JHEP02(2019)157 Springer February 5, 2019 February 14, 2019 February 25, 2019 : November 16, 2018 a : : : , Revised Accepted Published Received Published for SISSA by https://doi.org/10.1007/JHEP02(2019)157 and Christiane Scherb a -triplet scalar field, which develops an induced -doublets. When the components of the triplet L L [email protected] , A. Hammad b [email protected] , . 3 Oliver Fischer, 1811.03476 a The Authors. c Phenomenological Models

The type II seesaw mechanism is an attractive way to generate the observed , [email protected] Hermann-von-Helmholtz-Platz 1, D-76344 Eggenstein-Leopoldshafen, Germany E-mail: [email protected] Department of Physics, UniversityKlingelbergstr. of 82, Basel, CH-4056 Basel, Switzerland Institute for Nuclear Physics, Karlsruhe Institute of Technology, b a Open Access Article funded by SCOAP Keywords: ArXiv ePrint: potentially leading to a characteristiccomponent displaced vertex decays signature into where same-sign thethe doubly-charged charged reconstructed leptons. level By wewould performing be find possible a that for detailed already thevertex analysis at considered signatures. at parameter the The point, current via discoveryFCC-hh/SppC. run dedicated prospects searches of are for further the displaced improved LHC at a the discovery HL-LHC and the model, taking into account alltion relevant as constraints, well including as charged colliderII lepton searches. flavour seesaw viola- We scenario, point where outYukawa that an couplings the of approximate symmetry the “lepton protected triplet number”-like lowrent to symmetry LHC scale the suppresses results. type lepton the In doublets, part is of still this largely parameter space untested the by triplet the components cur- can be long-lived, light neutrino masses. It postulatesvacuum a expectation SU(2) value after electroweaktrinos symmetry via breaking, its giving couplings masses to tofield the the have lepton neu- masses SU(2) around theWe discuss electroweak the scale, currently the allowed model parameter features space a of rich the phenomenology. minimal low scale type II seesaw Abstract: Stefan Antusch, Low scale type IIprospects seesaw: for present displaced constraints vertex and searches JHEP02(2019)157 8 ]. ]. T v 32 10 – , 9 29 -doublets. De- 2 L 14 ]. 19 6 ], or studied in its minimal 12 , ], and at the Tevatron [ 11 28 – -triplet field (a “triplet Higgs field”) L 4 26 7 6 – 1 – decays of the triplet to the lepton SU(2) ]. 14 8 – ∆ 3  Y  H H -doublets. This mechanism for neutrino mass generation is often referred 1 16 L ] is evidence that at least two of the neutrinos are massive. Since the SM 2 ], and also for a 100 TeV proton-proton collider in ref. [ , 1 ], and similar analyses exist for LEP [ 18 – 25 – 13 20 Searches for prompt decays to same-sign lepton pairs and pair-produced doubly charged In particular the “low scale” version of the type II seesaw mechanism, where the com- 4.1 Impact on4.2 the Higgs-to-diphoton rate LHC searches4.3 for prompt Signatures of long-lived violating Yukawa coupling (matrix) tailed phenomenological studies of suchin signatures refs. have [ been conducted for the LHC, e.g. Higgs bosons havegies) been [ performed at the LHC (for the different center-of-mass ener- It may be embedded fortional instance interesting in phenomenology left-right at symmetricversion the extensions with LHC, of only cf. the one refs. SM,its triplet with [ doubly addi- Higgs charged component added isdecay to of into the particular a SM. importance pair for Regarding phenomenology, of since the same-sign it triplet charged can Higgs leptons field, via the above mentioned lepton number two lepton SU(2) to as the type-II seesaw mechanism [ ponents of the tripletimplications field for have various masses well around known the observables electroweak at scale different energy (or scales, TeV scale), see has e.g. [ cannot account for these massesSM in (BSM). a An renormalizable attractive way,freedom possibility this for of calls generating the for the SM physics masses consists beyondto for the in the the adding scalar neutrino a sector degrees scalarafter of of SU(2) the electroweak theory, symmetry which breaking, obtains giving an masses induced to vacuum expectation the value neutrinos via its couplings to 1 Introduction The Standard Model (SM)observed of phenomena elementary at particles many different is energyoscillations successfully scales. [ describing However, a the observation plethora of of neutrino 5 Summary of present6 constraints Displaced vertex signature:7 analysis for Conclusions a benchmark point 4 Signatures from doubly charged scalars at the LHC Contents 1 Introduction 2 The minimal type3 II seesaw extension Constraints from of non-collider the experiments Standard Model JHEP02(2019)157 ) ]. 1 2 , 33 2 (2.2) (2.1) , (1 is not too ∼ ∆ ]. When the Y 42 Yukawa − L . ∆) , ! 2 (Φ + ], the larger Lorentz factors and √ ++ ∆ V 45 ∆ − , − 0 2 + 44 √ ∆ ∆ ∆)) µ

D ( 2). Their matrix representation is given by: † , 3 , ∆) – 2 – µ (1 and ∆ = D ∼ ], and also at the Tevatron, cf. e.g. [ 1 TeV, provided the center-of-mass energy is 3 TeV, (( ! 41 ∼ 0 T r + Φ Φ invariant Lagrangian for this scalar sector is

