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Detecting Hidden Sector Dark Matter at HL-LHC and HE-LHC Via Long-Lived Stau Decays

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Detecting Hidden Sector Dark Matter at HL-LHC and HE-LHC Via Long-Lived Stau Decays PHYSICAL REVIEW D 99, 055037 (2019) Detecting hidden sector dark matter at HL-LHC and HE-LHC via long-lived stau decays † Amin Aboubrahim* and Pran Nath Department of Physics, Northeastern University, Boston, Massachusetts 02115-5000, USA (Received 14 February 2019; published 27 March 2019) We investigate a class of models where the supergravity model with the standard model gauge group is ð1Þ extended by a hidden sector U X gauge group and where the lightest supersymmetric particle is the neutralino in the hidden sector. We investigate this possibility in a class of models where the stau is the lightest supersymmetric particle in the minimal supersymmetric standard model sector and the next-to- ð1Þ lightest supersymmetric particle of the U X-extended supergravity model. In this case the stau will decay into the neutralino of the hidden sector. For the case when the mass gap between the stau and the hidden ð1Þ ð1Þ sector neutralino is small and the mixing between the U Y and U X is also small, the stau can decay into the hidden sector neutralino and a tau which may be reconstructed as a displaced track coming from a high-pT track of the charged stau. Simulations for this possibility are carried out for HL-LHC and HE-LHC. The discovery of such a displaced track from a stau will indicate the presence of hidden sector dark matter. DOI: 10.1103/PhysRevD.99.055037 I. INTRODUCTION highly suppressed couplings to the visible sector. Let us suppose that one of the two neutralinos which lie in the Most of the searches for dark matter (DM) are focused on hidden sector is the lightest supersymmetric particle (LSP) dark matter being a particle interacting weakly with the of the extended model and further the next-to-lightest standard model (SM) particles and having a cross section in supersymmetric particle (NLSP) is a stau which lies close a range accessible to direct detection and indirect detection to the hidden sector neutralino. In this case the stau will experiment. For example in the context of supersymmetry decay into the hidden sector neutralino with a long lifetime. (SUSY) if the lightest particle is neutral with R parity Such a decay can leave a track in the inner detectors (ID) of conservation, it is a candidate for dark matter. However, it is the ATLAS and CMS experiments. In this work we explore entirely possible that dark matter resides in hidden sectors this possibility within the framework of supergravity grand which are ubiquitous in supergravity (SUGRA) and string ð1Þ unified model with an extended U X sector including models (see, e.g., [1]). Further, SUGRA models with a both the gauge kinetic mixing and the Stueckelberg mass minimal supersymmetric standard model (MSSM) spec- ð1Þ ð1Þ mixing. U extensions of supersymmetric models and trum extended by a U X gauge group bring in an their implications on dark matter and collider analyses have additional vector superfield with a particle content of 0 λ 0 λ been studied extensively in the literature [7]. However, the Bμ; X, where Bμ is the new gauge boson and X is its setup in the present work is quite different from these. ð1Þ gaugino superpartner. The U X can mix with hyper- The outline of the rest of paper is as follows: In Sec. II, ð1Þ charge U Y via kinetic mixing [2,3]. Additionally with we discuss the Uð1Þ -extended SUGRA model with gauge ð1Þ ð1Þ X Stueckelberg mass mixing of U X and U Y one brings kinetic mixing and Stueckelberg mass mixing. In Sec. III, ψ in a chiral superfield which contains a Weyl fermion we discuss implementation of this model and the mecha- – [4 6]. After electroweak symmetry breaking the above nism that leads to a long-lived stau consistent with the leads to a 6 × 6 neutralino mass matrix, where the addi- current experimental constraints on the light Higgs boson tional two neutralinos reside in the hidden sector with mass as measured by the ATLAS and CMS Collaborations [8,9] and the relic density as measured by the Planck *[email protected] Collaboration [10]. In Sec. IV, further details of the † [email protected] generation of relic density for the