Model characterization and dark matter in the secluded Uð1Þ0 model Yaşar Hiçyılmaz ,1,2,* Levent Selbuz ,3,† Levent Solmaz,1,‡ and Cem Salih Ün 4,5,§ 1Department of Physics, Balıkesir University, TR10145 Balıkesir, Turkey 2School of Physics & Astronomy, University of Southampton, Highfield, Southampton SO17 1BJ, United Kingdom 3Department of Engineering Physics, Ankara University, TR06100 Ankara, Turkey 4Department of Physics, Bursa Uludağ University, TR16059 Bursa, Turkey 5Departamento de Ciencias Integradas y Centro de Estudios Avanzados en Física Matemáticas y Computación, Campus del Carmen, Universidad de Huelva, Huelva 21071, Spain (Received 29 November 2021; accepted 8 March 2022; published 29 March 2022) We consider a class of Uð1Þ0-extended minimal supersymmetric extension of the Standard Model (MSSM) in which the Uð1Þ0 symmetry is broken by vacuum expectation values of four MSSM singlet fields. While one MSSM singlet field interacts with the MSSM Higgs fields, three of them interact only with each other in forming a secluded sector. Assigning universal Uð1Þ0 charges for three families, the anomaly cancellation condition requires exotic fields which are assumed to be heavy and decoupled. We discuss a variety of Uð1Þ0 charge assignments and anomaly cancellation, Z0=Z hierarchy, neutralinos, charginos and the Higgs sector. We find that the typical spectra involve two CP-odd Higgs bosons lighter than about 200 GeVand 600 GeV respectively, which are mostly formed by the MSSM singlet fields. If the relic density of dark matter is saturated only by a neutralino, compatible solutions predict LSP neutralinos formed by the MSSM singlet fields in the mass scales below about 600 GeV, while it is possible to realize MSSM neutralino LSP above these mass scales. One can classify the implications in three scenarios. Scenario I involves NLSP charginos, while Scenario II involves charginos which do not participate coannihilation processes with the LSP neutralino. These two scenarios predict MSSM singlet LSP neutralinos, while Scenario I leads to larger scattering cross sections of dark matter. Scenario III has the solutions in which the MSSM neutralinos are considerably involved in LSP decomposition which yields very large scattering cross section excluded by the direct detection experiments. DOI: 10.1103/PhysRevD.105.055029 I. INTRODUCTION Despite the lack of any direct signal of new physics beyond the Standard Model (SM), the minimal super- symmetric extension of the StandardModel (MSSM) is still one of the forefront candidates because of the motivation of resolution to the gauge hierarchy problem [1–5], stability of the Higgs potential [6–11], pleasant candidates for the dark matter, with an additional attraction from the gauge coupling unification at the grand unification theory (GUT) scale (MGUT ≃ 2.4 × 1016 GeV). On the other hand, the lack of a direct signal might point to a deviation from the minimal point of view in constructing models beyond the SM. For instance, if the lightest supersymmetric particle (LSP) is not a mixture of MSSM neutralinos [12–14], many of the signal processes currently under the collider analyses may not be available at the collision energies of today. A similar discussion can be followed also for the null results from the dark matter experiments [15–17]. In addition to the current results from the experiments, possible resolutions to some long standing problems such as absence of the right-handed neutrinos and the μ problem in MSSM [18] can motivate us to construct models beyond the SM which extends the particle content and/or symmet- rical structure of the MSSM. In this context, a larger symmetry group which supplements the MSSM gauge group with an extra Uð1Þ0 can address the resolution to the μ problem. If the extraUð1Þ0 symmetry is imposed in a way that the MSSM fields are also nontrivially charged under it, the μHdHu is not allowed in the superpotential due to the gauge invariance under Uð1Þ0. On the other hand, it can be generated effectively through the vacuum expectation value (VEV) of a field S, which is preferably singlet under the *yasarhicyilmaz@balikesir.edu.tr †selbuz@eng.ankara.edu.tr ‡lsolmaz@balikesir.edu.tr §cemsalihun@uludag.edu.tr Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3. PHYSICAL REVIEW D 105, 055029 (2022) 2470-0010=2022=105(5)=055029(20) 055029-1 Published by the American Physical Society https://orcid.org/0000-0002-3222-7942 https://orcid.org/0000-0001-8128-521X https://orcid.org/0000-0002-0595-8803 https://crossmark.crossref.org/dialog/?doi=10.1103/PhysRevD.105.055029&domain=pdf&date_stamp=2022-03-29 https://doi.org/10.1103/PhysRevD.105.055029 https://doi.org/10.1103/PhysRevD.105.055029 https://doi.org/10.1103/PhysRevD.105.055029 https://doi.org/10.1103/PhysRevD.105.055029 https://creativecommons.org/licenses/by/4.0/ https://creativecommons.org/licenses/by/4.0/ MSSM gauge symmetry so that its VEV breaks only the Uð1Þ0 symmetry. In this case the superpotential involves a term such as SHuHd, and through theUð1Þ0 breaking, the μ term is generated effectively as μeff ∼OðhSiÞ [19–28]. In this way, the radiative electroweak symmetry breaking (REWSB) is linked to the Uð1Þ0 symmetry breaking through the renormalization group equations (RGEs). Such an extension can still be considered to be minimal, and it is well motivated in superstring theories [29], grand unified theories [30], and in dynamical electroweak break- ing theories [31]. In addition to extending the symmetry, the Uð1Þ0 models also extend the particle content of MSSM by adding Z0— the gauge boson associated with the Uð1Þ0 group and the right-handed neutrinos. The right-handed neutrinos can be considered to complete the representations of matter field families so that the model can be embedded in a larger GUT group such as E6. Besides, the right-handed neutrinos contribute to the anomaly cancellations, and they can provide a natural framework to implement seesaw mech- anisms [32] for nonzero neutrino masses and mixing [33]. In this context, hSi significantly contributes to the right- handed sneutrino and Z0 masses as well as their super- partners. However, the presence of a neutral gauge boson Z0 brings a strong impact on this class of models, since the current experimental results exclude the solutions with MZ0 ≲ 4 TeV. Such a strong exclusion results in a Uð1Þ0 breaking scale at the order ofOð10 TeVÞ and consequently μeff ∼ a fewTeV, which softly brings the μ problem back to the Uð1Þ0 models, even though a resolution to the natu- ralness problem can be accommodated [34]. Note that this strong bound can be avoid if the gauge coupling of Uð1Þ0 is significantly small (≲10−5) [35–37], or negligibly couple to the fermions of the first to families [38,39]. However, these conditions on the couplings cannot be met if the gauge coupling unification is imposed at MGUT and/or the family universal Uð1Þ0 charges are assumed. On the other hand, if the Uð1Þ0 symmetry breaking involves three more MSSM singlet fields (S1, S2, S3) [40,41], a μ term at the order of electroweak symmetry breaking can be realized, while Z0 remains heavy to be consistent with the current experi- mental results. These three MSSM singlet fields form the secluded sector, and their number can be determined by considering the physical properties of vacua of the scalar potential. The minimal setup of Uð1Þ extended super- symmetric models (κ → 0 in κ=3S1S2S3), the unstable vacua of the scalar potentials can be avoided by setting the Uð1Þ0 breaking scale very large (Oð10 TeVÞ), which leads to a heavy S field and its neutralino. In these cases, the testable low scale implications of Uð1Þ0 models are not distinguishable from the MSSM implications [42–44]. Even though extending the scalar sectors with one or two more MSSM singlet fields can allow a relatively lower breaking scale for Uð1Þ0 symmetry, the requirement of physical vacua is still effective, since the solutions in such frameworks can still yield vanishing VEVs for the MSSM Higgs fields or vs ∼ vu ∼ vd, which also cancels the Z0 − Z hierarchy [40]. In this context, the minimal form of the secluded sector can be spanned by