Φ) + 600 GeV (for the part of parameter space where Y µ ∼ D boson pairs have recently been performed at LHC in ref. [ Φ = ( † U(1) ] and CMS [ W × Φ) ]. µ 40 L , 38 D 39 = ( SU(2) L × C ], where it has been claimed that the high-luminosity (HL) LHC can probe a broad 43 In this paper we discuss the currently allowed parameter space of the minimal low The possibility that the scalar particles do not decay promptly, but can be rather long The SU(3) larger luminosities would further enhance the sensitivity of these displaced2 vertex searches. The minimal typeIn the II minimal seesaw type-II seesaw extension modeland of the an scalar the additional sector triplet Standard consists scalar of Model the field SM ∆ scalar Φ lifetimes are not large enoughthe to displaced pass vertex through a signature,for sufficient we part a perform of selected a the benchmark detector. detaileddiscovery point. analysis would Finally, for be at We possible the findhigher for reconstructed center-of-mass that the level, energy already considered like the parameter at FCC-hh/SppC point. the [ current At a run future of collider the with LHC, a lepton flavour violation as wellcalculate as carefully various (prompt the andthe non-prompt) constraints simulated collider from events searches. which the We analyses. satisfy prompt the Reconsidering constraints searches, “promptness” from criteria HSCP takingcannot searches, applied we into be in find account applied that the the to only experimental existing the analyses triplet components of the minimal type II seesaw because their ref. [ part of the parameter spaceby via the such HSCP displaced constraints. vertex searches, restricted however severely scale type II seesaw model, taking into account all relevant constraints, including charged the tracker). The corresponding signaturedeposition would in be, the among different others,LHC subdetectors. a by characteristic Searches energy ATLAS for [ HSCPsdecays of have a been long performed lived particlesearch at are for the non-prompt the but displaced occur secondary inside vertices. the detector, This one possibility might has also recently been discussed in as discussed in ref. [ lived, has important consequencesconstraints for from LHC prompt searches: same-signconsider charged while them leptons as the can heavy abovelong no Stable mentioned for longer Charged strong them be Particles to applied, pass (HSCPs) one through if the might their relevant lifetime parts of is the sufficiently detector, i.e. the muon system (or Without any significant excessprovide stringent of constraints events, from direct thecharged searches, scalars LHC to which be require analyses above the mentionedsmall). masses above of Moreover, the presently searches doubly atdoubly future charged lepton scalars with colliders masses could have the potential to discover Searches for same-sign JHEP02(2019)157 . and (2.8) (2.9) (2.4) (2.6) (2.7) (2.14) (2.11) (2.12) (2.13) T 0 λ , and , h, H, A 2 T ,  v T ) λ T ,H 0 , λ  HT + H λ T . , λ T 2 λ 2 v 2( T 2 . The tadpole equations , κv − ∆)) 2 ij √ Φ κv , † | ) † ! 2 T (with mass dimension = 1), . 2 2 v : , Φ , ∆ + 0 2 √ † )) (2.10) (∆ Φ (2.3) κ κ κv Y 2 ∆ 2 2 λv √ µ ∆∆ Φ T v µ + | 0 0 † 4 1 B B T r ) v B 4 ( λ B 0 = Φ 2 . T 0

2 g T + v 2 T HT g 2 T i + 4 + 4 − C 0 λ 2 i HT T 2 v 1 0 ) (2.5) 2 2 λ κv v H.c. . HT √ T ) ) − λ 0 ) 2 0 ∆) are absorbed by the SM gauge bosons + λ C C † λ Φ + + and = √ − h.c. a 0 µ ∆) HT ` ∆] + ) i 0 − − + + † , (∆ HT 2 G The scalar potential and the new Yukawa λ ∆ κv W a ∆ + 2 2 2 µ λ A A 2 a 2 h Φ + ( (∆ v v ( ( T T r + ∆) [ † T 1 2 √ iσ 2 † 2 T 2 4 v c p p and ∆ – 3 – T r ig ¯ HT HT igT 2 ` 0 0 − 2 M − HT κv and Φ − +  ∆ λ λ √ ((∆ † λ v 2 T iσ Y − ( G T v Φ C C ! > + + Φ + ∆ + 2 1 , the seesaw parameter = ) v T r . Evolving the scalar fields around their VEVs and Φ = 0 v µ µ ) T Φ T + + † T 0 v T T 0 ∂ ∂ HT 0 + 2 2 κ 2 A ∆ v v

Φ λ λ λ ( M A A Y HT 2 2 2 T 0 ( ( 2  m κv κv L µ + − − − 1 λ √ 1 2 1 2 √ κv √ Φ = in terms of the couplings and ∆ = T T and 2 µ + µ v = = = = λ T = √ ( µ D D 2 h  2 H i M ∆) = − − HT  2 H , m Φ λ m 2 H h ( = = m (Φ m 2 − and 2 T V µ and the new Yukawa couplings matrix ( µ = M T v B , 2 v and 2 λ . The masses for the physical Higgs bosons are v − Z = A , two mass parameters and  HT 0 allow us to express Physical masses andterm parameter contain space. theλ following parameters: fivethe coupling VEVs parameters with where (as we willminimizing see the later) potential leadsThe to three seven massless physical GoldstoneW massive bosons eigenstates: and the new Yukawa terms After electroweak symmetry breaking bothvalues (VEVs) scalar fields acquire their vacuum expectation the scalar potential with the covariant derivaties JHEP02(2019)157 ) 1 ). . = κ . and (3.1) (3.2) 2.10 3 = 0  ij (2.15) 0 such ) H and T ∆ < λ m Y HT − 0 HT λ . λ  λ ] (with the ad- H m 50 , = 0, which leads to the relation , respectively. Their 49 T 0 HT v HT ) thus fixes the Yukawa 0 λ λ 3.2 , but we keep , and the doubly charged scalar 0 HT ) on λ  . 246 GeV. By solving the tadpole PMNS 2.8 2 2 H T U ≈ to all the mass terms are suppressed κv M are used from [ v we obtain for T diag ν ∆ . 0 ) it avoids additional decay modes, but Y λ m 2 T /κ ) and ( are effectively free parameters. 