Probing Long-lived Particles at Higgs Factories

We study displaced vertex signatures of long-lived particles (LLPs) from exotic Higgs decays in the context of a Higgs-portal model and a neutral-naturalness model at the CEPC and FCCee. Such two models feature two representative mass ranges for LLPs, which show very different behavior in their decay signatures. The Higgs-portal model contains a very light sub-GeV scalar boson stemming from a singlet scalar field appended to the Standard Model. Such a light scalar LLP decays into a pair of muons or pions, giving rise to a distinctive signature of collimated muonjet or pion-jet, thanks to the sub-GeV mass. On the other hand, the neutral-naturalness model, e.g., folded supersymmetry, predicts the lightest mirror glueball of mass O(10) GeV, giving rise to long decays with a large transverse impact parameter because of the relatively large mass. Utilizing such distinct characteristics to remove the background, we estimate the sensitivities of searches for light scalar bosons and mirror glueballs at the CEPC and FCC-ee. We find either complementary or stronger coverage compared to the previous results in the similar contexts. ∗ cheung@phys.nthu.edu.tw † zerensimon.wang@apctp.org 1 ar X iv :1 91 1. 08 72 1v 1 [ he pph ] 2 0 N ov 2 01 9


I. INTRODUCTION
Since the discovery of a Standard Model (SM)-like Higgs boson at the LHC in 2012 [1,2], there has been no sign of new physics in collider experiments so far. As most effort at high-energy colliders e.g. the LHC has been paid for searching for promptly decaying new heavy fields, new physics (NP) that would emerge in the form of long-lived particles (LLPs) predicted in various models beyond the Standard Model (BSM) might have been missed, as the current triggers for events are not designed specifically for such purposes. In fact, the rising interest in searches for LLPs has injected life into both theoretical and experimental communities [3]. Many BSM models have been proposed that predict existence of LLPs, either charged or neutral: Higgs-portal models, R-parity violating (RPV) supersymmetry with small RPV couplings, quirky models, gauge-mediated models, etc. For a summary see Ref. [3]. Some searches for LLPs have also been performed at ATLAS and CMS: see for examples Refs. [4][5][6][7][8]. Nevertheless, the current triggers are not optimized for detecting LLPs so that perhaps many signals might have been missed. Specific triggers will be installed in future runs at the ATLAS and CMS experiments [9,10].
Other than the high-luminosity run at the LHC there are also proposals for the next generation e − e + colliders, such as CEPC [11], FCC-ee [12], and ILC [13]. These future colliders, if they can be approved, all involve an important phase of operation as a Higgs factory running at center-of-mass energies √ s = 240−250 GeV. In such machines, the Higgs bosons are dominantly produced by Higgsstrahlung together with a relatively small contribution from W W/ZZ fusion. Producing the Higgs bosons copiously with relatively little background, such Higgs factories are expected to be ideal avenues for precision measurements of the Higgs couplings and other properties of the Higgs boson, including searching for rare decays of the Higgs boson. One particularly interesting rare decay possibility is the Higgs decay into LLPs. Though charged LLPs could be easily identified as stable charged tracks in tracker detectors at the LHC, neutral LLPs would be easily missed in the current searches.
In this work, we study the sensitivity reach of the CEPC and FCC-ee for some neutral LLPs produced from rare Higgs decays. We use a Higgs-portal model and a dark glueball model as the prototype models. These models share the same features that the neutral LLPs are scalar bosons pair-produced from the SM Higgs decays, and followed by their predominant decays into a pair of leptonic or hadronic jets. We first investigate the dimuon decay of the new scalar bosons of the Higgs-portal model. It has the advantage that the muons can be detected quite cleanly in both the inner tracker detector (IT) and muon spectrometer (MS). The detection and identification efficiencies are in general very high.
The new scalar boson of the toy models mentioned above has distinct interesting mass ranges. The Higgs-portal model [14] that we are interested in allows the new scalar boson as light as sub-GeV. Because of the light mass, it will be traveling with a high transverse momentum in the Higgs decay, such that the opening angle between the dimuons would be order ∆R µµ ∼ 2m hs /p T = O(10 −2 ). Making use of this feature one can effectively eliminate the background events. The light scalar boson could as well decay into a pair of (charged) pions with the same feature as the collimated jets. We also take into account this possibility by considering reconstructing the displaced vertices in the IT, HCAL, or MS. On the other hand, the dark glueball lies in the mass range of a few ten's of GeV. We focus on the mirror glueball that decays to a pair of b-jets, given the fact that the decay branching ratios of the mirror glueball follow the pattern of the SM-like Higgs boson of the same mass. Given the relatively large mass of the mirror glueball, the b-jet pair will have a wide opening angle.