dark matter in the hidden sector is discussed. Currently, the LHC has completed its Published by the American Physical Society under the terms of phase 2 and has shut down for 2 yr for the period 2019– the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to 2020 for an upgrade and the upgraded LHC will operate at the author(s) and the published article’s title, journal citation, 14 TeV in the period 2021–2023. During this period the and DOI. Funded by SCOAP3. upgraded LHC will collect about 300 fb−1 of additional 2470-0010=2019=99(5)=055037(15) 055037-1 Published by the American Physical Society AMIN ABOUBRAHIM and PRAN NATH PHYS. REV. D 99, 055037 (2019) 1 1 data for each detector. Thereafter there will be a major μ ¯ S ¼ ðρ þ iaÞþθχ þ iθσ θ ð∂μρ þ i∂μaÞ upgrade of the LHC to the high-luminosity LHC (HL- 2 2 LHC) during the period 2023–2026. This final upgraded 1 þ θθ þ i θθθ¯σ¯ μ∂ χ þ θθθ¯ θ¯ð□ρ þ □ Þ ð Þ HL-LHC will resume operations in late 2026 and is F 2 μ 8 i a : 3 expected to run for 10 yr till 2036. It is projected that at the end of this period each detector will collect about The gauge kinetic energy sector of the model is 3000 fb−1 of data. Future colliders beyond HL-LHC are 1 also being discussed. Among these are a 100 TeV pp μν μν μ ¯ μ ¯ L ¼ − ðBμνB þ CμνC Þ − iλBσ ∂μλB − iλCσ ∂μλC collider at CERN and also a 100 TeV pp collider in China gk 4 [11,12], each of which requires a circular ring of about 1 þ ðD2 þ D2 Þ: ð4Þ 100 km. Further, a third possibility of a 27 TeV pp collider, 2 B C the high-energy LHC (HE-LHC) at CERN, is also under ð1Þ study [13–16]. Such a collider can be built within the Next we allow gauge kinetic mixing between the U X ð1Þ existing tunnel at CERN by installing 16 T superconduct- and U Y sectors with terms of the form ing magnets using fcc technology capable of enhancing δ the center-of-mass energy of the collider to 27 TeV. If − μν − δðλ σμ∂ λ¯ þ λ σμ∂ λ¯ Þþδ ð Þ 2 B Cμν i C μ B B μ C DBDC: 5 built, the HE-LHC will operate at a luminosity of 2.5 × 35 −2 −1 −1 10 cm s and collect 10–15 ab of data. In this work ð1Þ As a result of Eq. (4) the hidden U X interacts with the we will focus on HL-LHC and HE-LHC. Thus in Sec. V, MSSM fields via the small kinetic mixing parameter δ. The we discuss the production cross section of the NLSP stau kinetic terms in Eqs. (4) and (5) can be diagonalized using at the LHC at 14 TeV and at 27 TeV (for previous work the transformation on HL-LHC and HE-LHC see [17–20]). In Sec. VI,an μ 0μ analysis of signal and background simulation and event B 1 −sδ B ¼ ð Þ selection is carried out. In Sec. VII, a cut-flow analysis and μ 0μ ; 6 C 0 cδ C the result of this analysis are discussed. Here the analysis is done with no pileup and with pileup. The analysis also 2 1=2 2 1=2 where cδ ¼ 1=ð1 − δ Þ and sδ ¼ δ=ð1 − δ Þ . makes a comparative study of the discovery potential of Aside from gauge kinetic mixing, we assume a HL-LHC and HE-LHC for the detection of hidden sector Stueckelberg mass mixing between the Uð1Þ and Uð1Þ dark matter. Conclusions are given in Sec. VIII. X Y sectors so that Z II. THE MODEL L ¼ θ2 θ¯2ð þ þ þ ¯Þ2 ð Þ St d d M1C M2B S S : 7 As discussed above we consider an extension of the standard model gauge group by an additional Abelian ð1Þ ð1Þ ð1Þ We note that Eq. (7) is invariant under U Y and U X gauge group U X of gauge coupling strength gX. The gauge transformation so that particle spectrum in the visible sector, i.e., quarks, leptons, Higgs and their superpartners are assumed neutral under ¯ δ B ¼ Λ þ Λ ; δ S ¼ −M2Λ ; Uð1Þ . We focus first on the Abelian gauge sector of the Y Y Y Y Y X δ ¼ Λ þ Λ¯ δ ¼ − Λ ð Þ extended model which contains two vector superfields, a XC X X; XS M1 X: 8 vector superfield B associated with the hypercharge gauge ð1Þ L group U Y and a vector superfield C associated with the In component notation, St is hidden sector gauge group Uð1Þ , and a chiral scalar X 1 1 superfield S. In the Wess-Zumino gauge the B and C L ¼ − ð þ þ ∂ Þ2 − ð∂ ρÞ2 − χσμ∂ χ¯ St M1Cμ M2Bμ μa μ i μ superfields have the following components: 2 2 2 ¯ ¯ þ 2jFj þ ρðM1DC þ M2DBÞþχ¯ðM1λC þ M2λBÞ 1 þ χð λ þ λ Þ ð Þ ¼ −θσμθ¯ þ θθθ¯λ¯ − θ¯ θθλ¯ þ θθθ¯ θ¯ ð Þ M1 C M2 B : 9 B Bμ i B i B 2 DB 1 In unitary gauge the axion field a is absorbed to generate ð1Þ and mass for the U X gauge boson.
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