threeMSSMsinglet fields. Of course it could include more fields; however, their effects can still be taken into account with three fields by varying the relevant couplings (λ and κ) and VEVs (vS and vi). We refer to the class of supersymmetric Uð1Þ0 models with three additional MSSM singlet fields as the secluded Uð1Þ0 model [40,41,45,46]. Even though we allow that the additional Uð1Þ0 symmetry can be broken at a scale of order multi-TeV [Oð10Þ TeV], we assume Uð1Þ-extended MSSM emerges at MGUT resulting from the breaking of a larger gauge symmetry such as E6. We perform random scans by imposing boundary conditions on the GUT scale parameters atMGUT, which is spanned by the universal soft supersymmetry breaking (SSB) mass terms for the super- symmetric scalars and gauginos. Note that the SSB masses of the Higgs fields are calculated by minimizing the superpotential, and in general, it implies nonuniversal SSB masses for the MSSMHiggs fields. Since the breaking scale of Uð1Þ0 is unknown, the set of the free parameters in secluded Uð1Þ0 model involves VEVs of the MSSM singlet scalar fields. The rest of the paper is organized as follows: We first briefly review the secluded Uð1Þ0 models in Sec. II with its superpotential, particle content, nontrivial Uð1Þ0 charges of the fields and anomaly cancellations, as well as the field content and the physical mass states. After we describe the scanning procedure and summarize the rel- evant experimental constraints in Sec. III, we present and discuss the LHC and dark matter implications of the model in Sec. IV. Finally, we conclude our findings in Sec. V. II. THE SECLUDED Uð1Þ0 MODEL In this section we present the relevant ingredient and some salient features of the secludedUð1Þ0 model, which is based on the gauge group SUð3Þc × SUð2ÞL ×Uð1ÞY × Uð1Þ0. Such an extension of the MSSM gauge group can emerge in the grand unified theories based on a gauge group larger than SUð5Þ such as SOð10Þ [47–50] and/or E6 [51–54]. In the common convention the Uð1Þ0 extension of MSSM results from the E6 through the following cascade of the symmetry breakings, E6 → SOð10Þ ×Uð1Þψ → SUð5Þ × Uð1Þχ × Uð1Þψ → SUð3ÞC × SUð2ÞL ×Uð1ÞY ×Uð1Þ0; ð1Þ where Uð1Þ0 group at the end of the breaking chain is, in principle, a linear combination of Uð1Þχ and Uð1Þψ with charge Q0 ¼ Qχ cos θE6 þQψ sin θE6 . On the other hand, a general configuration of the Uð1Þ0 charges cannot be restricted to these two classes of the Uð1Þ0 models [23,39,55–58]. A general set of equations for the charges HIÇYILMAZ, SELBUZ, SOLMAZ, and ÜN PHYS. REV. D 105, 055029 (2022) 055029-2 can be obtained from the anomaly cancellation condition, and these conditions also depend on the exotic fields involved in the model. In our work, we consider the following superpotential, Ŵ ¼ WMSSMðμ ¼ 0Þ þ λŜĤu · Ĥd þ hνL̂ · ĤuN̂ þ κ 3 Ŝ1Ŝ2Ŝ3 þ XnQ i¼1 hiQŜQ̂i ˆ̄Qi þ XnL j¼1 hjLŜL̂j ˆ̄Lj; ð2Þ where the matter superfields of the MSSM corresponding to the squarks and sleptons Q̂; Û; D̂; L̂, and Ê are included in WMSSM, and Ĥu; Ĥd are the MSSM Higgs doublets. The new ingredient from the Uð1Þ0 inclusion can be listed as the MSSM singlet scalars S; S1;2;3, right-handed neutrino super- field N̂ and exotic fields Qi, Li. In addition, the model includes a neutral gauge boson associated with the Uð1Þ0 symmetry and its supersymmetric partner. Note that we do not assume Q0 Hu þQ0 Hd ¼ 0 in our scans. In this case, the gauge invariance forbids the bilinear mixing (μĤuĤd) in the MSSM superpotential, which is stated as WMSSMðμ ¼ 0Þ in Eq. (2). It is generated effectively through the VEVof S so that μeff ≡ λhSi. However, the emergence of such an effective term induces mixed anomalies between Uð1Þ0 and the MSSM gauge group; cancellation of such anomalies also requires exotic fields in the particle spectrum, and the anomaly cancellation can be maintained by introducing exotic fields, which are vectorlike with respect to MSSM, but chiral under the Uð1Þ0 group. If a general Uð1Þ0 charge assignments is as shown in Table I, the gauge invariance condition yields the following equations, 0 ¼ Q0 S þQ0 Hu þQ0 Hd ; 0 ¼ Q0 Q þQ0 Hu þQ0 U; 0 ¼ Q0 Q þQ0 Hd þQ0 D; 0 ¼ Q0 L þQ0 Hd þQ0 E; 0 ¼ Q0 Q þQ0 Q̄ þQ0 S; 0 ¼ Q0 L þQ0̄ L þQ0 S; 0 ¼ Q0 L þQ0 Hu þQ0 N; 0 ¼ Q0 S1 þQ0 S2 þQ0 S3 : ð3Þ Note that if a special configuration with Q0 S ¼ 0 can be found, the μ term becomes allowed by the gauge invariance. However, a consistent Z − Z0 mass hierarchy and mixing require nonzero Uð1Þ0 charges for all MSSM singlet scalar fields S; S1;2;3. Another set of conditions for the charges is obtained from the vanishing Uð1Þ0 − SUð3Þc − SUð3Þc, Uð1Þ0 − SUð2ÞL − SUð2ÞL, Uð1Þ0 −Uð1ÞY − Uð1ÞY , Uð1Þ0 − graviton − graviton, Uð1Þ0 −Uð1Þ0 −Uð1ÞY and Uð1Þ0 −Uð1Þ0 −Uð1Þ0 anomalies, as follows: 0 ¼ 3ð2Q0 Q þQ0 U þQ0 DÞ þ nQðQ0 Q þQ0 Q̄ Þ; ð4Þ 0 ¼ 3ð3Q0 Q þQ0 LÞ þQ0 Hd þQ0 Hu ; ð5Þ 0 ¼ 3 � 1 6 Q0 Q þ 1 3 Q0 D þ 4 3 Q0 U þ 1 2 Q0 L þQ0 E � þ 1 2 ðQ0 Hd þQ0 Hu Þ þ 3nQY2 QðQ0 Q þQ0 Q̄ Þ þ nLY2 LðQ0 L þQ0̄ L Þ; ð6Þ 0 ¼ 3ð6Q0 Q þ 3Q0 U þ 3Q0 D þ 2Q0 L þQ0 E þQ0 NÞ þ 2Q0 Hd þ 2Q0 Hu þQ0 S þQ0 S1 þQ0 S2 þQ0 S3 þ 3nQðQ0 Q þQ0 Q̄ Þ þ nLðQ0 L þQ0̄ L Þ; ð7Þ 0 ¼ 3ðQ02 Q þQ02 D − 2Q02 U −Q02 L þQ02 E Þ −Q02 Hd þQ02 Hu þ 3nQYQðQ02 Q −Q02 Q̄ Þ þ nLYLðQ02 L −Q02 L̄ Þ; ð8Þ 0 ¼ 3ð6Q03 Q þ 3Q03 D þ 3Q03 U þ 2Q03 L þQ03 E þQ03 NÞ þ 2Q03 Hd þ 2Q03 Hu þQ03 S þQ03 S1 þQ03 S2 þQ03 S3 þ 3nQðQ03 Q þQ03 Q̄Þ þ nLðQ03 L þQ03 L̄ Þ: ð9Þ All these conditions from the gauge invariance and the anomaly cancellations should be satisfied for particular pattern of charges and parameters, which requires the number of exotics. Based on the choice of exotics in the model, one of the simplest solution to the mixed anomaly constraints requires nQ ¼ 3 color triplets with YQ ¼ −1=3, and nL ¼ 2 color singlets with YL ¼ −1. Recall that these exotic fields are singlets under SUð2ÞL as mentioned before and listed in Table I. In our analyses, we assume the exotics to be very heavy and decouple from the low-scale spectrum. In this sense, their charges are considered only for the anomaly cancellation in our work. A. Gauge Boson Masses and Mixing As mentioned before the model introduces a new neutral gauge boson Z0 and its superpartner B̃0 associated with the gauged Uð1Þ0 symmetry. The symmetry breaking in this model being realized is very similar to the Higgs mecha- nism, but in this case, the electroweak and Uð1Þ0 symmetry breaking are correlated. The fields developing nonzero VEVs during the symmetry breaking, SUð2ÞL ×Uð1ÞY× Uð1Þ0 → Uð1ÞEM, can be listed as follows: hHui ¼ 1ffiffiffi 2 p � 0 vu � ; hHdi ¼ 1ffiffiffi 2 p � 0 vd � ; hSi ¼ vSffiffiffi 2 p ; hSii ¼ vSiffiffiffi 2 p : ð10Þ MODEL CHARACTERIZATION AND DARK MATTER IN THE … PHYS. REV. D 105, 055029 (2022) 055029-3 Since S; S1;2;3 fields are singlet under the MSSM gauge group, theW and Z bosons acquire their masses through the VEVs of Hu and Hd as in the usual electroweak symmetry breaking; thus, the condition v2u þ v2d ¼ v2SM should still hold in this model. On the other hand, because of the nontrivial charges of all the superfields under Uð1Þ0 as listed in Table I, the Z0 boson receives its mass from all the VEVs. In this case, since vS and/or vSi are expected to be much greater than vu and vd, the secluded sector can be accounted for as the main source of the Z0 mass. However, apart from the mass acquisition, nontrivial Hu and Hd charges induce a nonzero mixing between Z and Z0 associated with their mass-square matrix, M2 ZZ0 ¼ � M2 Z Δ2 Δ2 M2 Z0 � ; ð11Þ written in ðZ; Z0Þ basis in terms of M2 Z ¼ 1 4 ðg21 þ g22Þðv2u þ v2dÞ; M2 Z0 ¼ g021 � Q02 Hu v2u þQ02 Hd v2d þQ02 S v 2 S þ X3 i¼1 Q02 Si v2Si � ; Δ2 ¼ 1 2 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi g21 þ g22 q g01ðQ02 Hu v2u −Q02 Hd v2dÞ: ð12Þ Diagonalizing the mass-square matrix in Eq. (11) yields the following mixing angle between Z and Z0, θZZ0 ¼ 1 2 arctan � 2Δ2 M2 Z0 −M2 Z � ; ð13Þ and the electroweak precision data strongly bounds the Z − Z0 mixing angle as θZZ0 ≲ 10−3 [59–61]. Applying such a strict constraint to the mixing between Z and Z0 allows only solutions with the following properties: (1) g01 ≪ g1. (2) MZ0 ≫ MZ. (3) Q0 Hd =Q0 Hu ≃ vu=vd ≡ tan β. The first two conditions