˜ − − ρ ˆ ˆ h h (orange), the projected reach for direct searches m m ˆ h = 0 (left) and ˜ -boson – 14 – ρ Z (orange), exclusion by the current LHC direct searches > m ˆ h ˆ h > m ˆ h (dashed red) are shown for ˜ ZZ f → (dashed red) are shown for ˜ gg h µ ZZ f → gg h . These plots show parameter space in . These plots show parameter space in µ (purple), the projected reach for direct searches at the HL-LHC (light-green), and exclusion by the SM Higgs signal-strength measurements hh ZZ → → ˆ ˆ Figure 6 of heavy twin Higgs cross-sectionsignal-strength to a pair SM Higgsread bosons as: unphysical parametersh (gray), Γ at the LHC run-1 (red). of heavy twin Higgs cross-sectionstrength to the SM as: unphysical parameters (gray),h Γ exclusion by the SM Higgs signal-strength measurements at the LHC run-1 (red). Figure 5 JHEP02(2018)048 ]. 6. 56 . (4.1) 0 the 0) not f/v ρ < ρ > , hence the VV 24 is by CMS [ . 0 5 as compared to . ≤ is about an order of ) . = 0 5 (right). Moreover, in hh inv . f ρ → gg ˆ h → σ = 0 h ( ρ B , ) b . H H, VV ( eff than the Higgs coupling measurements. V 5 − ] which implies constraints up to = 0 (left) and ˜ is comparable to that of the ˆ 2 ˆ 3 44 ρ ˆ L hh – 15 – + . We summarize results for the MTH parameter 3, however the reach for the signal-strength mea- 321 . ZZ for details. Note the indirect probes via the SM-like L f ]. The Lagrangian for the FTH model is, → plane for ˜ 5 5 would be accessible. gg ˆ h and/or the SM Higgs invisible (twin) branching fraction = 2.2 σ f/v . we show the contours of the ratio of heavy twin Higgs width f/v fth sm hhh 7 L − /g f/v ˆ h one can notice a clear enhancement in the heavy twin Higgs hhh m g 6 as: (solid orange), the ratio of the SM-like Higgs trilinear coupling over its (dashed purple), and the SM Higgs invisible (twin) branching fraction 6 and ˆ h 1 TeV and 5 sm hhh /m and . ˆ h /g 5 ˆ h 3 for heavy twin Higgs decays to the SM ) (dotted), in hhh m . . g we also show 95% C.L. constraints on the TH parameter space due to the EWPT inv) are far less constraining at the LHC inv straints are more effectiveindirect constraint in implies the highsurement at mass the regions HL-LHC is of about the 5% MTH [ model. Current f/v with 7 Direct searches are more sensitive to the low mass region, whereas the indirect con- Projected reach of direct searches at the HL-LHC indicates that the MTH model The LHC run-1 and early run-2 data only constraints a small region of parameters → → For completeness in figure From figures The most stringent current bound on the SM Higgs invisible decays 5 h h (i) = 0 case. As we discussed above, by turning on the hard breaking effects (˜ ( ( (ii) (iii) ˜ The FTH model has the minimalcorrections twin sector to the content required SM to Higgs cancel mass the radiative [ B However, at the future colliders they can be complimentary probe4 channels. Heavy Higgs phenomenology in Fraternal Twin Higgs SM value B figure (gray hatched region), see section Higgs trilinear coupling over its mass Γ of TH mechanism. However noticemagnitude that less the than HL-LHC reach thatscan for of in the figure increase at colliders, on thestrength other measurements hand, the would indirect becomemixing constraints from angle stringent. the decreases, SM hence However, Higgsor making signal- we indirect it searches note harder at to that colliders.is exclude for As that the discussed heavy parameter ˜ above, Higgs a space branching genericsignal via prediction fractions of direct of to heavy the Higgs TH models to a pair of SM Higgs is very important for the discovery potential cross-sections to the SMρ vector bosons andonly the cross-sections Higgs of boson heavy twin forin Higgs ˜ the to the mixing visible angleon sector but would one increase hand, also due the the to observability increase SM potential Higgs of heavy signal-strength twin would Higgs increase. through direct As search a would result, JHEP02(2018)048 sm hhh (4.2) (solid /g ˆ h hhh = 0 (left) g /m ρ ˆ h ) (dotted). The . inv , i.e. there is no twin → L h ( B . c SU(2) × (Λ) ]: c g 5 . ˆ h ' c SU(3) > m (Λ) plane for the MTH model with ˜ ˆ h ˆ g is ˆ 2 ˆ 3 f/v ˆ ) is the scalar potential (same as the MTH L is required to be very close to the SM top − b , H ˆ h ˆ t y m H, (Λ) – 16 – ( s g eff V ' . These requirements are motivated by the naturalness t (Λ) s y ˆ g ' ˆ t ), which are necessary to cancel the SM radiative corrections τ y ˆ ν gauge group and hence, no twin in the FTH model. τ, ). However, the FTH model differs from the MTH case in the twin ˆ Y , especially in the matter content. The most salient features of the ˆ 2 ˆ 3 2.6 ˆ L ) could be substantially different from their SM counterparts. is the SM Lagrangian and ˆ τ ˆ y 5 (right). The contours of the ratio of heavy twin Higgs width over its mass Γ ) and leptons (ˆ . . These plots show parameter space in , b ˆ 321 b ˆ ˆ y t, L Similarly, twin top Yukawa couplingYukawa coupling, ˆ i.e. ˆ arguments in cancellation of the radiative corrections. Contrary to the(ˆ top Yukawa coupling, the light twin fermions Yukawa couplings Twin sector gauge couplingsof are the required SM to at be the very cutoff close scale (better Λ, i.e. than 1%) to that Gauge symmetry of the FTHhypercharge Lagrangian U(1) Twin fermionic part of the( FTH model contains only thirdto generation the of SM twin Higgs quarks mass. = 0 ρ     where model) given in eq. ( sector Lagrangian, FTH model as compared to the MTH case are as follows [ and ˜ orange), the ratio of the SM-like(dashed Higgs purple), trilinear coupling and over the itsgray corresponding SM SM area Higgs values corresponds invisible (twin) toEWPT branching at the fraction 95% unphysical C.L., parameters, and the the orange hatched-gray region region represents is Γ excluded by the Figure 7 JHEP02(2018)048 2 . 2) 1 are / h (4.4) (4.3) ). ˆ ' Z τ b ˆ ν < m /y ˆ τ, b ˆ ˆ and f y b, ˆ m ˆ W = ( , ˆ scale w.r.t. their f ) and subsequent ) remain same as  ˆ f 2 A ˆ V 1%) to the SM and g involve total widths qcd m ˆ V α ˆ ≥ + ˆ f 4 → 2 V ˆ g ˆ h 2 and 6, respectively, for → . , ˆ 1 Z ∗ f π enhancement in their masses ˆ V m m ' ∗ 2 48 ˆ f f f as compared to the MTH case. ˆ g ˆ b ˆ y y V 2 f ) are essentially free parameters. /y and fermions ˆ v v ˆ /y ˆ τ ). Moreover, the twin weak gauge f b ˆ → ˆ ˆ y /y y V ) = y ˆ 3 = , 2 ¯ ˆ f f ˆ h b ˆ m y ˆ ˆ f y f → 35 GeV (which corresponds to the lightest 1 to 6. The effect of explicit hard breaking ˆ . Z ), increases about an order of magnitude for ∼ , m 8 Γ( = 7 – 17 – V twin hadrons mix with the Higgs bosons and m ). Notice the heavy twin Higgs branching fractions b from ˆ ˆ v v qcd , ++ b m ˆ Λ ˆ = W π /y b ˆ ˆ m V (or y 48 2 b ˆ m ˆ g y of the FTH have the same masses and coupling to heavy twin ) = ˆ t τ = 0, and ¯ ˆ ν , which change as compared to the MTH case due to fewer light ˆ ρ τ ˆ V ), → ˆ = 50 GeV). For simplicity, in this work we take twin Yukawa as V ˆ = 3, ˜ are the vector and axial couplings of the twin fermions W m + ˆ 0 A Γ( enhancement factor as compared to that of the MTH model. The on-shell , we show the heavy twin Higgs branching fractions (  g m , which fixes the twin sector fermion masses up to only one free parameter, the 2 f/v and twin top ˆ b f 8 ) value as we increase ˆ f Z m /y and ˆ ˆ h b ˆ ) (shown as dotted curve in figure /y y b ˆ ˆ ˆ f m V b W, ˆ y g = scale (due to faster running ofhadronization the of twin QCD twin coupling /bottom constantrespectively. quarks ˆ In particular, to the twin 0 to glueball/bottomonium prompt states, and/ or displaced exotic decays to the SM light fermions. The light twin fermionsWhich implies Yukawa an couplings enhancement of (ˆ thedecay heavy rates Higgs to (and light the twin SM fermions Higgs by if The a most factor remarkable feature of the FTH model is the relative large QCD confinement SM counterparts as, where the light twin(and fermions also receive in their an couplings) extra as ˆ compared to the MTH model. Twin sector masses of the weak gauge bosons τ → In figure In the FTH model, the heavy twin Higgs decay rates and cross-sections to the SM sector    ˆ h /y ( ˆ τ twin bottom Yukawa coupling ˆ do not substantially change for theand twin 6 massive gauge cases. bosonsB and However, twin the top for heavy twina given Higgs branching fraction for twin , where ˆ twin states, where thefix left- values of and right-panelglueball are mass for y twin fermions. In(assuming the FTH model, total decay widths of the twin bosons enhancement. To be precise, heavyextra twin Higgs (ˆ decay rates to thedecays light of twin fermions heavy get Higgs an toin a the pair MTH of scenario. twinof massive However, the the vectors bosons vector off-shell ( bosons decays Γ would be almost samebosons as for the MTHHiggs as case those (section forwould the not MTH change substantially case. as comparedYukawa Therefore, to couplings their the can MTH the be case. branching enhanced, However, fractions/cross-sections light as twin fermion a result their production cross-sections would get JHEP02(2018)048 as 2000 qcd 1.2 qcd /α ˆ Λ Λ=5 TeV qcd , α at the high 50) GeV and Λ=5 TeV , 1.1 , . Notice that ] states. The b ˆ ¯ 1500 = 5. qcd =5 b ¯ ¯ ˆ ˆ ˆ t t 50) GeV b ˆˆ tt b α [Λ] qcd , /y b ˆ Λ /y ˆ ) = (15 y qcd 8 b ¯t ˆ 1 , . t + y [GeV] ˆ 0 /α 6 at the cutoff Λ = 5 TeV. )=(75 ˆ h =0 + ˆ 0 ˜ qcd ρ , m ' m ˆ as function of ˆ b α ˆ , qcd , m + m b ˆ 1000 ˆ 0 =3 /α m 0.9 qcd ( m , ˆ f/v Λ qcd = 0, and hhhh ˆˆ α WW ˆˆ ρ ZZ =0 as compared to ˆˆ ˆˆ ˜ WW ZZ ρ 0. , . The twin confinement scale bb ¯¯ ˆˆ FTH, bb ˆˆ 0.8 =3 qcd ZZZZ WWWW = 3, ˜ ρ < α 500 f/v