2 , with a mass splitting T = PMNS M v 4.3 125 GeV. Neglecting the terms in eq. ( T 2.9 2  T and κv U ) † v PMNS 0 /v H ∼ , we thus use the SM value for √ ( HT T 2 2 U T . Only for illustrating some of the phenomeno- – 4 – λ h λ m v h √ = T κv m v ∆ m 1 T 2 Y v ] for the evaluation of the model parameters and for and √ = (cf. section  to the SM value 48 = ν , H v m ij  47 m ) such that H ∆ Y λ ( to play the role of the SM Higgs boson (with the requirement h , and we will neglect this contribution in the following discussion. somewhat below In the type-II seesaw model the active neutrinos acquire masses after T v , such that T  ] and Spheno [ H for our choice of assumptions. κv ), the observed neutrino masses constrain the model parameters ( 2 m 46 ), and we fix ij is the Pontecorvo-Maki-Nakagawa-Sakata matrix. In the following, normal ) √ H 3.1 2. The masses of the singly charged scalar ∆ . is the lightest of the new scalars. The reason for this choice is that when we Y 4 + < m = 0 PMNS / 2  h U T v depend only via the first term in eqs. ( 0 H m λ Via eq. ( In the following, we allow in most cases for a non-zero The contributions from the couplings 0 HT . For a given neutrino mass ordering the Yukawa couplings can be obtained via  λ T where hierarchy is assumed andditional best assumption fit of values thecouplings for Majorana ( phase being zero). Eq. ( proportional to the triplet mass (squared). v electroweak symmetry breaking via the contributions from the new Yukawa term, yielding It is referred to as a “seesaw” model, because the light neutrino masses are inversely the numerical calculation of the constraints from non-collider experiments in3 section Constraints from non-collider experiments Neutrino masses. that discuss potentially long-lived allows to have logical constraints we will makenearly the degenerate simplifying masses assumption for that We all use extra Sarah scalars [ (controlled by the parameters and H masses are fixed− to the same scale by that that are proportional to the triplet VEV by the triplet VEV For definiteness, in our analyses we will fix the couplings in the following way: equations and taking the leading order in Furthermore, we chose In the following we fix the VEV JHEP02(2019)157 ) Z = > n → ]. l T m GeV (3.3) (3.4) 57 Z l  v – 9 k H l − 55 from the m 10 exchange. → = 300 GeV i 12 × GeV, l − 1 ( 9 .  ]:  5 − 10 H H 58 BR 10 > × m parameter is mea- 0 T × . ρ v 1 8 . 4 < ) ] on the branching ratio = 300 GeV and GeV, > 54 . 9 [ ¯ eee − T  2 | . v = 150 GeV, H 13 1 GeV. → 10 ki . 10 − ) m 2 × µ  .  − ( ∆ The anomalous magnetic moment a new on-shell decay mode 8 10 can be written as 4 H . H . Y 10 10 8 ( Z ρ m − × m T 2 BR 2 f m × v receives contributions from loops with > 2 mn 10 . , G ) T 4 3) < 2 2 T T . ∆ eγ × 2 2 v 64 v v v v Y with 2 4 < ( | → 0(6  = 150 GeV, . ) µ H ¯ eee , e.g. 1 + 1 + eγ – 5 – T m ) =  v can be mediated at tree level via n → = H In the type II seesaw model, lepton flavor violating l → µ ρ m m ]. In the model l µ ¯ eee GeV for masses = 11659183 k ( l ¯ 9 51 , where the appearing couplings to the new scalars are ]. α − → = 11659208 l SM µ → BR 73 a µ 10 i l −− exp µ ( × a 00023 [ 6 . ,H and . ]. Since the Yukawa couplings are inversely proportional to the 0 BR 1 k l 9 GeV [ ++ 53 .  j > From electroweak precision measurements the l i H ¯ 42 l T GeV for masses . v 9 or > T → − 00037 α v . τ 10  1 , ν H ]: − × ' m For a doubly charged mass, 1 52 ρ . = 600 GeV respectively. A discussion of the dependence of the LFV constraints ,H GeV and is allowed. The LEP experiment constrained the allowed decay width of the 3 + 9 −  > H ∓∓ H ]: 10 T H v m Also the lepton flavor violating process 51 ×  6 . The result deviates by aboutby three [ standard deviations from the SM predicted value, given and on the PMNS parameters and neutrino massThe spectrum anomalous can magnetic be moment found ofof e.g. the the in muon muon. refs. was [ measured very precisely by the Muon g-2 collaboration [ inversely proportional to themost triplet stringent VEV. upper boundof The of this MEG process, collaboration whichspectrum) states translates the into (for currently a our choice2 lower of limit PMNS of parameters the and neutrino triplet mass VEV of, e.g., neutrino mass spectrum) a lower limitand for 600 GeV respectively. virtual The most stringent bound arisesSINDRUM from experiment [ triplet VEV, the experimental bounds constitute (for our choice of PMNS parameters and Lepton flavor violating processes. (LFV) processes The contribution of the doubly chargedis scalars to given the by LFV [ branching ratio Z width. H boson into non-SM particles toon the be mass below 2 MeV at 95% CL, which implies the lower limit sured to be which leads to an upper bound for the triplet VEV Constraints on JHEP02(2019)157 → → (4.1) pp 1).  . 1 GeV, . H = 0 = 0 T as v T υ  , such that ) H , depending on the 0 0 HT ¯  f λ and H f 1 2  m , which has the clearest +  W  H , . HT → H 2 µ 2 µ λ ∗ ( ) GeV. This region is, however, m m ). The corresponding Feynman   2 2 2 10 | | 2 H υ   − ] and references therein. ij ij W ), it is the lightest of the new scalars  m ) ) ( , to two on-shell W-bosons, H 2 H 2 2 H 10 60  ∆ ∆  β m l m ≈ Y Y m 2 ( (  . α W is dominant, the contribution from top 2 − l π = ij ij π GeV the decay to two same-sign leptons is H ) ) T  → 96 4  + υ → 12 ∆ ∆ − W H Y Y ( ( hH  | | 10 m  – 6 – 2 2 = 13 TeV and the example value H H < s − − , g T is twice the production through the neutral current √ v ∓ HT ) = ) = λ  H . In comparison, the t-channel production cross section for , the production cross section for the s-channel charged  , but falls off less strongly with H . For  1 