Searching for light neutralinos with a displaced vertex at the LHC (2024)

Table of Contents
1 Introduction 2 Model and benchmark scenarios 3 Simulation and event selection 4 Results 5 Conclusions Appendix A Reinterpretation of monolepton search References References
aainstitutetext: Departamento de Ciencias, Facultad de Artes Liberales,
Universidad Adolfo Ibáñez, Diagonal Las Torres 2640, Santiago, Chilebbinstitutetext: Millennium Institute for Subatomic Physics at the High Energy Frontier (SAPHIR), Fernández Concha 700, Santiago, Chileccinstitutetext: Departamento de Física,Facultad de Ciencias, Universidad de La Serena,Avenida Cisternas 1200, La Serena, Chileddinstitutetext: Departamento de Ingeniería Eléctrica-Electrónica, Universidad de Tarapacá, Arica 1010069, Chileeeinstitutetext: Department of Physics, National Tsing Hua University, Hsinchu 300, Taiwanffinstitutetext: Center for Theory and Computation, National Tsing Hua University, Hsinchu 300, Taiwan

Giovanna Cottingiovanna.cottin@uai.clc,b  Juan Carlos Helojchelo@userena.clc,b  Fabián Hernández-Pintofhernandezp@alumnosuls.cld  Nicolás A. Neillnaneill@outlook.come,f  Zeren Simon Wangwzs@mx.nthu.edu.tw

(June 17, 2024)

Abstract

We study a bino-like light neutralino (χ~10superscriptsubscript~𝜒10\tilde{\chi}_{1}^{0}over~ start_ARG italic_χ end_ARG start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 0 end_POSTSUPERSCRIPT) produced at the LHCfrom the decay of a scalar lepton (e~Lsubscript~𝑒𝐿\tilde{e}_{L}over~ start_ARG italic_e end_ARG start_POSTSUBSCRIPT italic_L end_POSTSUBSCRIPT) through the process p⁢p→e~L→e⁢χ~10→𝑝𝑝subscript~𝑒𝐿→𝑒superscriptsubscript~𝜒10pp\to\tilde{e}_{L}\to e\tilde{\chi}_{1}^{0}italic_p italic_p → over~ start_ARG italic_e end_ARG start_POSTSUBSCRIPT italic_L end_POSTSUBSCRIPT → italic_e over~ start_ARG italic_χ end_ARG start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 0 end_POSTSUPERSCRIPT in the context of R-parity-violating (RPV) supersymmetry where χ~10superscriptsubscript~𝜒10\tilde{\chi}_{1}^{0}over~ start_ARG italic_χ end_ARG start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 0 end_POSTSUPERSCRIPT is the lightest supersymmetric particle.For small masses and RPV couplings, the neutralino is naturally long-lived and its decay products can be identified as displaced tracks.Following existing searches, we propose a displaced-vertex search strategy for such a light neutralino with a single RPV coupling switched on, λ111′subscriptsuperscript𝜆′111\lambda^{\prime}_{111}italic_λ start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT start_POSTSUBSCRIPT 111 end_POSTSUBSCRIPT, in the mass range 10⁢GeV≲mχ~10≲230⁢GeVless-than-or-similar-to10GeVsubscript𝑚superscriptsubscript~𝜒10less-than-or-similar-to230GeV10\,\mbox{GeV}\lesssim m_{\tilde{\chi}_{1}^{0}}\lesssim 230\,\mbox{GeV}10 GeV ≲ italic_m start_POSTSUBSCRIPT over~ start_ARG italic_χ end_ARG start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 0 end_POSTSUPERSCRIPT end_POSTSUBSCRIPT ≲ 230 GeV.We perform Monte Carlo simulationsand conclude that at the high-luminosity LHC, the proposed search can probe values of λ111′subscriptsuperscript𝜆′111\lambda^{\prime}_{111}italic_λ start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT start_POSTSUBSCRIPT 111 end_POSTSUBSCRIPT down to two orders of magnitude smaller than current bounds and up to 40 times smaller than projected limits from monolepton searches.

1 Introduction

In recent years,searches for heavy new particles at the Large Hadron Collider (LHC), inspired by supersymmetry (SUSY) and other new physics (NP) scenarios, have yielded no concrete fruit.On the other hand, the lifetime frontier has become increasingly important.In particular, the LHC and other high-energy experiments are now actively looking for long-lived particles (LLPs)Alimena etal. (2020); Lee etal. (2019); Curtin etal. (2019).After such exotic states are produced, they can travel macroscopic distances before decaying into Standard Model (SM) or other NP particles, leading to distinctive signatures such as displaced leptons or displaced vertices.A series of far-detector experiments with the main purpose of searching for LLPs, such as FASERFeng etal. (2018) and MoEDAL-MAPPStaelens (2019), have been proposed or approved at different interaction points (IPs) of the LHC.