1 1 5 0

with mass

.

01

25 20 15 10

[GeV] 0 Λ .

qcd f/v

0 ˆ ) XX → h ( B ˆ + Figure 9 a function of ˆ 0 ˆ G , = 0. ρ – 18 – qcd 2000 qcd α (4.5) α state would be ++ Λ=5 TeV , = 3 and ˜ . qcd 0, and vice versa for ˜ 25 . ˆ f/v Λ 1 1500 ¯ ¯ ˆ ˆ t t 50) GeV ˆˆ tt , ρ > . has the correct quantum numbers to mix with the SM Higgs (and we plot the twin confinement scale ¯t t [GeV] 9 + (Λ) (Λ) )=(15 0 ˆ h + ˆ ˆ 0 G m qcd qcd , m ˆ α α b ˆ 1000 m . ( , hhhh ˆˆ on the heavy Higgs branching fractions is similar to the MTH case, i.e. there WW 75 ˆˆ ZZ =0 . ˆˆ ˆˆ ˜ ρ WW ZZ ρ 0 . Since the number of quark fla- , . These plots show branching ratios of heavy twin Higgs to different final states as a =3 qcd WWWW ZZZZ ˆ 500 Λ f/v , the twin QCD confines to form twin glueball and bottomonium [ The most notable difference of the FTH 1 1 . 50) GeV, respectively, where

01

0 .