separately bring a naive application of the large electron-positron collider (LEP) two bound on MZ0 asMZ0=g01 ≥ 6 TeV [62]. The first condition cannot be realized when the secluded model is constrained by the gauge coupling unification at MGUT, since the gauge coupling unification yields g01 ∼ g1; g2 at the low scale. Thus, a consistent Z − Z0 mixing with the precision data can be satisfied by spectra involving heavy Z0. Alternatively, one can apply the third condition by adjust- ing Q0 Hu and Q0 Hd ; however, since it enhances the model dependency in the results, we do not consider it in our study. Note that the gauge invariance also allows a tree-level mixing between the gauge bosons of two Abelian gauge groups through ξBμνB0 μν, where Bμν and B0 μν correspond to the field-strength tensors for Uð1ÞY and Uð1Þ0 in our work respectively. This term leads to a gauge-covariant derivative in a noncanonical form [63,64], which also induces tree- level mixing between the MSSM Higgs fields and MSSM singlet scalar fields of the secluded sector. It also induces a mixing between the photon and Z0 in addition to Z − Z0 mixing, which alters the mixing angle given in Eq. (2.13) such that the physical mass states of the gauge bosons involve a massless photon [65,66]. Even though the gauge kinetic mixing can yield relatively lighter Z0 in the mass spectrum [67], it is severely bounded from above. The analyses over the LEP data yields an upper bound on the gauge kinetic mixing as ξ≲ 2.5 × 10−3 [59], and the current collider analyses have upgraded this bound as ξ≲ 3 × 10−4 from searches over different decay modes of Z0 [68–70]. In addition, the direct detection experiments can severely restrict the gauge kinetic mixing through the scattering of DM, since it raises the photon and Z-boson abundance [71], unless the scattering is not sufficiently suppressed by the Z0 mass. Thus, the gauge kinetic mixing does not loosen the severe bound on the Z0 mass which is also required by the resonance searches of the collider analyses [72,73]. In this context, we assume the available spectra in our model involve heavy Z0, and we set the gauge kinetic mixing to zero, since its impact would be negligible after imposing the relevant constraints on it. B. Neutralinos and charginos Depending on the hypercharges of the exotic fields (Q and L), the secluded Uð1Þ0 model extends both the charged and neutral sectors of MSSM. Their interference enriches the phenomenology such as lowering the mass bound on Z0 [67,74], triggering Uð1Þ0 breaking by TABLE I. Gauge quantum numbers of quark (Q̂; Û; D̂), lepton (L̂; N̂; Ê), Higgs (Ĥu; Ĥd), MSSM-singlet (Ŝ; Ŝ1; Ŝ2; Ŝ3), exotic quark (Q̂; ˆ̄Q) and exotic lepton (L̂; ˆ̄L) superfields. Field Q̂ Û D̂ L̂ N̂ Ê Ĥu Ĥd Ŝ Ŝ1 Ŝ2 Ŝ3 Q̂ Q̂ L̂ ˆ̄L SUð3ÞC 3 3̄ 3̄ 1 1 1 1 1 1 1 1 1 3 3̄ 1 1 SUð2ÞL 2 1 1 2 1 1 2 2 1 1 1 1 1 1 1 1 Uð1ÞY 1=6 −2=3 1=3 −1=2 0 1 1=2 −1=2 0 0 0 0 YQ −YQ YL −YL Uð1Þ0 Q0 Q Q0 U Q0 D Q0 L Q0 N Q0 E Q0 Hu Q0 Hd Q0 S Q0 S1 Q0 S2 Q0 S3 Q0 Q Q0 Q̄ Q0 L Q0̄ L HIÇYILMAZ, SELBUZ, SOLMAZ, and ÜN PHYS. REV. D 105, 055029 (2022) 055029-4 guaranteeing negative m2 S [19] etc. Even though it is possible to have exotic fields coupling the quarks to leptons depending on baryon and lepton numbers [75], in the standard configuration they can couple only to quarks or leptons. Besides, it is possible to configure the Uð1Þ0 charges in which the exotics are allowed to couple only to S field at tree level. In this case, SUð3Þ triplet exotic field Q is still allowed to be produced at the collider experi- ments; thus, the resonance searches are still able to bound their masses as mQ̃ ≳ 5 TeV [76]. In this context, we assume the exotics can couple only to the MSSM singlet S field, and they are heavy. Thus, their observable effects at the low scale become suppressed, while they are still effective in Uð1Þ0 symmetry-breaking, anomaly cancella- tion etc. Assuming the exotic fields to be decoupled at a high scale, only the MSSM singlet fields can be involved in the spectrum, and the neutral sector of this class of secluded Uð1Þ0 models significantly extends the neutralinos with S̃; B̃0; S̃1;2;3. After the Uð1Þ0 and electroweak symmetry breakings, these neutralinos together with the MSSM neutralinos mix each other, and the resultant mass matrix for the neutralino sector can be obtained in the usual basis ordered as (B̃, W̃, H̃d, H̃u, S̃, B̃0, S̃1, S̃2, S̃3) as follows: Mχ̃ ¼ 0 BBBBBBBBBBBBBBBBBBBBB@ 0 MBB0 0 0 0 0 0 0 0 0 MSSMðμ ¼ μeffÞ − λvu 2 g01Q 0 Hd vd 0 0 0 − λvd 2 g01Q 0 Hu vu 0 0 0 0 0 − λvu 2 − λvd 2 0 g01Q 0 SvS 0 0 0 MBB0 0 g01Q 0 Hd vd g01Q 0 Hu vu g01Q 0 SvS MB0 g01Q 0 S1 vS1 g01Q 0 S2 vS2 g01Q 0 S3 vS3 0 0 0 0 0 g01Q 0 S1 vS1 0 − κvS3ffiffi 2 p − κvS2ffiffi 2 p 0 0 0 0 0 g01Q 0 S2 vS2 − κvS3ffiffi 2 p 0 κvS1ffiffi 2 p 0 0 0 0 0 g01Q 0 S2 vS3 − κvS2ffiffi 2 p − κvS1ffiffi 2 p 0 1 CCCCCCCCCCCCCCCCCCCCCA ð14Þ The upper block called MSSM in the mass matrix given above represents the usual MSSM neutralinos and their mixing. However, since the μ term is not allowed at tree level and is effectively generated by the VEV of S, the secluded Uð1Þ0 is effective in generating the masses of MSSM Higgsinos and interfering in the mixing of MSSM neutralinos. In addition, B̃0 can mix with B̃ through the kinetic mixing, and MSSM Higgsinos through Z − Z0 mixing which are quantified with MBB0 , g01Q 0 Hd vd, and g01Q 0 Hu vu in the neutralino mass matrix, respectively. Similarly, S can mix with the MSSM Higgsinos and its mixing is proportional to its coupling to the Higgs fields as λvd and λvu. On the other hand, S̃1, S̃2, and S̃3 mix only with the Uð1Þ0 neutralinos, while they leave the MSSM neutralinos intact. In addition to their effects in the neutralino sector, these fields including B̃0 can also escape from the experimental detection and they can easily be much lighter than the MSSM neutralinos. For instance, heavy mass bounds on gluinos as mg̃ ≥ 2.1 TeV [77] also bounds the bino and wino masses at about 300 GeV and 600 GeV, respectively when the universal gaugino mass is imposed at the GUT scale (for a recent study with universal gaugino mass at the GUT scale, see Ref. [78]). In addition, the current measurements of the Planck satellite on the relic density of the dark matter can lift the mass bound up to about 1 TeV, especially when the dark matter is composed mostly by binos [17]. Even though the LHC bounds can be loosened when the LSP is formed mostly by the MSSM Higgsinos (μ ≪ M1;M2), the current null results from the direct detection experiments require μ≳ 700 GeV for the Higgsino-like dark matter [17,79,80]. Note that this bound is significantly reduced to about 200–300 GeV if the DM is realized to be Higgsino-bino and/or Higgsino- wino mixture [81]. As a consequence of such severe bounds on the MSSM neutralinos, the non-MSSMneutralinos can bemore likely to form the LSP neutralino in the low-scale mass spectrum, and in this context they yield quite different phenomenology in both the collider and the darkmatter experiments. If theLSP is formedmostly by the secludedUð1Þ0 sector, then some of the particles in the MSSM spectrum might be realized to be a long-lived state, since they do not directly couple to the LSP. Even though, the current LHC constraints on the strongly- interacting particles such as squarks and gluinos yield a consistent lifetime for these particles, it is still possible to have long-lived staus and charginos in the low-scale spectrum, and the model should be constrained to avoid possible missing electric charges from such states escaping from detectors. MODEL CHARACTERIZATION AND DARK MATTER IN THE … PHYS. REV. D 105, 055029 (2022) 055029-5 On the other hand, even though the stop and gluino are not allowed to be long lived by the LHC constraints, the current bounds on these particles can be significantly modified depending on the decay of the lightest MSSM neutralino into the LSP. Since these particles do not directly couple to the LSP, their possible signal processes remain the same as those which are excessively analyzed in the collider experiments [82]. In these processes, if the lightest MSSM neutralino does not decay in the detector and it forms the