2 ( 1  −− H . µ 2 H υ (   H H µ 2 H m δa H δa m → ++ m ≈  H dominates above about 300 GeV. The t-channel production of a −− W → H ]. The production cross sections for all production modes of the triplet −− ∗ → ++ 59 , and multi-vector bosons, these searches are not as stringent compared ¯ t H /γ t pp ∗ hH g ++ Z H is suppressed by the triplet VEV (which in the plot is chosen as = 0 for illustration (such that . In the SM the contribution of →  → or into the three body final states  pp 0 HT W λ ∓  H for some range of the triplet mass and We remark that, although we will focus on searches for doubly charged scalars, also As one can see from figure The type II seesaw model modifies the theory prediction for this amplitude: at one µ W W a   quarks is smaller andcharged scalars has are opposite proportional sign. to the The couplings contributions from the doubly and singly 4.1 Impact on theThe Higgs-to-diphoton decay rate of thelevel (SM-like) in Higgs the boson SM,bosons and into it two is photons dominated is by introduced the at contribution the from one-loop top quarks and the gauge W single the singly charged scalars arefrom subject single to LHC top, searches. Here,to due those to for the the large doubly backgrounds charged scalars, see e.g. ref. [ diagrams are shown in figure current process process is subdominant for small W triplet VEV and the mass dominant, cf. e.g. [ components are shown infixing figure 4 Signatures from doublyIn charged the scalars following, at we thecollider will signatures. LHC focus Under on our assumptions the (cf.and doubly section can charged decay scalar to two same-sign leptons, We notice that, in principle, the modifiedof theory prediction could explain thealready observed value excluded by the LFV experiments. loop level the amplitude receives new contributions from both JHEP02(2019)157 – = s 20 √ (i.e. the  H ±± ∓∓ ±± j j j j H H H = 0. ± ]). ∓ ± ± W W W 62 W 0 HT λ = 7 TeV, 8 TeV and 13 TeV [ s p p p √ p ∓ ±± ±± ∓∓ H H H H At the LHC, searches for decays to same-sign decays – 7 –  ], which limits the contribution from the doubly and H where this is satisfied (cf. e.g. [ 61 [ ∗ ±∗ 32 3 1 GeV for the triplet Higgs vev and 0 HT /γ . . . ∗ W 0 λ Z +0 − = 0 1 . T and υ = 1 ) ) HT λ γγ γγ → → 300 GeV, the strongest constraints stem from the data sets with 36.1/fb h h ( ( > SM exp p p p p σ σ  = H µ . Production cross section for the dominant production channels at the LHC with . Dominant Feynman diagrams for the production of doubly charged scalers m The currently reported signal strength from CMS in terms of the SM prediction is ]. For 4.2 LHC searchesSearches for for prompt same-sign leptonleptons have pairs. been performed at center-of-mass25 energies where we neglected a suppressednents from dependency the on doublet the and mixing triplet angle scalar of fields, the whichgiven CP-even is by compo- assumed to besingly small. charged scalars toregion be of less parameters than 100% of the SM predicted value. There is a broad Figure 2 doubly charged components of thevia triplet neutral Higgs and field charged current ∆ interactions. in the minimal type II seesaw mechanism) Figure 1 13 TeV, the example values JHEP02(2019)157 ],  74 , [ H (4.3) (4.2)  T m υ to decay  2 W GeV. 2 H 4 m . The decay  − m f pairs. In the H  10 bosons has been lies between 200 F × −− decays mainly via 3   W H 160 GeV, the domi- is not too small (or  2 of the reconstructed | & 0  H 0 , and values of . ∆ ++ d T shows the total decay m H q,q Y v H  decays are dominant and V is proportional to 3  | H 0 0 H ¯ f W For parameter values of the m q,q f m X ]. For the numerical analysis, c  . The most stringent constraint 74 N W eµ and dominates for smaller value of ]. Figure = 130 GeV, where the red and black → 3 + 75 ∆ ∗ and   ) Y   H into a pair of same-sign leptons is domi- ] a search for pairs of µµ  3 W . , m H π ( 33 1 mm and  ee  m pairs from decaying < for 2 T H | W – 8 – υ 6144 1, which is satisfied for T θ 2 mm 6 ) is given in ref. [ eµ . is the isospin partner of the fermion υ g and the scalar mass → ∼ 0 0 In ref. [ , sin  ) f T < 2 H v   µµ  × ) = | 0 0 0 , ¯ H W H f d z /m | |  f ee is kinematically forbidden and the 2 W  pairs. W , where 0 m  ¯ ( W f and the (transverse) impact parameter → F f W W ]), where the “promptness” condition is defined via the longitu- might be comparatively long-lived, we take only the fraction of → 0   z 22 ∗ GeV, the decay of  ) ). For larger W W 4  T  H − is the dominant decay mode, i.e. as long as ( GeV), the cross section depends only on → H /v W 10  β 4 ∗ ( 1 l ) − BR   α .  