These two models thus provide two distinct representatives in the search of such LLPs.
The organization of this paper is as follows. In the next section, we highlight on the two representative models studied in this work. In Sec. III, we describe briefly the layout of the CEPC and FCC-ee detectors, and detail our search strategies and simulation procedures.
We present the results in Sec. IV, and conclude in Sec. V.

A. A Higgs-portal model
In this work we consider a toy Higgs-portal model where an additional real SM-singlet scalar field X is added to the SM Lagrangian, and the field X mixes with the SM Higgs doublet field Φ, in the presence of a new Z 2 symmetry. The new scalar field X is odd under the Z 2 such that no X or X 3 terms appear, while all the SM fields are even. The renormalizable Lagrangian is given by where the SM Higgs sector is expressed with After the electroweak symmetry breaking (EWSB), both the SM Higgs doublet field Φ and the new scalar singlet field X are expanded around their vacuum-expectation values φ ≈ 246 GeV and χ : We may express the two tadpole conditions by imposing ∂V /∂φ = 0 and ∂V /∂χ = 0, with V labeling the scalar potential part of Eq. (1): Note that if we take the decoupling limit λ ΦX → 0 from the above equations, we can reproduce the SM condition of φ 2 = µ 2 /λ and χ 2 = µ 2 X /λ X . One can easily see from Eq. (1) that the two scalar fields in the model, i.e. φ and χ will mix with each other and form new mass eigenstates which we label with h and h s , respectively. The mass terms of the two scalar bosons are It is possible to rotate (φ χ) T to (h h s ) T through an angle θ The angle θ has to be small because of various existing constraints [14] so we will focus on small θ values for the rest of this section. As a result, we may express the masses of h and h s , the mixing angle θ, and the interaction term for a 3-point vertex hh s h s in terms of the parameters in Eq. (1) as Because of its mixing with the Higgs boson, the scalar boson h s can decay into SM particles with the decay rate proportional to sin 2 θ. We calculate the partial decay widths for h s → + − in the following [15] Γ For our interested mass range m hs 1 GeV 1 , the light scalar almost only decays to either µ + µ − , a pair of pions, or four pions, depending on the phase space allowed. For h s → ππ, a similar tree-level analytic expression given in Ref. [15] is insufficient as it fails to take into account strong final-state interactions near the pion threshold. Therefore, we adopt the following numerical treatment. We extract Γ(h s → ππ) and Γ(h s → 4π) from Ref. [18] and calculate Γ(h s → µ − µ + ) with Eq. (10), in order to obtain Γ(h s ), the total decay width of h s . Then it is trivial to compute Br(h s → ππ). Further, we calculate Br(h s → π + π − ) with the following formula: since Γ(h s → π + π − ) = 2 Γ(h s → π 0 π 0 ). In Table I we list the decay branching ratios of h s The partial decay width of the Higgs boson into a pair of the light scalar bosons h s is expressed with the following analytic formula [14]: where the first approximation makes use of the fact that the interested mass range of h s is negligible compared to the Higgs-boson mass and so is the phase space effect consequently, and the second approximation follows from sin θ ≈ θ for small θ and Eq. (9). We can then calculate the decay branching ratio of the SM Higgs into a pair of h s as follows: where Γ SM charged. In general, the mirror glueballs lie at the bottom of the mirror-sector spectrum in these models, including folded supersymmetry (SUSY) [20], (fraternal) twin Higgs [21,22], quirky little Higgs [23], and hyperbolic Higgs [24,25]. As we will see, the sensitivity reach for these models can be derived from one another by a simple re-scaling, and we therefore focus on one of the models, e.g. the folded SUSY [20]. In this model, the squarks are charged under SU (3) B (but not the SM SU (3) C gauge group), and the EW gauge group SU (2) L × U (1) Y is shared between the SM particles and superpartners. Since the LEP limits require that the mirror stops to be heavier than ∼ 100 GeV, the mirror glueballs are supposed to be the lightest states in the mirror sector. The lightest mirror glueball 0 ++ can be pair-produced from the Higgs boson decay, followed by the mirror-glueball decay into a pair of SM particles via the top-partner loop-induced mixing with the SM Higgs boson, and so giving rise to displaced-vertex signatures at high energy colliders.