,

30% in the SM Higgs mass. A small variation of ˆ 0 ) XX → h ( B ˆ qcd ˆ 4.1 Fraternal Twin hadronIn production the FTH and model decays dueΛ to fewer twin quarklightest flavors of and potentially the large twinthe confinement glueballs lightest scale is glueball a 0 ∼ scale Λ significantly change theconsequences. confinement scale In which figure has veryat crucial phenomenological the cutoff scale Λ = 5 TeV, where we kept fix ploy the NNLOhowever, twin we QCD require at corrected the cutoff ˆ scale Λ, The above variation in the twin strong induce a rather mild fine-tuning scale vors is less in thea FTH result (so the faster confinement running) scale larger as than the SMIn QCD the confinement scale. following numerical analysis we em- sector branching ratios for ˜ model as compared torunning the of MTH twin QCD case, coupling isfrom constant the ˆ the cutoff scale Λ to the confinement function its mass in the(75 FTH model. The left and right plots are for ( parameter ˜ is an enhancement in the SM branching fractions and subsequently suppression to twin Figure 8 JHEP02(2018)048 ], is i 42 (4.6) (4.7) (4.8) – had ] and a 39 N , h and twin 63 5 [ + 0 , ˆ G . Note that we , via the scalar # has the correct ) + 0 is a free parame- b ˆ ˆ 0 s χ ( PYTHIA 0 m m ) is the twin QCD 2 N s qcd ( , ), and next to lightest , ' α + ˆ + 2 χ ˆ qcd χ ˆ 2 h − ˆ ln ˆ 2 ˆ 0 2 h α m decays in the visible sector m m (0 m m  4 0 4 η 0 ˆ b ˆ χ f are the number of twin quark − is the fraction of glueball or π − n ˆ 1 f 5 0 1 54 n κ v u u t u u t v 0 + 0 ˆ κ ˆ 1 4 κ with mass i ] i , and 0  b ¯ ˆ ˆ s b ˆ G = 2. The above hadron multiplicity for [ χ and twin bottomonium ˆ + √ N N twin hadrons mix with the SM Higgs and h ) h + 125 ) s ) 0 i ( ˆ g b ˆ ˆ ˆ G G ˆ g b ˆ ++ 6 N – 19 – qcd h → → ˆ α . The normalization constant π ˆ ˆ h h ] with showering/hadronization in qcd s p-wave state ˆ ˆ Λ 62 0 1 b ˆ " ) = Γ( ) = Γ( ++ state. Twin QCD hadronic average multiplicity 0 + ˆ 0 , respectively. Whereas, ˆ χ ˆ h ) is the twin QCD , ˆ ˆ ++ exp G π = 50 GeV, a scalar at mass 125 GeV can produce roughly two → m 0 → + ˆ h N ]. The twin QCD hadronization of twin gluons and bottom quarks ˆ 0 (12 are the hadronic multiplicities of glueball and bottomonium states by the condition ˆ h / Γ( = m ) i 42 0 ˆ ] ]. In this work, we follow these analyses closely but focus on the f Γ( , i b ¯ ˆ ) b ˆ N n [ 60 s states, i.e. twin glueball 2 ( 41 – N , states as, h − 0 (left-panel) we plot the average multiplicity of twin glueballs as a function ++ had 39 57 χ , , ], N 10 h and 11 61 11 i – , = (33 ˆ 6 5 G ) state. However, the 0 0 N b ˆ h −− In figure We parametrize heavy twin Higgs partial decay rate to twin glueball Since twin hadronization is poorly understood, especially, without the proper knowl- ˆ Υ(1 glueballs, so we fix the dark QCD has beenvery tested good by agreement [ has been found. of the twin Higgs mass for different choices of the lightest glueball mass where coupling evaluated at the center-of-massflavors energy below the confinement scale ter which we fix byfor setting the a number glueball of of twin hadrons mass at a fixed low energy. For example, bottomonium states in thedefined 0 as [ where at the heavy Higgs mass bottomonium ˆ instance [ lead to a dozen ofproduction meta-stable of states 0 in theirsector spectrums. of However, we the are FTH interestedlead in model. to the exotic Such decays that to the the SM 0 light fermions. see also [ production of twin hadrons due to heavy twin Higgs. edge of thetwin non-perturbative hadron twin production. QCD effects,rately However, and its the the hard perturbative ignorance to estimates of make can twin a hadronization be can precise made be estimate quite controllably accu- of parametrized, see for bottomonium spectra, the lightest twinis bottomonium state is ˆ quantum numbers to mix with theare TH also scalar sector possible. such that Phenomenologicaland aspects ˆ twin of bottomonium production and states decays due of to the the twin SM-like glueball Higgs has been discussed in [ also twin Higgs) which allows its decay to the SM light fermions. In analogy to the SM JHEP02(2018)048 is > 2) , ] + and b ¯ ˆ 3 = 0. 0 b ˆ [ , ˆ ˆ (solid) G Z ρ 4 = 25% m , f 0 κ ], however, = 10 GeV as quarks lead = (6 5 + b ˆ ˆ 0 glueballs. The 125 = 3 and ˜ m i ˆ G → ] N f/v = 0), such that only h b ¯ ˆ b ˆ ˆ f n with mass + 0 as a function of the heavy Higgs ˆ i G ˆ G N h = 25% (red) for the lightest glueball = 10% (blue curves) and ˆ = 15 GeV ( 0 0 b ˆ κ quark to twin bottom κ m ˆ t (left). In the following, we calculate decay 11 – 20 – (dashed curve) at the LHC with center-of-mass boson and ˆ 50) GeV, respectively, which are rather conservative Z vbf , = 10% (blue) and ˆ mixes with the TH scalar sector, which leads to its decay + 0 40 f κ + , 0 to the SM light fermions. The first step is to calculate the ˆ 25 G + , 0 ˆ G (right-panel) we consider parameter. Nevertheless, the above parameterization provides a = (10 show the production cross-section of the lightest glueball state with 0 10 κ + , we take a conservative choice of ˆ ˆ 0 10 0 m κ (dashed). We take ˆ (solid curve) and gg , as the decays of twin ˆ t = 10 GeV via the heavy twin Higgs. The heavy Higgs production is considered vbf f . The left-graph shows average glueball multiplicity + + ˆ 0 then all the bottomonium states decay to the glueballs, i.e. [ f m The lightest twin glueball gg + ˆ 0 m multiplicity and the ˆ reasonable estimate for the production of fraternal twin hadrons. to the SM light quarks andwidth leptons, of see the figure twin glueball The bumps in thetop curves quark of glueball cross-sectionto indicate hadronize thresholds and for decayeffects the to in the twin glueball the states. productionwe of Note assume the that they there twin are could glueballs within be as the non-perturbative large uncertainty as of 10% our as approximation argued for in the [ average hadron by the gg energy 14 TeV. Asstable mentioned glueball above, states around are formed aparameterized and dozen by the ˆ (depending probability to on produce(red their the lightest curves). masses) glueball In meta- figure stable twin hadrons are the glueballs, whereas, other parameters are glueball, then through the relaxation/annihilationgluons these bottomonium which states then decay hadronize to to twin form2 the glueballs. Inright-panel the of figure following we assumemass if normalize the glueball multiplicity w.r.t. tocorresponding the to SM Higgs, i.e. wenumbers. take Moreover, when the twin bottomonium states are heavier than the lightest mass for different choicesof of glueball the states lightest at glueballfraction the of mass SM the and heavy Higgs the twin mass.a Higgs corresponding function decaying In normalized to of the number the the right-panel lightestand twin glueballs we Higgs plot mass. cross-section Themultiplicity. times twin branching Higgs at the 14 TeV LHC is produced via gg Figure 10 JHEP02(2018)048 , , ). ˆ h +  ˆ 0 and 2 h (4.9) 16 m (4.12) (4.10) (4.11) (4.13) + as, 2 0 /m ˆ ˆ 2 t Y G < m ˆ χ , ) i m . , = 4 τ + , ( ˆ t Y Y + ˆ 0 decays to the SM 2 ˆ ˆ 0 τ χ w.r.t. its radius. / m 0 1 m ) is the SM Higgs m 0 ˆ χ = F = χ (see also figure h h in comparison to the SM i YY m m α