l ∝ 10 W T W ∆ v → 300 GeV comes from the di-muon final state searches with 8 TeV (e.g. from the ( ∼ Y →  <  W being the color factor and the factor of 3 stems from the sum over the three lepton  bosons are on-shell has been considered. No excess above the SM predictions has = 13 TeV for same-sign  c H H → H N s It is important to stress that the analyses mentioned above require the W Γ( is below m √ . The rate of three body decays  T T with generations. The function we use the decaywidth (blue rate dotted calculated line) as with a MadGraph function of [ into a pair ofv same-sign leptons is proportional to Lifetime of the doublytriplet charged VEV scalars atnant the (since LHC. nant decay to on-shell H the been found. This leadsand 220 to GeV an for exclusion of the mass4.3 region where Signatures of long-lived searches where the events into account which satisfy thesein “promptness” the criteria. next We section. will discuss this in detail Searches for same-sign performed at ATLAS with 36.1/fb. Only the region where the When we apply the constraints on the cross section from prompt same-sign lepton pair promptly to three different modes,for same-sign ATLAS analysis in ref. [ dinal impact parameter track as following we useput the stringent bounds bounds on from theWhen the production ATLAS cross section analyses. ofv the Their doubly charged negative Higgsbelow search bosons. about results 620 GeV can be excluded. at JHEP02(2019)157  l  l → GeV and  4 − H particles that 10 ×  1 H ∼ T v GeV. as a function of the triplet 3 . − T  v 10 H ∼ -8 T 10 mm 10 υ -6 10 mm 10 is the proper lifetime, of the doubly charged 0.0001 mm 0.0001 τ 0.0001 mm 0.0001 0.01 mm 0.01 0.01 mm 0.01 1 mm 1 – 9 – , where cτ = 130 GeV) is at . It can be seen that between 1 cm 1 4  155 GeV a proper decay length above 1 mm is possible. H respectively. 0 < m 10 cm 10 ff   H in figure W m T v → ∗ ) as a function of its mass and the triplet VEV  and = 130 GeV (blue). Red and black lines are partial decay widths for W (   GeV and   H H 3 H W − m m 10 → . Total decay width of the doubly charged scalar field . Contours of proper decay length for × T  1 v The resulting small total decay width gives rise to lifetimes for the H ∼ T can be macroscopic forfunction certain of parameter choices. Wev show the proper decay length as a lines are the partial decaycan width for get three a body minimal andthe same-sign total two di-leptons lines decay respectively. cross, width One which (and (for hence a maximal lifetime) at the point where Figure 4 scalar particle Figure 3 VEV and JHEP02(2019)157 ) 1 1 γ − ≈ (4.5) (4.6) (4.4) being cτ we use L , and the  5 H , and , of  2 lab x x γ H decays for a given ∆ − e  − H = 130 GeV, where , is shown as a function of L 1 lab γ ) x ]. For the current LHC run x  = 13 TeV, 14 TeV and 100 TeV. s ∆ H 67 s , √ − ( e √ m 1 =  − for ) H 2 1 σ γ − )  2 2 γ p H x √ , x m GeV and cτ 1 cτ 4 x ) is the probability for a particle with a given − = − ( ( 2 e P 10 lab 1 , x – 10 – × τ 1 | − x ) = . We remark that this first look is on the parton ~v ( 2 | T L The number of displaced = 5 1 P γ v = s, T p v √ with two pairs of same sign di-lepton in the final state. as a function of lab , = 1 m. The numbers of displaced events are shown in cτ and 2 γ x ) with the average Lorentz factors from figure 2 ∓∓ dx ∆ , x x  1 2 H 4.4 x 1 x H x (  Z m N H ) = 2 → ∗ , x to decay within given boundaries in the detector, defined by the range 1 . /Z x τ 5 = 1 mm and ∗ ( ) being the inclusive production cross section of a single γ s P 1 . We use eq. ( is the decay length in the laboratory frame given by (with the Lorentz factor Γ with the total decay width Γ. For the Lorentz factor . It is given by: x 1 √ / 2 → ( − ~ x lab = 14 TeV and the FCC-hh with 100 TeV, and integrated luminosities of 3000 fb . Average Lorentz factor x  pp as a function of ≤ = s in figure H 6 x σ √ τ In the next section we will describe a possible LHC analysis to search for long lived For a first look at the prospects for displaced vertex searches, we consider the HL-LHC  ≤ H 1 level and serves illustrative purposes only. doubly charged scalar bosons with cm. We willcurrent consider the pair production of doubly charged scalar through the neutral m with and 20 ab boundaries figure and average values obtained from simulationsat with center-of-mass MadGraph energy [ 13 TeV,the the FCC-hh HL-LHC with at center-of-mass a energy center-of-mass energy 100 TeV 14 TeV, the and average for where ∆ with the considered integrated luminosity. proper lifetime x Displaced vertex probabilities. parameter point can be expressed as: Figure 5 JHEP02(2019)157 , , . ]. X ∓∓  15 as a + 1 H H 7 100  ∓∓ H H production 10  →  6 4 ∗ ]) and CMS (cf. H 10 . The resulting H themselves could 0 d /Z 40 or  , ∗ γ H 39 X → + Searches for heavy stable is shown in figure 8 10 pp only.   β l H  α ∓∓ l H → ]. To simulate samples for a wide  22 H  H → ∗ . In this case the charged current process /Z + ∗ γ W – 11 – → + pp ∓∓ as well as the impact parameter 1 | H θ 100 sin = 1 m, for the HL-LHC (left) and the FCC-hh (right). For this 2 × x 4 0 10 z | . T υ to decay into 6 ∓ 10 ) are satisfied. We did this by simulating samples of events for the and H = 1 mm and 4.2 can add additional signal channels, such as 1  x H ∓ m H . Total number of doubly charged Higgs bosons decaying with a displacement between ], and extracted  ]). They require that the HSCP candidate are stable on collider scales, i.e. they pass 22 H 41 In the following, we will focus on the production channel We note that, in general, including also the singly charged scalars is expected to → function of Searches for heavy stable chargedcharged particles particles at (HSCPs) the have LHC. beene.g. performed [ by ATLAS (cf. e.g.the [ relevant parts of the detector. For the ATLAS analysis, the HSCP candidate has to production cross section to obtainwith the the “effective” constraints production from crossrange the section of experimental to be parameter analysis compared [ points,as we in performed [ aexcluded fast region detector from simulation prompt using searches the for same decays cuts As mentioned in the previous section, whencross