For any scenario of the above mentioned models, the partial decay width of 0 ++ into a pair of SM particles is given by [26][27][28]: where v = 246 GeV is the SM Higgs doublet vacuum expectation value, m 0 denotes the mass of 0 ++ , the expression for y 2 /M 2 depends on the model and will be given in Eq. (15), and Γ SM h→ξξ (m 2 0 ) is the partial decay width of a SM-like Higgs boson with mass m 0 into a pair of ξ's calculated with HDECAY 6.52 [29,30]. α B s and F S 0 ++ are respectively the mirror strong coupling and the mirror glueball annihilation matrix element with 4πα . The expression for y 2 /M 2 is a compact notation for parameters in various models of neutral naturalness [27]: , Fraternal Twin Higgs and Quirky Little Higgs, where m t is the SM top-quark mass, mt is the stop mass, m T is the top partner mass, and v H is the hyperbolic scale and tan θ ≈ v/v H encodes the tree-level mixing effects induced by the mixing between CP −even neutral scalars.
As for the production of the lightest mirror glueballs from the SM Higgs decay, we calculate the relevant branching ratio as where Br(h → gg) ≈ 8.6 % is the decay branching ratio of the SM Higgs boson h into a pair of gluons, and α B is the ratio of the couplings of the hidden and SM QCD sectors. 2 For a conservative estimate of α B s (m h )/α A s (m h ), we extract the information from the lower green curve of Fig. 5 of Ref. [26] for (α B s (m h )/α A s (m h )) 2 , where the one-loop RGE extrapolation from m 0 was used assuming that mirror glueballs are the only mirror states below m h . κ is a parameter taking into account the effect of the glueball hadronization and non-perturbative mixing effects between the excited glueball states 0 (++ * ) and the SM estimate while the minimal value κ min is the most pessimistic case, which can be estimated under democratic Higgs-decay principle as follows: where i runs over the active states among the 12 stable glueball states, since for relatively large values of m 0 , some heavier mirror-glueball states are forbidden to be produced from the Higgs decay. This is because in the mirror-glueball spectrum only the ratios m i /m 0 are known [31,32].
Here L h is the integrated luminosity at the Higgs mode, σ h is the total cross section for the SM Higgs production by combining the three processes at the e − e + colliders (e − e + → HZ These average decay probabilities may be calculated as follows: where N MC is the total number of MC-simulated events, and P [X Refs. [34,35] are listed in Table II, Table III, and Table IV, respectively. We now describe each fiducial volume for the calculation of P [X the expression for P [X i in IT] is given by where β t i is the speed of the X i in the transverse direction with γ i its boost, and τ X is the lifetime of X. R I (R O ) is the inner (outer) radius of the inner detector, and L d is its half length. d res = 5 µm is the inner-tracker spatial resolution for both CEPC and FCC-ee [12,33]. As long as one of the LLPs travels inside the IT window, and decays before it leaves  [34] while the geometries of the IDEA detectors of the FCC-ee are reproduced from Ref. [35]. V represents the volume and similarly in Table III and Table IV. the IT (including the case that the secondary vertex is inside the beam pipe up to d res ), we treat the decay vertex as a displaced vertex that can be reconstructed. The kinematical variables may be obtained with the following relations: where p t i , E i and m are respectively the transverse momentum of X i , its energy, and its mass.
Note that for the HCAL and MS we require both displaced vertices to be reconstructed, in order to render the event as a signal. The formulas of P [X 1/2 i in HCAL/MS] for the CEPC and FCC-ee are the same, though the geometrical parameters are slightly different. The expression for P [X i in HCAL/MS] is given by where R in (R out ) is the inner (outer) radius of the barrel, L b its full length, and L e (R e ) is the width (inner radius) of the two endcaps.

IV. RESULTS
In this section, we present the numerical results of the sensitivity reach of the CEPC and FCC-ee for the two models considered in this study.