X 4 ) ) h ) → ˆ h ˆ v sin h π qcd YY YY ( /m 4 − ˆ α h h . b b ˆ ˆ b . ¯ ˆ state to the SM sector would → SM → m =  b ˆ 0 h h (right), and the interaction is h ≡ − ( ( ] χ b g ¯ ˆ a,µν α h ˆ g b . ˆ [ ˆ 0 g SM h SM 11 G c ˆ χ ], Γ Γ sin 5 a µν 2 b ˆ 2 ) G ˆ v and twin bottomonium ˆ ˆ  m 2 χ ! ˆ 2 χ ]. Above, Γ ) + m + 0 + m = Tr 64 ˆ 0 where 2 ˆ 0 ˆ [ ) G 3, whereas ˆ b − ¯ ˆ α F b ˆ α / m + 2 h decay to the SM light fermions via an off-shell ], which employs linear confining potential, but 4 h 3 ˆ 0 α – 21 – (2 5 sin − ) are heavy enough such that the invisible twin m 0 h 2 Y Y m ( ˆ ˆ ν g 2 h χ which is given by, ˆ v 2 2 h , b ˆ sin sin 2 π τ, v decays to the glueballs, otherwise for m 06 → − qcd 6 y  . ( √ 3 ˆ evaluated at the twin glueball mass α is the decay constant of the lightest glueball ) 0 32ˆ ˆ v ˆ t = ˆ − i χ qcd − τ 2 Y a,µν π = 3 ˆ ` (

ˆ α 6 = h 2 given by [ = G ++ + / b ˆ ˆ 0 1 ˆ 0

(0) ˆ g 2 b ˆ | 0 a µν ˆ | ˆ g ] F int h F int h are kinematically forbidden. Then, as mentioned above, for R G L ˆ ˆ t t

 L (0) ) = ˆ ` 0 qcd a,µν π ˆ ` ˆ 27 4 ˆ α R Tr ˆ t G ˆ | hadrons also decay to the SM light fermions via an off-shell heavy twin Higgs Υ π YY h a µν ˆ g ++ ˆ ˆ ) = g → → G ν µ ˆ g ˆ ˆ g g c 0 ] we can write decay rate of the glueball to the SM light states + 0 Tr[ YY + χ = | ˆ 0 11 G 0 ˆ ˆ g G (dominant contribution is by twin top loop) and in the limit → ˆ g Γ( , bottomonium state ˆ int h b ˆ 0 ≡ h + L χ ˆ t, ˆ 0 . Schematic diagrams of twin glueball + (0) is derivative of the radial wave-function of p-wave state ˆ 0 (mostly bottom quarks) via an off-shell SM Higgs ˆ 0 Γ(ˆ m = 2 R F i Y Assuming the twin leptons ( > Note that the twin 0 decays to the visible sector fermions. The decays of ˆ 6 ˆ χ 0 ˆ where We use the estimate of however, these processes canHiggs be mediated neglected decays. as they are suppressed by ( An estimate of theHiggs bottomonium using state non-relativistic ˆ quantum mechanism is [ m χ meditate through thegiven SM by, Higgs, as shown in figure where its value by lattice isdecay 4 rate to the SM light states weak decays of ˆ Now following [ where 1 the triangle loopHence function in the low-energy effective theory, twin gluon coupling to the SM Higgs is twin gluon coupling to the SM Higgs, Figure 11 states JHEP02(2018)048 ] ++ ++ 12 72 0 f/v cτ (4.14) (4.15) − ˆ h and twin = 6 and m + 0 = 10 GeV is ˆ 125 G i + ˆ ˆ 0 G m, such that the m N 2 h 25, the probability . ] and the LHCb [ 10 For this purpose, we 71 . = 0 7 , = 10 GeV in 0 70 + κ ++ ˆ 0 0 ) their decay-length 30 GeV are unstable and we with mass m cτ ++ ' + . 0 . ] b ¯ ˆ ˆ 3 G b ˆ m [ [m]. For very short decay-length ]. On the contrary, for very long / + 3 2 10 ˆ 0 m − h 66 ], the CMS [ 10 , m . 3 m / with mass 69 65 & ˆ 5 χ – c ++ + 0 ~ m 0 67 is comparable to its cross-section to the SM Γ plane. The decay length of the twin 0 ˆ G + = 0 002 = 15 GeV. The left and right panels of figure . ˆ – 22 – G f/v 0 b ˆ ++ . The shaded regions correspond to the unphysical 0 m + ≈ − 0 cτ 2 ˆ h ˆ