applying section the constraints we on have the tocriteria take of care eq. that werelevant ( parameter only points count the to events obtainpoint) where the satisfy the fraction the “promptness” of “promptness” events which criteria. (for the This given fraction parameter is then multiplied with the total which might increase the sensitivity.be Searching for viable the if singly they charged have sizable branching ratios intowhich electrons means and that muons, our see results e.g. should ref. be [ Application viewed of as constraints conservative from estimates. prompt searches to potentially long-lived enhance the discovery prospects ofwhich this allows model, the in particularpp when there is a mass splitting Figure 6 the boundaries figure we consider the production channel JHEP02(2019)157 , σ ) ∞ 2 (4.7) GeV, = , x . Also 4 1 2 3 x − x − ( 10 P 10 from HSCP × ∼ 5 ) . (for passing the  ∞ , H = 7 47 − T v 10 (11 m ∼ P ) ∞ = 8 TeV) searches for same-sign , GeV, i.e. the benchmark point s 4 56 and = 90 GeV, . √ − actually pass through the relevant (1 m 0 . 10 P  ∼  H 1 × lab ) x x H m ∆ ∞ , − , they assume the candidate to be a lepton- = 5 e e T LHC TeV 8 v (1 m ). ) = = 2 P – 12 – ∞ Q , 1 x dE/dx (for passing the muon system). This clearly means ( P ], taking the possible displacement into account. The dashed 182 = 130 GeV, 22 − 10  5, one obtains H ∼ ∼ m ) γ ]). On the other hand, for being the outer radius of the respective detector part, and 4, ∞ , 1 43 ∼ x γ (11 m P 35 cm and )) with ∼ . Parameter space constraints from prompt LHC ( 4.5 cτ To evaluate the constraint on the production cross section for this parameter point ispasses not the excluded muon by system, thequite whereas ATLAS a likely analysis “tracker exclude which only” it. requires analysisand for a (as So doubly performed track far, charged that by scalars. however,to CMS) It this scalars could would analysis with therefore lower does be masses, highly not and desirable exist ideally to for also extend the to such search the low case masses of finite lifetimes. For example, for we will consider intracker) the and next section,that we HSCP roughly constraints get cannot excludeclaimed this recently parameter in point [ (inwhere contrast to what has been i.e. the probability characteristic ionization energy loss ( searches, we must only count theparts events of where the the detector.(cf. This eq. means, ( we have to use the “effective” cross section the tracks have tohave pass to the pass muon through system, theHowever, and while tracker the (such a ATLAS that “tracker analysis multiple only” goes100 GeV, hits down analysis and in to for where 50 the HSCP GeV, they candidates tracker thelike only with can CMS fermion be analysis (not only recorded). a starts scalar at as in our case). For a well reconstructed track the signature is a Figure 7 dileptons at 95% confidenceblack level line [ indicates where theyellow effective line cross shows section where is the smaller limit than from the the observed prompt limit. search The would dotted bepass if the all muon decays were system, prompt. while the CMS performed two versions of the analysis, one where JHEP02(2019)157 . ] 65  – H 63 . 0 ¯ f f  W (for our example choice eγ parameter ρ → allowed µ 90 GeV. For finite lifetimes one may also ∼ γ e → – 13 –

μ LHC TeV8 LHCTeV 13 90 GeV would not have been missed. In the following, we muon anomalous magnetic moment magnetic anomalous muon masses above this value. .   H H m LHC TeV 7 with ] for prompt searches). They put stringent limits on the production cross 26 LLP  . The red, yellow and brown areas are excluded by the LHC searches for same sign 1 mm. Above this line the dominant decay is the three-body decay to H . Parameter space of the type-II seesaw model. The black area in top is excluded because ¯ eee parameter. The cyan vertical area is the estimate for the excluded region by searches at LEP ρ cτ > → Finally, we note that HSCPs can be searched for very well in the particularly clean bosons. Finally, the white area is allowed. The part of the white area inside the dashed and µ collider a will therefore focus on environment of a lepton collider.(cf. also At ref. LEP, [ thesesection searches of have been heavy done, chargedthem cf. particles for refs. that masses [ manage upreconsider to to escape the these kinematic from limits, limit the however of detector we and expect exclude that in the cleaner environment of a lepton The lower dashed linetext. is obtained The from upperwhere the dotted limit line on (where the no prompt experimental decays constraints as exist described to in the date) main shows the region of PMNS parameters andon neutrino mass spectrum) anddi-lepton final the states green at 7, areaW 8 is and excluded 13 TeV. by The constraints dotted purple area black is lines excluded by on LHC searches the for left same-sign (denoted by LLP) features displaced decays from long-lived Figure 8 of the LEP. The orange region onanomalous the magnetic bottom moment. is excluded The by the magenta experimental area measurement is for excluded the muon by JHEP02(2019)157 . 1 6 T ]). → v 8 37 GeV , 4  17 − H 10 × ) in figure 2 = 5 T v decays, we perform conversion in nuclei in the low scale type 200 GeV there exists e  700 GeV. We note that  . → H ∼ GeV, the decays H µ 4  GeV is still largely untested 1 cm, we consider the three −  4 H − H 10 ≈ and m m 10 e > 3 cτ > T v → T v µ = 0 and the other parameters fixed as ], which is shown by the purple area in GeV and ) GeV for 1 33 9 0 HT − − λ 10 (10 – 14 – . is long-lived and not excluded by neither prompt O T v 220 GeV [  H . .  