missing energy, then the current constraints on the stop and the gluino still hold. On the other hand, if the lightest MSSM neutralino is allowed to decay into the LSP in the detector, then such processes can significantly modify (probably loosen) the current bounds on the stop and gluino (see Ref. [13] for the case in which stop does not directly couple to LSP). The non-MSSMLSP also yields an interesting phenom- enology in the dark matter experiments. Since S is allowed to interact with the MSSM Higgs fields at tree level, its superpartner (S̃) scatters at nuclei through Higgs portal. Even though its scattering cross section is expected to be rather low, such solutions will be able to be tested soon under the current and future projected sensitivity of the results fromXENONexperiment [83]. The scattering cross section can be further lowered when the LSP is formed by S̃1;2;3, since they interact only with S. However, their annihilation processes can still yield interesting results for the indirect detection of dark matter and can be tested under light of the current results from FermiLAT [84,85]. Before concluding the neutralino sector in the model, we should also note the chargino sector. Since only the MSSM singlet fields can be involved in the detectable low-scale spectrum, the physical states of the chargino sector is formed by the MSSM fields such as wino and Higgsino. On the other hand, as discussed in the neu- tralino mass matrix, the charged Higgsino mass (μ) is determined effectively by the VEVof S, thus the secluded Uð1Þ0 sector is still effective in the phenomenology of the chargino sector. C. Higgs bosons The presence of the MSSM singlet S and Si fields significantly extends the Higgs boson sector of the MSSM in the secludedUð1Þ0 model. In the physical spectrum there are six CP-even Higgs bosons, while the number of the CP-odd Higgs bosons is four. In addition to the enrichment in the Higgs boson spectrum, the Higgs sector becomes more complicated through the tree-level mixing, which does not exist in the MSSM framework. The Higgs potential generated with F terms can be written as [41] VF ¼ jλj2½jHdHuj2 þ jSj2ðH† dHd þH† uHuÞ� þ jκj2 9 ðjS1S2j2 þ jS2S3j2 þ jS1S3j2�; ð15Þ where the SUð2ÞL indices are suppressed for simplicity. While the F terms allow mixing only among the MSSM Higgs doublets and the MSSM singlet S scalar, the other MSSM singlets can mix with the MSSM Higgs fields through the scalar potential generated by D terms, which is VD ¼ g21 þ g22 8 ðH† dHd −H† uHuÞ2 þ g22 2 jH† dHuj2 þ g021 2 � Q0 Hd H† dHd þQ0 Hu H† uHu þQ0 SjSj2 þ X3 i¼1 Q0 SjSij2 � 2 : ð16Þ After all, the scalar potential generated by the F and D terms induce tree-level mixing among all the Higgs scalars. In addition, the soft supersymmetry breaking Lagrangian contributes to the Higgs phenomenology through the following terms, LSUSY ¼ m2 Hd H† dHd þm2 Hu H† uHu þm2 SjSj2 þ X3 i¼1 m2 Si jSij2 − λAλSHdHu − κ 3 AκS1S2S3 −m2 SS1 SS1 −m2 SS2 SS2 −m2 S1S2 S†1S2: ð17Þ The tree-level mass-square matrix for CP-even and CP- odd Higgs bosons is generated through the SSB masses and the vacuum expectation values defined as Hd ¼ 1ffiffiffi 2 p � vd þ h0d þ iAdffiffiffi 2 p h−d � ; Hu ¼ 1ffiffiffi 2 p � ffiffiffi 2 p hþu vu þ h0u þ iAu � ; ð17aÞ S ¼ 1ffiffiffi 2 p ðvS þ Sþ iASÞ; Si ¼ 1ffiffiffi 2 p ðvSi þ Si þ iASiÞ: ð17bÞ Note that the gauge boson associated with Uð1Þ0 group (Z0) receives its mass from the VEVs of all the scalar fields given in Eqs. (17a) and (17b); however, since vS; vSi ≫ vd; vu, the VEVs of MSSM singlet fields are dominant in Z0 mass. Thus, a heavy mass bound on Z0 is expected to yield a strong impact in the MSSM singlet scalar sector. In a class of Uð1Þ0 extended supersymmetry models, the absence of the fields Si results in high Uð1Þ0 breaking scale (vS ≳ 10 TeV) [34,86] to realize MZ0 ≥ 4 TeV–5 TeV [87]. In addition, the VEVs, in principle do not have to align in the same direction, so they can be also a HIÇYILMAZ, SELBUZ, SOLMAZ, and ÜN PHYS. REV. D 105, 055029 (2022) 055029-6 source for CP-violation. However, we assume the CP-conservation in our work by setting θi ¼ 0 (for a detailed discussion about CP-conservation and breaking, see Ref. [41]). The scalar potentials involving the Higgs fields yield the following symmetric mass-square matrix for the CP-even Higgs fields, M2 even ¼ 0 BBBBBBBBB@ M2 11 M2 12 M2 13 M2 14 M2 15 M2 16 M2 22 M2 23 M2 24 M2 25 M2 26 M2 33 M2 34 M2 35 M2 36 M2 44 M2 45 M2 46 M2 55 M2 56 M2 66 1 CCCCCCCCCA ; ð18Þ where, in the basis of fhd; hu; S; S1; S2; S3g, M2 11 ¼ ðg2 1 þg2 2 Þv2d 4 þ g021Q 02 Hd v2d þ AλλvSvuffiffi 2 p vd ; M2 12 ¼ − AλλvSffiffi 2 p − ðg2 1 þg2 2 Þvdvu 4 þ ðλ2 þ g021Q 0 Hd Q0 Hu Þvdvu; M2 13 ¼ λ2vdvs þ g021Q 0 Hd Q0 SvdvS − Aλλvuffiffi 2 p ; M2 1iþ3 ¼ g021Q 0 Hd Q0 Si vdvSi ; i ¼ 1;2;3 M2 22 ¼ AλλvdvSffiffi 2 p vu þ 1 4 ðg21 þ g22 þ 4g021Q 0 Hu Þv2u; M2 23 ¼ − Aλλvdffiffi 2 p þ ðλ2 þ g021Q 0 Hu Q0 SÞvuvS; M2 2iþ3 ¼ g021Q 0 Hu Q0 Si vuvSi ; i ¼ 1;2;3 M2 33 ¼ 1 2vS ð2g021Q02 S v 3 s − 2m2 SS1 vS1 − 2m2 SS2 vS2 þ ffiffiffi 2 p AλλvdvuÞ; M2 3iþ3 ¼ m2 SSi þ g021Q 0 SQ 0 Si vSvSi i ¼ 1;2;3 and mSS3 ¼ 0 M2 44 ¼ 1 2vS1 ð2g021Q02 S1 v3S1 − 2m2 SS1 vS þ ffiffiffi 2 p AκκvS2vS3Þ; M2 45 ¼ 1 9 κ2vS1vS2 þ g021Q 0 S1 Q0 S2 vS1vS2 − AκκvS3ffiffi 2 p ; M2 46 ¼ 1 9 ðκ2 þ 9g021Q 0 S1 Q0 S3 ÞvS1vS3 − AκκvS2ffiffi 2 p ; M2 55 ¼ 1 2vS2 ð2g021Q02 S2 v3S2 − 2m2 SS2 vS þ ffiffiffi 2 p AκκvS1vS3Þ; M2 56 ¼ 1 9 ðκ2 þ 9g021Q 0 S2 Q0 S3 ÞvS2vS3 − AκκvS1ffiffi 2 p ; M2 66 ¼ g021Q 02 S3 v2S3 þ AκκvS1vS2ffiffi 2 p vS3 : Diagonalizing the mass-square matrixM2 even yields six mass eigenstates for the CP-even Higgs bosons in the spectrum. Similarly for the CP-odd Higgs fields, M2 odd ¼ 0 BBBBBBBBB@ P2 11 P2 12 P2 13 P2 14 P2 15 P2 16 P2 22 P2 23 P2 24 P2 25 P2 26 P2 33 P2 34 P2 35 P2 36 P2 44 P2 45 P2 46 P2 55 P2 56 P2 66 1 CCCCCCCCCA ; ð19Þ and, the nonzero elements of M2 odd are P2 11 ¼ AλλvSvuffiffiffi 2 p vd ; P2 12 ¼ AλλvSffiffiffi 2 p ; P2 13 ¼ Aλλvuffiffiffi 2 p ; P2 22 ¼ AλλvdvSffiffiffi 2 p vu ; P2 23 Aλλvdffiffiffi 2 p ; P2 33 ¼ 1 2vS ð−2m2 SS1 vS1 − 2m2 SS2 vS2 þ ffiffiffi 2 p AλλvdvuÞ; P2 34 ¼ −m2 SS1 ; P2 35 ¼ −m2 SS2 ; P2 44 ¼ 1 2vS1 ð−2m2 SS1 vS þ ffiffiffi 2 p AκκvS2vS3Þ; p2 45 ¼ AκκvS3ffiffiffi 2 p ; P2 46 ¼ AκκvS2ffiffiffi 2 p ; P2 55 ¼ 1 2vS2 ð−2m2 SS2 vS þ ffiffiffi 2 p AκκvS1vS3Þ; P2 56 ¼ AκκvS1ffiffiffi 2 p ; P2 66 ¼ AκκvS1vS2ffiffiffi 2 p vS3 : MODEL CHARACTERIZATION AND DARK MATTER IN THE … PHYS. REV. D 105, 055029 (2022) 055029-7 When the mass-square matrix of the CP-odd Higgs fields are diagonalized, two eigenstates out of six happen to be the massless Goldstone bosons, and thus there remain four CP-odd Higgs bosons in the mass spectrum. As can be seen from the mass-square matrices above, the MSSM Higgs fields and the MSSM singlet scalars of the secluded Uð1Þ0 model nontrivially mix in forming the physical Higgs boson states. Such a mixing can yield non- SM Higgs bosons of light mass, which can potentially lead signals in the collider experiments [64]. In this context, profiling the Higgs bosons in the spectrum is of importance in constraining the allowed parameter space of the model. If a Higgs boson mass state, except the SM-like state, is formed mostly by the MSSM Higgs fields, then the current constraints from rare B-meson decays such as Bs → μþμ− and B → Xsγ bound their masses at about 400–500 GeV [78–80]. Thus, if the spectrum involves Higgs bosons lighter than the SM-like Higgs boson are excluded by these constraints if they are significantly formed by the MSSM Higgs fields. Even though the constrained mentioned above can distinguish the MSSMHiggs fields from the MSSM singlet scalars, they can still interfere through their nontrivial mixing with the MSSM Higgs fields. First, such mixing can allow some decay modes of the light Higgs bosons into the SM particles, which potentially yield a signal at low mass scales. Besides, since the mixing induce a tree-level coupling with the SM-like Higgs boson, the light Higgs boson states can enhance the invisible decays of the SM-like Higgs bosons. One can avoid such inconsistencies by constraining the decay modes of these light Higgs bosons into the SM particles, and the invisible