G m (0) 0 [m] to very long R 3

5 GeV, respectively. For the chosen masses of twin hadrons − . 10 ], ]. 5 = 0 42 . – ρ 39 states via heavy twin Higgs at the 14 TeV LHC. state is [ 0 0 we plot the contours of production cross-section [fb] (solid blue) and proper 10 m in most of the FTH parameter space, so it decays outside the detector χ χ 12 & for ˆ = 3 for the twin glueball and bottomonium states, respectively. Note that for = 0 GeV and ˜ 2 | ρ 125 (0) i 0 ] In figure In the following subsection we calculate the production cross-section for the twin b ¯ ˆ = 15 GeV the twin bottomonium states with mass In this work, we do not discuss the production of twin hadrons via the SM Higgs in the FTH model, R b ˆ [ 7 | b ˆ N Higgs/vector bosons. The decayrather length large of twin glueball and hence would appear as a missing energy signal. however, we refer to refs. [ assume they decay 100% toto the produce twin the glueballs. lightest glueball Moreover, state weparameters set (gray), ˆ exclusion byexclusion by the the SM SM Higgstwin invisible Higgs signal-strength branching cross-section fraction measurements to (hatched twin (red), glueballs light-gray). and Notice that heavy decay-length [m] (dashed green)plane, of and glueballs the twin bottom quarkare mass for ˜ we normalize averageh hadron multiplicity atm the SM Higgs mass as In this subsection, we calculatebottomonium the production ˆ cross-section ofchoose twin glueball several benchmark casesbottomonium where state. either the lightest twin hadron is a glueball or a signatures would appear as displaced verticesthe at LHC the for colliders. long-lived There particles are atexperiments. ongoing the searches ATLAS at [ 4.2 Fraternal Twin hadron phenomenology the daughter decays tocolliders the could SM be light highdecay-length fermions the multiplicity would twin-hadrons jets, would be see escape prompt, theenergy. e.g. detectors so [ and However, the signatures the signature wouldhadrons be most at decay-length missing the promising is of signals the would size of appear detectors, for i.e. 10 the case when the twin hadron is, Depending on kinematics ofcan be the produced from very twin short hadrons (0 of hadrons via heavy twin Higgs in neglecting the relativistic corrections which could be potentially important. The estimate JHEP02(2018)048 ¯ ˆ b]. ˆ b ¯ ˆ b][ = 3 for ˆ b [ = 50 GeV → 200 + i ˆ 0 ˆ G m 5 (right). N . h = 0 ρ = 25 GeV (left-panel + = 10 GeV (solid blue) and ˆ 0 25) GeV (left-panel) and + , m ˆ 0 m, which would give prompt , respectively. Whereas, in m 3 2) for the twin hadron masses − , 13 1 m, which is an ideal range for = 25 GeV and 10 = 0 (left) and ˜ + . ]. For glueball mass ˆ 0 ) = (50 . ρ plane for the FTH model. The contours ˆ χ 25. Note that the twin bottomonium m 72 . ++ = 75 GeV, such that they annihilate – 0 ++ with mass , m 0 b ˆ f/v cτ 67 4) and (1 + = 0 + cτ m ˆ 0 , 0 − 0 . ˆ ˆ h G m κ . = 25 GeV and 50 GeV we show the contours m = 6 for m + m 2 ˆ 0 5 ) = (2 – 23 – − 200 − m i 125 ˆ G i we take ˆ ] are shown. We normalize the average multiplicity at 40) GeV, respectively. Moreover, for the probability b ¯ ˆ N b ˆ , 0 χ [ h χ ] for long-lived particles are not sensitive for the cross- N h , 72 = 1. Notice for glueball mass – 125 67 i 200 ˆ (dashed green) are shown for ˜ i G ] b ¯ ˆ ˆ 0 N b ˆ [ h cτ N h 40) GeV (right-panel), where contours of the cross-section and the decay- 25) GeV and (100 , ), the decay-length is 10 , bottomonium state ˆ , we consider the case when the twin glueballs are heavier than the light bot- 13 plane in the left- and right-panel of figure twin glueballs with masses 14 ++ . These plots show parameter space in ++ ) = (100 ) = (50 f/v , we fix the twin bottom quark mass ˆ ˆ χ χ − 13 = 50 GeV, and , m , m ˆ h ), its decay-length is in the range 10 Current LHC searches [ In figure For 0 + + m ˆ 0 ˆ 0 + ˆ 0 13 m m ( to produce 0 decay-length is in a range to give displaced verticessections at obtained the here for LHC. the twin hadron production via heavy twin Higgs so we do not get tomuium states such that theyIn decay to particular, two bottomonium we states,( i.e. consider glueballs twolength cases of with twin bottomonium ( statethe ˆ SM Higgs mass as ( of the observation of displaced vertices(right-panel at of the LHC [ decays, however, as wehadrons have via neglected heavy any twin effects Higgs due decays, to which could boosted potentially production increase of the the decay-length. twin in figure to the twin glueballs.hadron multiplicity For at the 200 above GeVm masses as of twin hadrons we normalized the average of heavy twin Higgsthe cross-section glueball to decay-length twin glueball of their production cross-sections (solid blue) and proper decay-lengths (dashed green) Figure 12 JHEP02(2018)048 = 0. ρ = 25 GeV and 50 GeV in the left- + ˆ 0 m = 0. = 25 GeV and 40 GeV in the left- and right- ρ ˆ χ with mass m + = 50 GeV (left) and 100 GeV (right) for ˜ 0 – 24 – ˆ + G ˆ 0 m with mass = 75 GeV and ˜ b ˆ 0 χ m . These graphs show the contours of production cross-sections (solid blue) and proper . These graphs show the contours of cross-sections (solid blue) and decay-lengths (dashed Figure 14 green) of twin bottomoniumpanel, state respectively. ˆ Moreover, we consider Figure 13 decay-lengths (dashed green) of twinand glueball right-panel, respectively, with JHEP02(2018)048 ZZ f → h gg Gold- µ 7 30 GeV, = 25 GeV ' + ˆ τ ˆ 0 m m , the dominant 8 2), whereas, their are allowed. The / ¯ ˆ τ h shows the concours τ m 15 . ]. However, the twin hadron = 75, we have (solid orange), the