H GeV 5 m 620 GeV, constraints from LFV processes are the most powerful, − . & ]). . For this benchmark point with to be above about  for the coupling to the Higgs doublets would be suppressed by the approximate 36 2 T is suppressed. Searches for di-W bosons are efficient only in the narrow H – v κ m  β l 34  α , the HL-LHC with 14 TeV center-of-mass energy and integrated luminosity start to dominate the branching ratio, and the number of prompt decays l 1 . −  = 130 GeV, and for definiteness 8 → W , and the FCC-hh with 100 TeV center-of-mass energy and integrated luminosity 1   . For each of these colliders we generate a Monte Carlo event sample with 10  1 − H in the future, the sensitivitieswill of strongly searches improve, for allowing(see, to e.g., test [ more of the high mass region with small range of 200 GeV figure Finally, for constraining an allowed region wheresearches the at LHC nor by the constraintsWhen from the the existing triplet HSCP vacuum analyses. W expectation value is H We find that for 10 − m An alternative option consists in assigning lepton number to the triplet Higgs field (cf. e.g. [ • • • 1 3000 fb 20 ab Then the parameter symmetry. This part ofLFV parameter bounds. space for the low type II seesaw mechanism is strongly constrained by an analysis at the reconstructedand level. As benchmark pointdiscussed we in consider section different hadron colliders: the LHCnosity with 100 13 fb TeV center-of-mass energy and integrated lumi- part of this physically well-motivated parameter space. 6 Displaced vertex signature:To analysis study in for detail a the prospect benchmark for point displaced vertex searches from could be motivated bywould an suppress approximate the “lepton Yukawaprovide couplings number”-like a of symmetry. “natural” the explanation The triplet fort’Hooft symmetry sense to the that smallness the neutrino masses of lepton go theSearches to doublets for zero observed and when displaced neutrino the vertex can masses approximate signatures, symmetry (in thus as is the discussed restored). in the next section, can help to probe It is striking that the partby current of experiments. parameter space However, this where is the region where the low type II seesaw mechanism We summarise the present constraints onII doubly seesaw charged scalars scenario (underThe the various simplifying constraints assumptions have been discussed discussed in in section the previous sections. 5 Summary of present constraints JHEP02(2019)157 2 ]. . 0 72 1 [ ]. For . 25 GeV R > 0 67 , we find > < 1 ) ) 4 mm. This µ ]. Finally, a (  > T 72 20 GeV. – P 0 H candidate. In fig- track and its dis- ( d  decays may occur 70 R     H H H H m = µµ candidate. Therefore we require M 1 and we impose a cut of ∆  . H ], while the fast detector simulation is 68 – 15 – For lifetimes as small as for the here considered 8 mm and the impact parameter > xy L shows the resulting displacement of the secondary vertex For signal event selection we require at least one pair of 9 decays dominantly within the first (few) layers of the pixel ]. plane  69 32000 events remain that are conform with our selection criteria. ) of reconstructed and generator events to be ∆ H decay) and the transverse momentum of the ∼  XY H  ( H R 5. We consider here only muons for simplicity, also in parts because it is not . 2 500 and From the simulated event samples we reconstruct the < | ∼ ) µ we show the invariant mass of the lepton pair (here two muons) and the transverse ( η | After applying the selection cuts, the cut flow of which is shown in table Furthermore, we require at least one displaced decay with same sign dimuons with a In general, for benchmark points with larger lifetimes the 10 luminosity, before applying any cuts. that about 13 eventsmany remain as in the LHCIt data is set, worth while mentioning for that, while the the HL-LHC same and benchmark FCC-hh point as is used for different detector placement parameters from theevent-by-event observed basis. distribution of Figure the(defined same-sign by lepton the pairs onure an displacement of the secondary vertex.ber All of histograms events are at normalized the to LHC, the HL-LHC expected and num- FCC-hh, considering the corresponding integrated matching condition between our reconstructed eventsto and ensure generator that level the events reconstructed is tracksthe imposed stem difference from the ∆ Results. between two same sign muonsimpose to further ensure a their separation. cut on To increase the the invariant dimuon cut mass efficiencydisplacement to we in be the is expected to remove possible SM backgrounds and detector effects [ Selection requirements. charged tracks for the final stateand leptons, with lepton transverseclear momenta to us whatmuon kind system. of We signal use an a muon electron isolation would cone cause radius of that 0 appears inside the HCAL or ID algorithms, which dependfected on by the the displacement full ofand detector each has information, event. a are very Sincedetected characteristic our thus and dE/dx parent non-trivially we particle identified, af- assume, is providedselection