A. The light sub-GeV scalar boson case
We present the sensitivity estimates in the plane (sin 2 θ vs m hs ) for the light sub-GeV scalar-boson model in Fig. 2 and Fig. 3 for the channels h s → µ − µ + and h s → π − π + , respectively. We consider the number of signal events larger or equal to 3 as the sensitive region, which corresponds to the exclusion limit of 95% C.L. with 0 background event. The We apply a selection cut on the opening angle of the two muons/pions produced from the h s decays inside the IT: 1 > ∆R > 0.01. This can effectively eliminate the contributions from background events of heavier particles while respecting the tracking spatial resolution.
As for the HCAL and MS, we assume 0 background events. The LHC results from Ref. [14] are reproduced here in Fig. 2  is the experimentally excluded region by fixed-target experiments, LHCb, and B-factories [14,[36][37][38], while the dark gray area is the experimentally allowed and LHC-sensitive region [14]. in order to remove the ZZ background. It was shown in Ref. [22] that such a cut can reduce the ZZ background down to less than 10 −2 . In order to remove the prompt H/Z → bb decay and the SM bottomonium background events of displaced vertices taking place in the IT, we further impose an invariant-mass cut on the bb pair: 10 GeV < M bb < 80 GeV, which has no effect on the signal events. Furthermore, we require the transverse impact parameter d 0 > 2 mm for both b-jets stemming from any secondary vertex in the IT, so as to make sure that the corresponding vertex is a displaced one and can be reconstructed. This would cut away some sensitivity at the ultra-short decay length regime (corresponding to the lower right corner in the shown plane mt vs. m 0 ). Similar to the previous model we have assumed that for the HCAL and MS the SM background is negligible.
We present our sensitivity estimates in two ways. In Fig. 4, we make plots of contour curves for N signal denoting the number of signal events. The selected isocurves are for N signal = 3, 10, 100. The left and right columns correspond to the CEPC and FCC-ee, respectively. The black (red) curves are for κ max (κ min ). In Ref. [27], the limits for the same model were also shown for the CEPC/FCC-ee with N h = 1.1 × 10 6 . Compared to the results therein, our estimates for the IT (with 3 signal events or 95% C.L. with 0 background) are more optimistic with the maximal potential reach of mt roughly 2 times better. This is largely due to the fact that we include both l − l + and jj decay channels of the Z−bosons while Ref. [27] considered only leptonic Z decays. Our sensitivity reach in m 0 is however smaller, because the requirement on the transverse impact parameter cuts away most signal events for large decay width. Compared to the IT, the HCAL and MS may have smaller sensitivity but still useful coverage in the parameter space.
In Fig. 5 we present another set of plots with contour curves for log 10 (κ). The selected values of log 10 (κ) = −3, −2, −1, 0, 1, 2. We may compare our results with those for the HL-LHC with √ s = 14 TeV and 3 ab −1 integrated luminosity presented in Ref. [26]. Our IT search may probe mt roughly 1.5 times better while our HCAL and MS limits are similar or slightly worse.
Note that we only show our results for the folded SUSY model. For the other neutralnaturalness models, as the parameter y 2 /M 2 is also inversely proportional to the square of the new scale, one can easily obtain the corresponding sensitivity estimates by simple rescaling.

V. CONCLUSIONS
We have investigated the potential of the future e − e + colliders operated as the Higgs factories, with the profiles of CEPC and FCC-ee as examples, in detecting the long-lived particles predicted by a number of models beyond the SM. We have employed two representative models, i.e. the hidden scalar model and folded SUSY model, which feature two distinct mass ranges, including sub-GeV and O(10) GeV, respectively.
The decay of the sub-GeV scalar boson gives rise to a pair of collimated muons or pions, which provides a distinctive signature against possible SM backgrounds. As a result of a much larger decay branching ratio into the pion pair the sensitivity reach at CEPC and FCC-ee can be substantially better than the LHC.
The decay of relatively heavier mirror glueballs of mass O(10) GeV leads to a pair of b−jets with a clean secondary vertex. With a series of selection cuts all possible SM backgrounds can be rejected while the signal events remain largely unaffected. By including both the leptonic and hadronic decays of the Z−bosons, the sensitivity reach at the CEPC and FCCee is about a few times better than previous studies.
We offer a few more comments as follows.
1. In this study, we have assumed that with the selection cuts, such as collimated muon or pion pairs for the sub-GeV scalar boson and b−jet pairs with a secondary vertex and large invariant mass for the folded SUSY model, most SM backgrounds can be eliminated.
2. In principle, one can also study the sensitivity reach for the ILC with the proposed geometries. However, the designed luminosity is relatively low so that one expects