SM Higgs b ˆ 39 ˆ h m /m ˆ h 60], [ , are “eaten” by the SM and twin weak [10 we plot contours of the twin Higgs cross- 6 ≈ are forbidden but to ˆ 15 (shaded purple), and the SM Higgs invisible + b ¯ ˆ ˆ 0 b ˆ m sm hhh ) (dotted gray). The shaded regions represent: – 25 – . bosons and the SM Higgs signal-strength /g inv Z hhh g plane. The right-panel of figure → h ( f/v B Goldstone bosons, − 7 = 75. Moreover, we assume that twin mass (Yukawa) ˆ h b ˆ m m . In the left-panel of figure τ = 0 in m ρ b b ˆ m m = ˆ ]. Projected reach for the HL-LHC is to explore the TH parameter space up to τ m 42 6 in the twin glueball mass window – 39 . We consider one benchmark scenario for the choice of twin glueball mass discrete and SU(4) global symmetries. These explicit breaking terms are the source 2 gauge bosons, andSM hence Higgs leaving boson. only We onebreaking consider Goldstone structure an for boson EFT the approach whichZ and TH plays employ scalar the the potential role mostof including of general generating explicit symmetry the the soft SM and Higgs hard mass. breaking These terms are model dependent quantities and are 5 Conclusions In this work, we haveHiggs explored models, phenomenological when implications the of THglobal the symmetry symmetry breaking radial for is TH mode linearly models ofstone realized. which Twin bosons. is We spontaneously consider Out broken an of to SU(4) SU(3) these and gives scalar searches at the(light LHC blue). (purple), Note and that the for HL-LHC ourwhich projected choice implies of reach that twin for bottom the direct mass invisible SM decays searches Higgs of the decays SM to Higgs are only in twin gluonic and twin leptonic channels. trilinear coupling over its SM(twin value sector) branching ratio unphysical parameters (gray), exclusion(red), by exclusion by the the SMthe SM Higgs EWPT invisible at signal-strength branching 95% fraction measurements C.L. (hatched (below light-gray), the exclusion gray by line, hatched area), exclusion by the direct heavy and twin bottom mass scale as section (solid blue) to(dashed a red) for pair ˜ ofof SM the ratio of heavy twin Higgs width over its mass Γ bosons and the SMFTH Higgs. model Roughly is speaking, verycrucial phenomenology similar of for to heavy indirect that twin constraints,enhance Higgs of is the in the SM the the MTH Higgs flexibility case. invisible of decay The twin width. light only fermion difference, masses which can which may be production via heavy Higgs decay offers chances to4.3 probe heavier twin Heavy hadrons Twin asIn Higgs well. this phenomenology subsection, we brieflythe discuss heavy the twin direct Higgs and indirect indecay phenomenological the modes prospects weak of of sector. the As twin we have Higgs learned in from figure the FTH model are the SM and twin massive gauge probed by these searches. TheFTH studies model of seems twin to hadron offersee production more [ via feasibility for the the SM observation Higgsf/v of for twin the hadrons at theproduction LHC, through the SM Higgs is limited only for the low mass ( any constraints, however in future some of the regions of the FTH parameter space can be JHEP02(2018)048 plane of = 25 GeV + f/v ˆ 0 − m ˆ h m are equal. Furthermore, the , this universal behavior changes ,Z 4  W and , can discover/exclude the heavy twin 1 3 − – 26 – = 75 GeV, whereas the details of shaded regions are given in (dashed purple), and the SM Higgs invisible (twin) branching b ˆ m sm hhh /g hhh g (solid orange), the ratio of the SM-like Higgs trilinear coupling over its = 0. The right-plot show the contours of the ratio of heavy twin Higgs ˆ h ρ ) (dotted). For these plots we take the twin glueball mass /m . ˆ h 3. However, as shown in sections / inv 4 500 GeV mass. Whereas, the searches in the other decay channels especially ∼ → . h . The left-panel shows the contours of the cross-section of the heavy Higgs to the SM ( B We have considered two Twin Higgs scenarios; the MTH, which has an exact mirror of of the TH models.boson Current LHC constraint direct a searches small fortwin region a Higgs of heavy scalar the to MTHto a parameter pair a space, of pair in weak of particular gauge that SM excluding the Higgs the HL-LHC are not reach, constraining at with 14 TeV the with available data. 3000 fb However, it is shown radial mode (heavy twinfractions Higgs) to are the fixed. SMtwin Higgs Higgs As branching a and fractions result, weakproximately to the gauge the heavy bosons SM twin sectorconsiderably Higgs when as explicit branching hard compared breaking to isdirect turned the and on. twin indirect Employing searches sector the at current are experimental the ap- LHC for a heavy scalar we explore the parameter space the SM field content inneeded the to twin sector, solve and themechanism the little is FTH, such hierarchy which that problem. has the the SMare The minimal Higgs the field symmetry and Goldstone weak content breaking gauge bosons pattern bosons, of and of same twin the weak broken gauge TH symmetry, bosons therefore their interactions with the the text. calculable in a givenHiggs and perturbative the UV twin Higgs completecould (radial mode) TH potentially provide lead model. a to portal the to The discovery the of mixing SM and TH of twin mechanism. sectors, the which SM-like vector bosons (solid blue)the and FTH the model SM withwidth Higgs over ˜ mass, signal-strength Γ (dashedcorresponding red) SM values, in fraction and the twin bottom quark mass Figure 15 JHEP02(2018)048 , (A.1) 2 states / 3 0 χ ! 6. ˆ f 2 ˆ 2 h . m m 4 f/v − 1