however, electrically they requirements. that charged are 100% being of caught its by decays the can triggers be and the analysis tracker, and we consider theprompt corresponding signatures. reconstruction efficiency We note to that be thepoints track-only equal with analysis to is such those not small of sufficient to lifetimes. probe parameter anywhere in the detector system, e.g. in the ECAL or in the muon system. The particle background is carried outparton shower with and the hadronisation we eventcarried use generator out Pythia6 by [ MadGraph5 Delphes version [ 2.4.3 [ Event reconstruction efficiency. benchmark point the events, using pileup events = 50 per vertex. The Monte Carlo simulations of signal and JHEP02(2019)157 to same sign 31759 = 130 GeV was 105864 203586 209883 244050 345323 FCC-hh   H H m 467 2749 6332 6508 8135 10640 -triplet scalar field, which HL-LHC affect the analysis, greatly L -doublets. L γ GeV and , respectively. In our analysis we 4 1 − 76 − 175 180 220 280 13.6 LHC 10 × integrated luminosity), the detector only. 2 . × 0 200 GeV, there exists an allowed region = 5 ∓∓ T > . H v , and 20 ab ) 1   − H H µ, µ ( – 16 – m → R ∗ Z , 3000 fb ∗ 1 150 GeV 5&∆ γ . − 2 < → GeV and < 8 mm 1  | 4 mm pp ) − H > µ Cuts > ( 10 0 η xy | d . < m L T v Two same sign muons . is long-lived and not excluded by neither prompt searches at LHC nor by 110 GeV 25 GeV& Expected events (detector level) GeV >  5 ) − H µ ( T . Cut flow of simulated signal samples for displaced decays of the P For the characteristic displaced vertex signature where the doubly-charged component For 10 We have also reconsidered constraints from present HSCP searches. We find that for Taking into account all relevant present constraints, including charged lepton flavour where the the constraints from the existing HSCP analyses. decays into same-sign charged leptons,structed we level have for performed a a selected detailed benchmark, analysis which at has the a recon- lifetime about 1 cm such that “tracker most of the relevant parameterbe space for applied the because long the lived lifetimesthe doubly are detector. charged not scalars large Nevertheless, they enough such cannot lifetimes to searches above pass could through a test the few the relevantlived cm part parts doubly of of via charged the scalars a parameter do “tracker not space only” exist with analysis. but would Such be analyses very applicable desirable. to long space of thethat minimal the low triplet scalefrom components type the can prompt II be searches, seesaw taking“promptness” long into model. criteria account lived, applied only in and the We the simulated calculated investigated experimental events carefully which analyses. the satisfy the possibility the constraints ate the observed lightobtains neutrino an masses. induced vacuum expectation Itmasses value postulates after to a electroweak the symmetry SU(2) neutrinos breaking, via giving its couplings to twoviolation lepton as SU(2) well as collider searches, we have discussed the currently allowed parameter 7 Conclusions In this paperprospects we in the have low investigated scale present type II constraints seesaw and mechanism, which displaced is an vertex attractive signature way to gener- consider the production channel simulation and normalization factorsdimensions (cross as section well theenhancing different the value number of of the signal events Lorentz at factor the FCC-hh. Table 1 dimuons. For this table,considered. the For benchmark the point LHC, with HL-LHC,and and an FCC-hh integrated we luminosity use of 13, 100 14, fb and 100 TeV center-of-mass energy JHEP02(2019)157 ]  45 , H about 44 FCC-hh HL-LHC LHC 1 500 and − FCC-hh HL-LHC LHC ∼ [GeV] [mm] T xy decaying to two muons. Track L Track P 200 400 600  H

4

10 10 GeV / Events 0 500 1000 3 2 1

10 10 Events / mm / Events – 17 – FCC-hh HL-LHC LHC 150 FCC-hh HL-LHC LHC decaying to di-muons. Right: transverse momentum of the reconstructed )[GeV] µ µ  M( Track d0[mm] H . Results from our simulations before applying any cuts. Left: invariant mass of 100 . Results from our simulations before applying any cuts. Left: impact parameter of the re- 0 100 200 300 5 4 Finally, we like to point out that the symmetry protected low scale type II seesaw 4 5 10

10 10

10 32000 events in their final data sets, respectively. Aside from the enhanced production 10 10

Events / mm / Events Events / GeV / Events couplings of the triplet toresults. the Searches lepton doublets, for is displacedwell-motivated still vertex parameter largely signatures space. untested can by help the to current LHC probe part of this physically ∼ cross sections and luminosities,would lead the to larger discovery Lorentz prospects factors in an at enlarged the partscenario, FCC-hh/SppC of where [ parameter space. an approximate “lepton number”-like symmetry suppresses the Yukawa only” analyses are notstruction efficient is and necessary. additional13 We information found events from that may secondary already be vertexwhich in recon- detected only present includes in the LHC this production datations. of way. with Furthermore, doubly the Note charged 100 fb HL-LHC scalars that and from this neutral FCC-hh have current result prospects interac- is to a discover up conservative to estimate Figure 10 decaying to two muons final state. 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