Higgs decays as BRðh → invisibleÞ≲ 10% [88–93]. III. SCANNING PROCEDURE AND EXPERIMENTAL CONSTRAINTS We employed the SPHENO4.0.4 package [94–96] gen- erated with SARAH 4.14.3 [96–98]. In this package, the weak-scale values of the gauge and Yukawa couplings are evolved to the unification scale MGUT via the renormaliza- tion group equations. MGUT is determined by the require- ment of the gauge coupling unification, described as g3 ≈ g2 ¼ g1 ¼ g01, where g3, g2, and g1 are the MSSM gauge couplings for SUð3ÞC, SUð2ÞL, and Uð1ÞY respec- tively, while g01 corresponds to the gauge coupling for Uð1Þ0. Concerning the contributions from the threshold corrections to the gauge couplings at MGUT arising from some unknown breaking mechanisms of the GUT gauge group, g3 receives the largest contributions [99], and it is allowed to deviate from the unification point up to about 3%. If a solution does not satisfy this condition within this allowance, SPHENO does not generate an output for such solutions by default. Hence, the existence of an output file guarantees that the solutions are compatible with the unification condition, and g3 deviates no more than 3%. After MGUT is calculated, all the SSB parameters, deter- mined with the boundary conditions at MGUT, along with the gauge and Yukawa couplings are evolved back to the weak scale. We performed random scans over the parameter space, shown in Table II, with the universal boundary conditions. Here m0 denotes the spontaneous symmetry breaking mass term for all the scalars, whileM1=2 stands for the SSB mass terms for the gauginos including the one associated with the Uð1Þ0 gauge group. tan β is the ratio of VEVs of the MSSM Higgs doublets, and A0 is the SSB trilinear scalar interact- ing term, λ is the coupling associated with the interaction of Ĥu, Ĥd, and Ŝ fields while κ is the coupling of the interaction of Ŝ1, Ŝ2 and Ŝ3 fields. Trilinear couplings for λ and κ are defined as λAλ and κAκ, respectively at the GUT scale. hν is the Yukawa coupling of the term L̂ĤuN̂. In analyzing the data and implications of the model, we impose the LEP2 bounds on the charged particles such that the model does not yield any new charged particles whose mass is lighter than about 100 GeV [100]. In addition, since it has been significantly being updated, we require that the consistent solutions yield gluino mass as mg̃ ≥ 2100 GeV. Another important mass bound comes from the Higgs boson. We require one of the Higgs bosons in solutions to exhibit the SM-like Higgs boson properties in terms of its mass and decay channels reported by the ATLAS [101–104] and CMS [105–108] Collaborations. Including the scalars, whose VEVs break the Uð1Þ0 symmetry, the low scale spectrum involves six CP-even Higgs boson mass. Since the mixing between the Uð1Þ0 breaking scalar fields and the MSSM Higgs fields is expected to be small, the SM- like Higgs boson should be formed mostly by the MSSM Higgs fields. In this context, the SM-like Higgs boson needs be identified not only with its mass, but also its mixing. If a solution yields one of the Higgs bosons (hi; i ¼ 1;…6) with a mass of about 125 GeV [109], we also require jZHði; 1Þj2 þ jZHði; 2Þj2 ≳ 80%, where ZH matrix quanti- fies the mixing among the Higgs bosons. Another one of the important constraints arises from the REWSB conditions [110–114] which requires the μ term consistent with EWSB. We also implement the constraints from rare B-meson decays such as BRðB → XsγÞ [115], BRðBs → μþμ−Þ [116], and BRðBu → τντÞ [117]. TABLE II. Scanned parameter space. Parameter Scanned range Parameter Scanned range m0 [0, 10] TeV vS [1, 20] TeV M1=2 [0, 10] TeV vS1 [3, 20] TeV tan β [1, 50] vS2 [3, 20] TeV A0=m0 [−3; 3] vS3 [3, 20] TeV λ [0.01, 0.5] Aλ [0, 10] TeV κ [0.1, 1.5] Aκ [−10; 0] hν [10−11; 10−7] ... ... HIÇYILMAZ, SELBUZ, SOLMAZ, and ÜN PHYS. REV. D 105, 055029 (2022) 055029-8 Then, we require that the predicted relic density of the neutralino LSP agrees within 5σ with the recent Planck results [118]. The relic density of the LSP and scattering cross sections for direct detection experiments are calcu- lated with MICROMEGAS (version 5.0.9) [119]. The exper- imental constraints are summarized in Table III. The following list summarizes the relation between colors and constraints imposed in our forthcoming plots. (a) Gray: Represents the points compatible with the radiative EWSB and neutralino LSP, (b) Blue: Forms a subset of gray and represents points satisfying the constraints on the SUSY particle masses, Higgs boson mass and its couplings, and B-physics constraints, (c) Red: Forms a subset of blue and represents the points which are consistent with the Planck bounds on the relic density of LSP neutralino within 5σ together with other constraints mentioned for blue points. IV. RESULTS In this section we present our results in light of the constraints discussed in the previous section. First, we focus on the Uð1Þ0 charges which characterizes the secluded Uð1Þ0 model. Figure 1 depicts the Uð1Þ0 charge sets satisfying various theoretical and experimental bounds. The color convention is as listed at the end of Sec. III. FIG. 1. The distributions of the Uð1Þ0 charges in secluded Uð1Þ0 model allowed by various theoretical and experimental conditions from Sec. III over the following planes: Q0 L −Q0 E, Q 0 U −Q0 D and Q0 S −Q0 Q. The color convention is as listed at the end of Sec. III. TABLE III. The experimental constraints employed in our analyses. Observable Constraint Reference mh ½122–128� GeV [101,120] MZ0 ≥4 TeV [68–73] mg̃ ≥2.1 TeV [121] mχ̃� 1 ; mτ̃ ≥100 GeV [100] BRðB → XsγÞ ½2.99–3.87� × 10−4ð2σÞ [115] BRðBs → μþμ−Þ ½0.8–6.2� × 10−9ð2σÞ [116] BRðBu → τντÞSecludedUð1Þ0 BRðBu → τντÞSM ½0.15–2.41�ð2σÞ [117] ΩCDMh2 ½0.114–0.126�ð5σÞ [118] MODEL CHARACTERIZATION AND DARK MATTER IN THE … PHYS. REV. D 105, 055029 (2022) 055029-9 Herein, we show charges for left and right chiral fermions and MSSM singlet by visualising our scan points over the planes Q0 L −Q0 E and Q0 U −Q0 D (top panels), and Q0 S −Q0 Q (bottom panel). Note that the charges are normalized to unity. As can be seen from the top left panel, the constraints allow a large number of different solution sets, and a wide range for the charges can be accommodated, e.g., the Q0 L;Q 0 E ≲ j0.9j. As for quarks, the right-handed up-type quark charges (Q0 U) and the right-handed down-type ones (Q0 D) exhibit almost the same behavior (as shown in the top-right panel of the figure). Furthermore, it can easily be read, from the bottom panel, that Q0 S charge is always far away from zero sinceQ0 S ¼ −ðQ0 Hu þQ0 Hd Þ. After applying all theoretical conditions and experimental constraints, Q0 S an Q0 Q charges are restricted to certain regions, Q0 S; Q 0 Q ≲ j0.5j. Since there is not a direct anomaly can- cellation condition between Q0 Q and Q0 S, it is possible to find various Q0 Q values for the fixed values of Q0 S. Figure 2 displays the mass spectrum of SUSY particles in mt̃ −mb̃ (left) and mτ̃ −mν̃ (right) planes. The color convention is as listed at the end of Sec. III. The left panel shows that sbottom and stop masses are heavy in general and should be 3 TeV≲mb̃, mt̃ ≲ 15 TeV. Even though these mass scales are far beyond the reach of the current LHC experiments, they can be probed in the future collider searches [122,123]. Similarly, the right panel also reveals that stau can be as light as only 2 TeV, compatible with all experimental bounds. Even though the sneutrino mass can be realized as low as about 500 GeV, it is, in general, heavier than stau for most of the solutions compatible with all experimental bounds. Figure 3 shows the neutralino and chargino mass spectrum with diagonal lines emphasizing the coannihila- tion and annihilation channels of LSP neutralino in mχ̃� 1 −mχ̃0 1 (top left), mH −mχ̃0 1 (top right), mA1 −mχ̃0 1 (bottom left), and mA2 −mχ̃0 1 (bottom right) planes. The color coding is the same as in Fig. 2. As is shown in the mχ̃� 1 −mχ̃0 1 plane, the chargino and neutralino can be as light as about 50–100 GeV. Even though the LSP neutralino mass can be realized, in principle, lighter than 50 GeV, the mass scales below 50 GeV trigger the invisible