ˆ 2 f m ˆ h m 2 and bottomonium ˆ π ˆ h ˆ g 2 ]. He also thanks Barry Dil- f + √ 0 ˆ G 4 73 ˆ G ) = ˆ f ˆ f ( ˆ h glueball Γ ++ The two body decays of heavy twin Higgs into – 27 – , 2 / 3 twin hadrons, their decays can be prompt, displaced ratio could be less or more constrained depending on ! 2 f ˆ 2 h ++ m f/v m 4 − 1

2 f m ˆ h , where the triangle loop functions are given below. m 2 π ˆ h 16 g 2 f 3 without explicit hard breaking contributions. In the presence of explicit , we have explored phenomenology of the twin Higgs in the FTH model. In √ G 4 4 . twin hadrons at the LHC is comparable to that of the SM vector bosons, and ) = f/v ++ ff ( ˆ h In section Γ the SM and twin sector fermions are given as: In this appendix, we collectmain partial text. decay widths The ofcollected most the in relevant heavy figure Feynman twin rules Higgs for employed in the the Heavy scalar Higgs sector decays of into the fermions. TH models are for Theoretical Physics (MITP)say, and for the their Laboratoire hospitalitypartially de and supported Physique support by Th´eorique(LPT) the whileDEC-2014/13/B/ST2/03969, Or- and National this DEC-2014/15/B/ST2/00108. work Centre was (Poland) in research progress. projects,A decision This work was Twin Higgs Feynman rules and partial decay widths Acknowledgments The author thanks Zackaria Chackothe and draft, Saereh and Najjari alsolon for and informing discussions Bohdan and about Grzadkowski comments their for on related useful comments. work [ He is grateful to the Mainz Institute or even can escape the detectors.to These search signatures for offer multi-jet acolliders. unique prompt experimental Hence, or opportunity any displaced signals ofHiggs objects such framework. and/or events at missing the energy LHC signals could at lead to the the discovery of twin have the correct quantum numberdecays to of mix these with twin thehave hadrons scalar learned back from sector to the of the twin theto SM hadron model, the light phenomenology as 0 fermions are: a are(ii) result, (i) possible. Depending The heavy on The Higgs the lessons cross-section masses we of 0 particular, we have discussed theof light consequences quark of flavors twin in the QCDformation FTH confinement. of model, twin twin In QCD glueball/bottomonium the confinement/hadronizationsignatures. states, absence leads to which We the have have discussed interesting thedecays phenomenological production at of the these LHC. twin More hadrons importantly, via the heavy 0 twin Higgs signal-strength measurements are quite constraining.excludes In particular, thehard current breaking LHC contributions, data the the sign of thesemeasurements terms. could potentially Moreover, exclude the the MTH HL-LHC parameter reach space for up the to SM Higgs signal-strength Higgs up to 1 TeV mass. On the other hand, indirect searches at the LHC by the SM Higgs JHEP02(2018)048 ,    1 µ 2 , 1 2 , ˆ , F k / ˆ  )  A 1 ν 1 µ 2 2 µ ˆ 2 + k F (A.3) (A.2) k + k V i 2 , ν 1 ν 1 2 1 − / k α / k 1 P V 1 ˆ F ( µν ˆ − i − c A ˆ sin ˆ v η Z ˆ h qcd ˆ i 2 π ˆ N α µν Γ ≡ µν 4 k 2 i ˆ η − P η · e h W, 2 2 2  i ˆ g : 1 k are given below is a symmetry : Twin fermions k 2 V ≡ . Moreover, in k ˆ − v · em · ˆ ˆ P f ˆ ˆ V f g Γ π α v/f µν 1 V 1 ˆ , g  2 W = 2 η − k ab G c k ≡ S ˆ 2 h 2 V ˆ h ˆ v em δ ˆ ) h A V g ξ ˆ ˆ h π i α h, ˆ 2 h ≡ ˆ h h, 2 m ˆ g 2 − Γ h, ˆ ˆ v g h, ˆ h, γ has similar form as the ˆ ˆ g 2 ˆ f g ˆ / ˆ g + Z ˆ ˆ v 2 V and V , and ˆ ≡ γ 2 2 ˆ c m γ ˆ 1 g ˆ v , 2 ˆ m ˆ ˆ Z γ g  v W ˆ i γ x 2 ξ ˆ 2 h α m F 2 ˆ γ ˆ − i i c i c i c A c 2 V 2 A − cos = ( , /m 1 m µ ν ν ds 1 2 µ ν µ µ,a ν,b ≡ , ˆ ¯ ˆ ˆ + 12 f ˆ ˆ ˆ ˆ ˆ ˆ ˆ γ γ γ f f Z V V g g and − 1 p F twin sector ˆ h ˆ 2  2 V f G g , s 1 F 2 = m ˆ = ˆ / A 1 2 2 2 1 1 1 ˆ v , x h 2 k k k k k k , g F 1 ) = 1 1 x ˆ s 2 F , 1 , 2 √ 2 x λ − / ˆ h h 1 ˆ ˆ ˆ ˆ ˆ h h h h h ˆ  F The heavy twin Higgs partial decay width m 2 h, h, h, h, h, ( where 0 with , , x Z   1  1 2 µ 2  1 2 1 , x ,  F k / – 28 – x  α 2 V  A 1 ν 1 α 1 2 µ 2 µ 2 + Γ k 2 F λ k + x k 1 i 2 ν 1 ν 2 1 ˆ h 4 2 1 − / 2 V V sin k / k 1 g ) cos V P 1 S κ ρ F m − µν − ˆ 3 h Γ i − c A π η 1 qcd 2 + i + 2 πv N α m V W, Z ) µν + 3 2 2 µν 4 k 2 i κ 2 : η − P η f  : SM fermions · e λ 2 m √ 2  x 1 i , 1 k V f k G ≡ 8 2 V 1 k · em α · + 3( P − , and twin Fermi constant is πv α µν 1 1 , m gg  2 λ η ds − k ab 1 α c k cos ˆ h em δ ˆ h − x ) = ˆ h πv α ˆ h, v ˆ h α ≡ 1 ˆ h h, 2 2  g − h, s g h, h, − V g . The SM triangle loop functions 2 f g sin g i Zγ 1 v 2 V ˆ h ≡ c m v v ˆ 2 h V = cos m (1 γγ Zγ gg i 2 ( γγ m + ≡ − ˆ h i i c i c i c − ˆ h c p 0 g Γ Z , ˆ ν µ ν ≡ ν µ µ sm sector ˆ hhh ν,b µ,a 2 ¯ α f V γ Z g V γ γ g f 1 ) ig π 2 h h − , x 2 2 2 1 1 1 1 ) = k k k k k k . Feynman rules for the interactions of SM and twin sector particles with the SM Higgs = sin ∗ x 2 ( V ˆ h λ ∗ g 1 V ( ˆ ˆ ˆ ˆ ˆ h h h h h ˆ h ˆ h, h, h, h, h, h and heavy twin Higgs Γ factor, for identical gauge bosonsHiggs it decays is with 2 off-shell otherwiseheavy Higgs, massive 1. as: gauge Moreover, we bosons, also which include allows the heavy four-body decays of the to on-shell SM massive gauge bosons is, where, where our numerical analysis we havethe allowed off-shell twin decays top of quarks). the heavy fermionsHeavy (the Higgs SM and decays into gauge bosons. Figure 16 h and the corresponding twinSM triangle ones loop but functions with twin particles in the loops. JHEP02(2018)048 → em (A.7) (A.8) (A.9) (A.4) (A.5) (A.6) being (A.12) (A.10) (A.11) V , α , f , ˆ ], the form   G ) ) i , , 74 ) κ 2 ˆ h W i → ( g τ g f ( 2 , κ

f 1 − ) W i ,G τ ) A τ ˆ h i ( ˆ τ g 1 + ( − . I , g 2  → W /   (2 ) 1 ) ˆ i 2 ˆ h τ A ) A i W , κ i i κ → t,b κ + 3 /τ τ ˆ , V , g 2 ( i = i , X − 2 i ˆ h 2 τ W τ

i g 2 h ˆ 2 h → τ A 3 ( 2 m m − I

! (5 + 2 4 V are adopted from the Higgs Hunter’s ) ) + ˆ 2 h 2 Z ) i and − W −  W m m W τ ) , κ 1 ( F w i w i A ) = 2 + 3 ). 1 ˆ θ τ θ , κ i − κ A s ( ( τ F 2 2 1 The heavy twin Higgs partial decay width 1 ( W ˆ h f , 1 τ I 1 and → 2.19