decays of the SM-like Higgs boson; thus, we consider the solutions with mχ̃0 1 ≲ 50 GeV to be excluded. Similarly, the chargino masses lower than 103.5 GeV are excluded as required by the LEP results. Apart from the lower bounds, the LSP neutralino happens mostly to be lighter than about 1 TeV. As discussed before, the MSSM neutralinos cannot be consistent if their masses are lighter than about 500 GeV due to the severe constraints from rare B-meson decays and their relic density. Thus the solutions with mχ̃0 1 ≲ 500 GeV should lead to LSPs which are formed mostly by the MSSM singlet fields. The chargino can be as heavy as about 1.5 TeV in the consistent spectra, while its mass can also be at the order of Oð100Þ GeV. The light chargino solutions are expected to be formed mostly by Higgsinos because of a sub-TeV scale μ term. In this case, if the LSP is formed by singlinos, while the lightest chargino is mostly a Higgsino, then one can identify the chargino-neutralino coannihilation scenario, through the interactions among the MSSM Higgsinos and Uð1Þ0 singlinos, in the approximate mass-degeneracy region represented with the diagonal line in the mχ̃� 1 −mχ̃0 1 plane. In this region, the LSP neutralinos coannihilate together with the lightest charginos which leads to lower the relic density of the LSP. Since the solutions compatible with the Planck bound are mostly accumulated around the diagonal line, the chargino-neu- tralino coannihilation scenario is required by the consistent DM solutions when mχ̃� 1 ≃mχ̃0 1 ≲ 0.75 TeV. Even though one can realize consistent DM solutions through chargino-neutralino coannihilation scenario, the FIG. 2. The mass spectrum of SUSY particles over the following planes:mt̃ −mb̃ (left) andmτ̃ −mν̃ (right). The color convention is as listed at the end of Sec. III. HIÇYILMAZ, SELBUZ, SOLMAZ, and ÜN PHYS. REV. D 105, 055029 (2022) 055029-10 mχ̃� 1 −mχ̃0 1 plane presents other solutions out of the mass degeneracy region (red points far above the diagonal line). These solutions cannot be identified in the chargino- neutralino coannihilation scenario; thus, the relic density of LSP neutralino should be lowered in other coannihilation and/or annihilation scenarios. Since other SUSY particles are either heavy (as stop, sbottom, and stau shown in Fig. 2) or they do not directly couple to the singlino LSP (as sneutrino), the relic density of LSP neutralino is most likely lowered by its annihilation processes into a neutral Higgs boson as displayed in the mH −mχ̃0 1 , mA1 −mχ̃0 1 , and mA2 −mχ̃0 1 planes of Fig. 3. The diagonal lines in these planes indicate the regions where 2mχ̃0 1 ¼ mH;mA1 ; mA2 , respectively. In the regions represented by the diagonal lines,mH can be as light as about 100 GeV, while it can also be realized as heavy as about 2 TeV. On the other hand, the lighter CP-odd Higgs boson masses are found to be bounded as mA1 ≲ 300 GeV and mA2 ≲ 600 GeV, as shown in the bottom planes of Fig. 3. One can conclude from such results that the LSP neutralino annihilations through the Higgs portal plays an important role to identify consistent DM solutions. Especially the annihilation proc- esses involving CP-odd Higgs bosons significantly lower the relic density of the LSP. Recall that the MSSM Higgs bosons contribute to rare B-meson decays at these mass scales and violate the constraints from B-physics. Thus, these light Higgs bosons should be formed mostly by the MSSM singlet scalars to be consistent with the constraints from rare B-meson decays. Besides, a MSSM singlet Higgs boson can strongly couple to the LSP neutralino and significantly lower its relic density. Even tough these light CP-odd Higgs bosons have MSSM singlet nature, they can interfere in the SM-like Higgs boson decays through h1 → AiAi, if they are formed by the MSSM singlet field S, which is allowed to interact with the MSSM Higgs fields at tree level through the coupling λ. If λ is considerably large, it also enhances the mixing between the MSSM FIG. 3. The mass spectrum of the lightest neutralino and chargino and relic density channels over the following planes;mχ̃� 1 −mχ̃0 1 (top left),mH −mχ̃0 1 (top right),mA1 −mχ̃0 1 (bottom left), andmA2 −mχ̃0 1 (bottom right). The color convention is as listed at the end of Sec. III. MODEL CHARACTERIZATION AND DARK MATTER IN THE … PHYS. REV. D 105, 055029 (2022) 055029-11 Higgs fields and the MSSM singlet S field. However, such a large mixing receives a strong impact from rare B-meson decays, especially from Bs → μμ. We observed that these light CP-odd Higgs bosons can lead to BRðh1 → A1A1Þ≲ 15%. However, such solutions are excluded by the Planck bound on the relic abundance of LSP neutralino, which favors BRðh1 → A1A1Þ ∼ 0. In this context, these light CP-odd Higgs bosons can escape from the current analyses which considers the rare and exotic decays of the SM-like Higgs boson [124–131]. If the spectrum involves charged particles which are nearly degenerate with the LSP neutralino in mass, the current analyses [132,133] yield a strong impact on their lifetime. In the models under phenomenological concern, the stability of such light charged particles can be con- trolled by the tree-level coupling between NLSP and LSP. Even though the current experimental constraints prevent the strongly-interacting charged particles to be NLSP, the chargino and the sleptons are, in principal, allowed to be NLSP. As discussed before, since the universal SSB gaugino mass terms do not allow the wino to be lighter than bino, the light chargino solutions can be observed only if they are formed by the MSSM Higgsinos, which couple to the MSSM singlet LSP neutralino at tree level. In addition, the universal SSB mass term for the scalar supersymmetric particles lead to stau to be the lightest slepton in the low-scale mass spectrum. However, there is no tree-level coupling between the stau and MSSM singlet LSP neutralino, and the NLSP stau solutions are more likely imply stable staus. Such solutions are strictly excluded by the collider analyses, since they would signal in the collisions as a missing charge. We have plotted the lifetime of these charged particles in Fig. 4 in correlation with their masses. All points are compatible with REWSB and the LSP neutralino condition. The blue points are consistent with the mass bounds and constraints from rare B-meson decays. The red points form a subset of blue and they satisfy the Planck bound on the relic abundance of LSP neutralinos within 5σ. The left panel shows the lifetime of lighter chargino, which is Higgsino-like. All solutions yield chargino lifetime shorter than about 10−2 ns and compatible with its current bound [132]. Furthermore, the solutions compatible with the Planck bound on the relic abundance of LSP neutralino (shown in red) can have the charginos, whose lifetime cannot be longer than about 10−8 ns. Similarly the right panel display the results for the stau lifetime, which undergoes immediate decay in the solutions within our data, since its life-time is realized to be always shorter than about 10−9 ns. This is because the stau is always heavier than some other MSSM particles (such as bino and Higgsinos), which couple to stau at tree level. The DM constraint shorten its lif-time further ðττ̃ ≲ 10−15 ns) as seen from the red points. Note that our plots are insensitive to the mass difference of about 1–2 GeV due to the point size used in plotting. Even though the mχ̃� 1 −mχ̃0 1 in Fig. 3 has some red points on the diagonal line, these solutions still lead to 1–2 GeV mass difference between the chargino and LSP neutralino, and such charginos undergo the χ̃�1 → qq̄0χ̃01 decay processes after they are being produced at the colliders, where q and q0 denote different quarks as required by the electric charge conservation. In addition to discussions about the coannihilation channels in Fig. 3, each species of neutralinos yield different phenomenology and implications in the dark matter experiments. If the LSP mass eigenstate χ̃01 is given in terms of interaction eigenstates by the following linear combination using the same basis as the neutralino mass matrix given in Eq. (14). χ̃01 ¼ Z11B̃þ Z12W̃3 þ Z13H̃0 d þ Z14H̃0 u þ Z15S̃ þ Z16B̃0 þ Z17S̃1 þ Z18S̃2 þ Z19S̃3; ð20Þ FIG. 4. Lifetime of charged particles such as the chargino (left) and stau (right) in correlation with their masses. The color convention is as listed at the end of Sec. III. HIÇYILMAZ, SELBUZ, SOLMAZ, and ÜN PHYS. REV. D 105, 055029 (2022) 055029-12 where Zij are elements of the diagonalization matrix encoding the possible mixtures in comprising the neutra- lino mass eigenstates, P jZijj2 ¼ 1 by the normalization condition and jZ1jj2 measures the fraction of the jth particle in the composition of LSP neutralino. The linear superposition of LSP neutralino given in Eq. (20) implies that Uð1Þ0 can deviate the LSP neutralino from the MSSM phenomenology by the total fraction of Uð1Þ0 particles expressed as jZ15j2 þ jZ16j2 þ jZ17j2 þ jZ18j2 þ jZ19j2. If jZ17j2 þ jZ18j2 þ jZ19j2 dominates the other elements of LSP mass diagonalization matrix, then the dark matter is realized to be mostly decouple from the other particles. In this case, the current sensitivity of the experiments in direct and indirect searches of dark matter cannot probe such solutions. On the other hand, if jZ15j2 is significantly larger, then the dark matter is again composed mostly by the MSSM singlet, i.e., S̃, which interacts with the MSSM particles through the Higgs portal. The current and projected sensitivity of the direct detection of dark matter experiments can provide a potential probe for such solutions. Moreover, even if it does not form the dark matter significantly, it can still alter the dark matter implications through its mixing with the MSSM neutrali- nos. Finally, even though B̃0 is also theoretically allowed to form the dark matter, the mass is mostly controlled by vS. Since the heavy mass bound on Z0 bounds vS at about a few TeV from below, the neutralino mass eigenstate, which is mostly formed by B̃0, is found rather to be heavy. We can summarize the discussion about the LSP neutralino composition and its testable implications in the dark matter experiments with plots given in Fig. 5. In the left panel, we visualize the branching fraction of each neutralino by using different colors and shapes with the mass of the LSP neutralino. The color and shape con- vention is given in the legend. The points represented in this plane are selected such that they are allowed by all the constraints including the Planck bound on the LSP neu- tralino relic density. As is seen from the blue pentagons, the light LSP masses (≲350 GeV) can be realized when the LSP neutralino is formed mostly by S̃ (≳80%). S̃ still plays a crucial role for relatively large mass scales, since its mixing in the LSP composition is realized at about 40% and more for mχ̃0 1 ≳ 400 GeV. Most of these solutions also reveal that the rest of the LSP neutralino is formed by the other MSSM singlets i.e., S̃1, S̃2 and S̃3. In this context, the dark matter is realized to be almost a MSSM singlet, while it can interact with the MSSM particles through the Higgs portal. As discussed before, the fraction for B̃0 is realized as large as only about 10% and less (black crosses in the left panel of Fig. 5). The MSSM neutralinos become effective in the LSP composition when mχ̃0 1 ≳ 600 GeV, which can be mea- sured as about 50% bino fraction (red 1), and about 25% for each MSSM Higgsino (turquoise 3 and orange 4). This mass scale bounding the bino-Higgsino mixture is a direct result of the gluino mass bound and the Planck bound on the relic density of LSP neutralino. Since we employ universal gaugino masses at the GUT scale, the gluino mass bound excludes the region where M1=2 ≲ 600 GeV. In addition, when the Higgsinos form the LSP neutralino, the relic density constraint is satisfied whenmχ̃0 1 ≳700GeV (see, for instance, Refs. [79,134,135]). The Higgsino fraction is also constrained by the results from the direct detection experiments, since it yields large cross sections for the dark matter scattering at nuclei. As is seen from the discussion above, the secludedUð1Þ0 model yield solutions in which the dark matter is mostly formed by the singlino (S̃). Even though there are not many channels in scattering of dark matter at nuclei, these solutions can be traced down in the direct detection experiments through the Higgs portal, and their signature FIG. 5. The composition of the LSP versus its mass (left) and DM-nucleon SI scattering cross section as a function of the mass of the lightest neutralino LSP (right). Limits from current (solid) and future (dashed) experiments are also shown. MODEL CHARACTERIZATION AND DARK MATTER IN THE … PHYS. REV. D 105, 055029 (2022) 055029-13 can be significant depending on how strongly it interacts with the MSSMHiggs fields. The right panel of Fig. 5 show the results for the spin-independent scattering cross section of dark matter with respect to its mass. The represented solutions are selected to be consistent with the constraints employed in our analyses. The experimental results from the direct detection experiments are represented with the curves. The black, blue, and red solid lines show XENON1T [136], PandaX-II [137] and LUX [138] upper limits for the SI χ̃01—nucleon cross section, respectively, while the black and blue dashed lines illustrate the prospects of the XENONnT and DARWIN for future experiments [139], respectively. We also display a color bar which relates the color coding to the Singlino fraction in the composition of LSP. The red points correspond to Singlino-like dark matter in which the singlino fraction is realized greater than about 70%. The solutions with mχ̃0 1 ≲ 350 GeV yielding scattering cross sections larger than about 2 × 10−48 cm2 can be tested in XENON experiment soon, while those with σSI ∈ ½3 × 1049 − 2 × 1048� cm2 are expected to be probed by the DARWIN collaboration. DARWIN will also be able to test the singlino dark matter when the LSP mass is relatively heavier (∼500 GeV). Finally, we also display a solution exemplifying the MSSM-like dark matter (blue). These solutions were iden- tified as Bino-Higgsino mixture in the previous discussion, and as is seen from the right plane, the direct detection experiments yield a strong negative impact on such sol- utions, since it predicts a large scattering cross section. Before concluding, we present six benchmark points in Table IV to exemplify our findings. The results discussed above can be classified into three scenarios as grouped in Table IV. Scenarios I and II involve the solutions of MSSM singlet LSP, and the MSSM-like LSP solutions refer to Scenario III. Scenario I and Scenario II differ from each other in chargino mass. The mass spectra in Scenario I includes charginos nearly mass degenerate with the LSP neutralino, while it is much heavier than the LSP neutralino in Scenario II. The first two points in Table IV exemplify the solutions in Scenario I. The correct relic density of LSP neutralino for these solutions is satisfied through the chargino-neutralino coannihilation scenario. Point 1 pre- dicts σSI ≃ 5 × 10−46 cm2 for the spin-independent scatter- ing of DM, which can be tested soon in XENON TABLE IV. The benchmark points for different scenarios. The points are selected to be consistent with the experimental constraints. All masses are given in TeV, and the cross sections in cm2. Scenario I Scenario II Scenario III Parameters Point 1 Point 2 Point 3 Point 4 Point 5 g01 0.36 0.57 0.41 0.41 0.45 tan β 15.7 21.3 12.3 45.7 20.0 μeff 0.110 0.105 0.389 0.419 0.630 ðλ; κÞ (0.02, 0.63) (0.017, 0.72) (0.09, 0.67) (0.09, 1.07) (0.05, 0.51) ðAλ; AκÞ (4.6, −4.2) (2.2, −3.3) (3.9, −3.2) (5.0, −8.6) (4.8, −3.1) ðvs1 ; vs2 ; vs3Þ (15.5, 14.6, 12.6) (13.0, 8.55, 11.8) (14.6, 11.2, 14.1) (11.5, 19.0, 9.65) (10.0, 10.0, 6.8) (m0Þ 3.835 4.569 9.610 7.267 5.512 ðM1=2Þ 3.345 9.359 5.500 3.502 1.450 (A0) 1.305 −2.572 1.154 −3.639 −0.305 mZ0 5.53 5.19 6.43 5.69 5.62 ðmH0 1 ; mH0 2 Þ (0.1243, 0.659) (0.127, 0.325) (0.1228, 0.242) (0.125, 0.783) (0.1234, 1.121) ðmA0 1 ; mA0 2 Þ (0.142, 0.188) (0.210, 0.223) (0.117, 0.157) (0.172, 0.253) (0.119, 0.179) ðmχ̃0 1 ; mχ̃0 2 Þ (0.103, 0.115) (0.102, 0.112) (0.056, 0.408) (0.124, 0.436) (0.611, 0.637) ðmχ̃� 1 ; mχ̃� 2 Þ (0.117, 2.783) (0.113, 7.813) (0.409, 4.638) (0.438, 2.973) (643, 1.239) mH� 2.872 2.201 4.327 9.796 7.847 ðmt̃L ; mc̃L ; mũLÞ (5.37, 6.89, 7.13) (12.1, 15.4, 16.3) (9.59, 12.8, 13.7) (6.61, 9.22, 9.53) (4.58, 5.92, 6.38) ðmt̃R ; mc̃R ; mũRÞ (6.41, 6.89, 7.13) (14.6, 15.4, 16.3) (12.2, 12.8, 13.7) (7.38, 9.22, 9.53) (4.89, 5.92, 6.38) ðmb̃L ; ms̃L ; md̃L Þ (6.41, 6.82, 7.13) (14.6, 15.4, 16.3) (12.0, 12.1, 13.7) (7.37, 9.39, 9.53) (4.88, 5.92, 6.51) ðmb̃R ;ms̃R ; md̃R Þ (6.75, 6.82, 7.13) (15.1, 15.4, 16.3) (12.2, 12.1, 13.7) (7.52, 9.39, 9.53) (6.29, 5.92, 6.51) ðmτ̃L ; mμ̃L ; mẽLÞ (3.96, 4.03, 4.34) (4.27, 4.58, 7.80) (8.87, 8.91, 10.2) (5.03, 7.55, 7.57) (4.87, 5.16, 6.24) ðmτ̃R ; mμ̃R ; mẽRÞ (4.31, 4.03, 4.34) (7.71, 4.58, 7.80) (10.1, 8.91, 10.2) (6.41, 7.55, 7.57) (6.12, 5.16, 6.24) ðmν̃τL ; mν̃μL ; mν̃eL Þ (3.97, 3.97, 4.34) (3.73, 3.73, 7.80) (8.87, 8.91, 10.9) (6.41, 7.26, 7.55) (4.98, 4.98, 6.24) ðmν̃τR ; mν̃μR ; mν̃eR Þ (4.30, 3.97, 4.34) (7.71, 3.73, 7.80) (10.9, 8.91, 10.9) (7.26, 7.26, 7.55) (6.12, 4.98, 6.24) ΩDMh2 0.1146 0.1161 0.1253 0.1178 0.1222 σSI 4.59 × 10−47 1.69 × 10−48 3.65 × 10−49 2.61 × 10−49 9.64 × 10−45 HIÇYILMAZ, SELBUZ, SOLMAZ, and ÜN PHYS. REV. D 105, 055029 (2022) 055029-14 experiments. Point 2 displays a solution for A-resonance. Points 3 and 4 represent the solutions in Scenario II in which the relic density constraint is satisfied only through A resonance. Point 3 yields σSI ≃ 10−48 cm2, and Darwin experiments will be able to test such solutions in near future. Point 4 depicts a solution in which two LSP neutralinos annihilate into the second CP-odd Higgs boson of mass about 250 GeV. Finally Point 5 displays solutions for Scenario III in which the LSP neutralino is formed by the MSSM neutralinos, which is mostly Higgsino in our model. Such solutions lead to very large cross sections in DM scattering with nuclei (∼10−44 cm2) and they are excluded by the current constraints set by the direct detection experiments. We also list the sets of Uð1Þ0 charges for these benchmark points in Table V. The solutions in Scenario I favor sets of charges in which the left-handed quark and lepton fields have relatively low charges under the Uð1Þ0 group. Scenario II depicts a certain magnitudes of the Uð1Þ0 charges, while their sign could be negative or positive. Scenario III reveals a fact that all the fields are considerably charged under Uð1Þ0 group if the LSP neutralino is formed by the MSSM neutralinos. V. CONCLUSION We realized that the Uð1Þ0 extension, which extends the MSSM with MSSM singlet particles considerably alter the DM phenomenology for the LSP neutralino masses from about 100 GeV to 1 TeV. This mass scale can be divided into three scenarios, which follow different manifestations in the results of the relic abundance of LSP neutralino and its scattering with nuclei. The typical mass spectrum in all scenarios involves two light CP-odd Higgs bosons whose masses are lighter than about 200 GeV and 600 GeV, respectively. Due to the strong impact from rare B meson decays employed in our analyses, the MSSM Higgs bosons cannot be lighter than about 500 GeV, and such light Higgs boson solutions can be consistent with the constraints from rare B-meson decays only when they are formed mostly by the MSSM singlet fields. These CP-odd Higgs bosons play important roles to reduce the relic abundance of LSP neutralino compatible with the current Planck bounds. Scenario I involves the LSP neutralino as light as about 100 GeV together with light charginos. It can be seen easily that the LSP composition involves more than about 80% singlino, while the remaining ≲20% also formed by the other MSSM singlet fields, S1;2;3. This composition holds in almost all the solutions with mχ̃0 1 ≲ 500 GeV. Thus, the secluded Uð1Þ0 model yields mostly MSSM singlet DM which can considerably interact with the MSSM particles through the Higgs portal. Singlino still takes part in the DM phenomenology for heavier LSP neutralino solutions, since its percentage in the LSP composition is realized greater than about 50% formχ̃0 1 ≲ 1 TeV. In this region, the MSSM Higgsinos are involved in the LSP decomposition up to about 40%. The correct relic density for the LSP neutralino is partly satisfied through the chargino-neutralino coannihi- lation scenario in Scenario I up to about mχ̃� 1 ≲ 750 GeV. The latest LHC constraints, especially the gluino mass bound, result in binos and winos heavier than about 300 GeV at the low-scale SUSY spectrum, and hence the lighter chargino state is formed mostly byMSSMHiggsinos, so the chargino couples to the MSSM singlet LSP neutralino at tree-level. We realized that this coupling lead to a life-time for such light charginos always shorter than about 10−2 ns. We observed that the chargino life-time lasts longer if the Wino takes part in decomposition of the lighter chargino, but the solutions with τχ̃� 1 ≳ 10−8 ns are excluded by the current Planck bound on the relic abundance of LSP neutralino. The solutions in Scenario II can also be characterized by the singlino LSP neutralino in the similar mass range, but these solutions involve relatively heavier charginos, and the chargino-neutralino coannihilation scenario is not realized in this Scenario. The correct relic density of the LSP neutralino is satisfied through its annihilation into the lighter CP-odd Higgs bosons, which are mostly formed by the MSSM singlet Higgs bosons in our model. One may expect small scattering cross section for the LSP neutralino due to its dominant singlet nature under the MSSM gauge group. However, as mentioned above, the singlino is allowed to interact with the MSSM particles through the Higgs portal, which can potentially enhance its scattering cross section. We observed that the singlino LSP solutions can predict DM spin-independent cross section in the range ∼4 × 1046 cm2–10−50 cm2 for the singlinolike LSP. These solutions are expected to be tested in XENONnT experiments up to about σSI ∼ 2 × 10−48 cm2, while Darwin can lower the testable cross section scale to about 3 × 10−49 cm2 in near future. TABLE V. Sets ofUð1Þ0 charges for the benchmark points listed in Table IV. The charges satisfy the conditions of gauge invariance (Eq. (3) in the secluded Uð1Þ0 model described by the super- potential (Eq. (2) and of anomaly cancellation (Eqs. (4)–(9)). Scenario I Scenario II Scenario III Parameters Point 1 Point 2 Point 3 Point 4 Point 5 Q0 Q 0.0 −0.05 −0.2 0.2 −0.15 Q0 U −0.45 −0.3 0.35 −0.35 0.35 Q0 D 0.9 0.1 0.5 −0.5 0.4 Q0 L 0.15 0.05 0.75 −0.75 0.6 Q0 N −0.6 −0.4 −0.6 0.6 −0.4 Q0 E 0.75 −0.3 −0.45 0.45 −0.35 Q0 Hu 0.45 0.35 −0.15 0.15 −0.20 Q0 Hd −0.9 −0.05 −0.3 0.3 −0.25 Q0 S 0.45 −0.3 0.45 −0.45 0.45 Q0 S1 0.45 −0.3 0.45 −0.45 0.45 Q0 S2 0.45 −0.3 0.45 −0.45 0.45 Q0 S3 −0.9 0.6 −0.9 0.9 −0.9 MODEL CHARACTERIZATION AND DARK MATTER IN THE … PHYS. REV. D 105, 055029 (2022) 055029-15 We identify another class of solutions which can be classified as Scenario III. In this scenario, the LSP neutralino can still exhibit MSSM singlet nature, but the MSSM neutralinos considerably takes part in its decom- position since their mixing with the singlino can be more than about 50%. Furthermore, this scenario can also yield MSSM-like LSP neutralino, which is mostly formed by the MSSM Higgsinos. The CMSSM-like gaugino mass rela- tion yield M2 > μ and results in Higgsino-like lighter chargino states. Such solutions typically yield nearly mass degenerate chargino and LSP neutralino and they fall into the chargino-neutralino coannihilation region. The light CP-odd Higgs bosons do not take significant part in satisfying the correct relic density in this region. Even though such solutions can be consistent with the exper- imental constraints employed in our analyses, they receive a strong negative impact from the direct detection DM experiments due to the large scattering cross sections of Higgsino-like LSP neutralino. We find that its scattering cross section is of the order about 10−44 cm2, which is severely excluded by the current results from the direct detection experiments. ACKNOWLEDGMENTS The work of Y. 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