( 2 ˆ h m sin cos − ) + 2  g F ) w F i ) I π θ τ w i A – 29 – 2 ( W θ 2 τ , ˆ hhh

2 ,  2 ,A 32 ( ) g 2  1 / i 1 /τ w ,F f ) w 1 τ ˆ F i cos  F θ θ (  F sin ) , κ 2 i 2 2 i c 2 w 2 i ( ) = / ) τ / , and θ → e 1 i f N ( 1 4 2 2 Z sin is given in ( 2 i cos κ 2 i (1 + 2 1 F hh f F e − ( ) κ  − i ˆ h − t,b 2 − ) sin i τ ,F /m i t,b are 1 i τ Γ = ˆ hhh + 2 2 i X 3 τ i τ 2 Z = / g X

( − i 1  m

W w f 2( m ˆ ˆ 3 h 4 F 4 θ ˆ ˆ 3 h h  A 3 3 4 i  c m ) Following the notations of the Higgs Hunter’s Guide [ + π ≡ π i m m π → N 2 2 w ) w cos i κ i i i 1 + (1 2 θ θ 2 2 qcd em em 64 κ e and √ √ /  w κ κ − i i 1 α α α , i θ − τ i f f f τ ˆ 2 h F κ 64 F − sin cos i 2 τ 128 i G G G A τ sin − − τ 2( , /m qcd 1 2 i 2( − ˆ α F ) = ) = ) = m ) = ) = ) = , i i i 4 2 are the squared invariant masses of the intermediate gauge bosons and Γ gg τ → γγ ) = ) = Zγ / ] and for completeness we collect them below. ( ( ( i i , κ , κ ≡ 2 ( 1 2 ˆ h , i i ˆ h ˆ h / i 1 F τ τ 74 Γ 1 , κ , κ Γ τ qcd ( ( s Γ i i 1 2 F τ τ / It is straightforward to obtain the heavy twin Higgs partial decay widths to the twin The partial decay widths of the twin Higgs to massless gauge bosons of the SM are, ( ( A 1 , α 1 2 A I I em ˆ where factors where the trilinear coupling The loop functions. gauge bosons from the above relationsα by interchanging Heavy Higgs decays intoto SM a pair di-Higgs. of the SM Higgs is, where the triangle loop functions Guide [ their total decay widths. where JHEP02(2018)048 B Phys. JHEP , (A.13) (A.14) , JHEP (2007) , (2009) 065 ]. , 11 D 75 Phys. Lett. (2010) 121 , (2006) 035003 SPIRE 08 IN JHEP ]. ][ , D 74 Phys. Rev. JHEP , , SPIRE IN ][ , . ]. 1 1 ]. ]. Phys. Rev. ≥ < , , , i i 1 1 τ τ hep-ph/0506256 SPIRE [ SPIRE SPIRE Folded and the LEP IN ≥ < ]. Natural little hierarchy from a partially IN i i IN if if ][ Naturalness in the Dark at the LHC τ τ A Pure-Glue Hidden Valley I. States and ][ ][ Phenomenology of hidden valleys at hadron SPIRE if if ]. Twin SUSY , hep-ph/0510273 ]. IN [ 2 ]. i ][ – 30 – , Mirror world at the iπ (2006) 231802 SPIRE 2 A Twin Higgs model from left-right symmetry The Twin Higgs: Natural electroweak breaking from , SPIRE i − IN  A Supersymmetric twin Higgs SPIRE i IN ]. 96  ][ τ iπ IN i i ][ τ τ √ (2006) 126 Echoes of a hidden valley at hadron colliders ][ Discovering the Higgs through highly-displaced vertices − arXiv:0712.2041 hep-ph/0609152 − − / [ arXiv:0903.0883 1 1  [ 1 ), which permits any use, distribution and reproduction in [ i i SPIRE 01 ]. ]. , √ √ τ τ  ]. 2 − IN i − − ]. 1+ 1 τ 1 1 ][ Macroscopic Strings and ‘Quirks’ at Colliders hep-ph/0605193  √ √ √ [ / SPIRE SPIRE − ln JHEP 1+ 1 SPIRE 1 h IN IN , SPIRE (2008) 008  IN (2007) 009 i 1 arcsin ][ ][ 2 (2009) 055 τ Phys. Rev. Lett. IN CC-BY 4.0 [ ][ ln − , 2 − hep-ph/0604261 07 Pure-glue hidden valleys through the Higgs portal h 1 02 i hep-ph/0512088 arXiv:1501.05310 [ 07 This article is distributed under the terms of the Creative Commons √ 1 4 τ [ [ (2008) 263 − arcsin − √       JHEP JHEP hep-ph/0604076 , JHEP , [ , ) = ) = B 661 i i (2007) 374 τ τ (2006) 108 (2015) 105 ( ( g f hep-ph/0604066 arXiv:0911.5616 arXiv:0805.4642 paradox [ 035009 Decays [ Lett. colliders [ 01 07 651 hep-ph/0509242 goldstone twin Higgs mirror symmetry M.J. Strassler and K.M. Zurek, T. Han, Z. Si, K.M. Zurek and M.J. Strassler, J. Kang and M.A. Luty, N. Craig, A. Katz, M. Strassler and R. Sundrum, M.J. Strassler and K.M. Zurek, R. Barbieri, T. Gregoire and L.J. Hall, Z. Chacko, Y. Nomura, M. Papucci and G. Perez, Z. Chacko, H.-S. Goh and R. Harnik, Z. Chacko, H.-S. Goh and R. Harnik, A. Falkowski, S. Pokorski and M. Schmaltz, S. Chang, L.J. Hall and N. Weiner, J.E. Juknevich, D. Melnikov and M.J. Strassler, J.E. Juknevich, G. 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