In various SUSY models, different new particles can be long-lived.For instance, one can have a long-lived gluino in split SUSYHewett etal. (2004), or a long-lived chargino in compressed SUSYGiudice etal. (1998); Randall and Sundrum (1999).In this work, we consider the production of the lightest neutralino in R-parity-violating (RPV) supersymmetry (see Refs.Dreiner (1997); Barbier etal. (2005); Mohapatra (2015) for reviews on the model).The minimal supersymmetric standard model (MSSM) with broken R-parity allows for the lightest supersymmetric particle (LSP) to decay into standard model particles via either bilinear or trilinear RPV couplings.In this work, we assume that the lightest neutralino is the LSP.

Current bounds on the lightest neutralino mass are much looser than those on the squark, slepton, and gluino masses.If the GUT-inspiredrelation between the gaugino masses (M1≈0.5⁢M2subscript𝑀10.5subscript𝑀2M_{1}\approx 0.5M_{2}italic_M start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT ≈ 0.5 italic_M start_POSTSUBSCRIPT 2 end_POSTSUBSCRIPT) is droppedChoudhury and Sarkar (1996); Choudhury etal. (2000) and dark matter (DM) does not consist of the lightest neutralinoBelanger etal. (2002); Hooper and Plehn (2003); Bottino etal. (2003); Belanger etal. (2004); AlbornozVasquezetal. (2010); Calibbi etal. (2013), then the lightest neutralino can have 𝒪⁢(GeV)𝒪GeV\mathcal{O}(\mbox{GeV})caligraphic_O ( GeV ) masses or even be masslessGogoladze etal. (2003); Dreiner etal. (2009).Such a light neutralino has to be bino-likeGogoladze etal. (2003); Dreiner etal. (2009) and it is in agreement with both astrophysical and cosmological boundsGrifols etal. (1989); Ellis etal. (1988); Lau (1993); Dreiner etal. (2003, 2013); Profumo (2008); Dreineretal. (2012a) as long as it decays (e.g.in the framework of RPV-SUSY) in order to avoid overclosing the UniverseBechtle etal. (2016).See Ref.Domingo and Dreiner (2022) for a recent study on the low-energy phenomenomology of a bino-like neutralino lighter than the tau lepton.

Besides the bounds on the lightest neutralino mass, the various RPV couplings are also constrained from both collider and low-energy observables Allanach etal. (1999).In this work, we focus on the single coupling λ111′subscriptsuperscript𝜆′111\lambda^{\prime}_{111}italic_λ start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT start_POSTSUBSCRIPT 111 end_POSTSUBSCRIPT,for which the most stringent current bounds stem from neutrinoless double beta decayMohapatra (1986); Hirsch etal. (1995, 1996); Bolton etal. (2021) as well as monolepton searches at the LHCAaboud etal. (2018a).Details of the neutrinoless double beta decay bounds are described in Sec.4, while a reinterpretation of the monolepton search for our scenario is presented in Sec.A.Both bounds are shown in Sec.4 together with the expected bounds from the displaced vertex (DV) search proposed in this work.If the coupling λ211′subscriptsuperscript𝜆′211\lambda^{\prime}_{211}italic_λ start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT start_POSTSUBSCRIPT 211 end_POSTSUBSCRIPT is instead switched on, the sensitivity results will be similar but the neutrinoless double beta decay constraints would no longer apply.

If either the lightest neutralino is light or the RPV couplings are small enough, the lightest neutralino becomes long-lived and may be searched for at collider, beam-dump experiments and even atmospheric neutrino detectorsCandia etal. (2021).Phenomenological studies on the exclusion limits in the same scenario already exist from the planned SHiP experimentGorbunov and Timiryasov (2015); deVries etal. (2016), proposed LHC far detectorsHelo etal. (2018); Dercks etal. (2019a, b); Dreiner etal. (2021, 2022); Gehrlein and Ipek (2021), Belle IIDey etal. (2021); Dib etal. (2022), and future lepton collidersWang and Wang (2020a, b).These works mainly focus on the lightest neutralino produced from either B𝐵Bitalic_B- or D𝐷Ditalic_D-mesons decays, or Z𝑍Zitalic_Z-boson decays, constraining masses below ∼45⁢GeVsimilar-toabsent45GeV\sim 45~{}\text{GeV}∼ 45 GeV.In contrast, in this work we consider the on-shell production of a heavy slepton, which then further decays to a charged lepton and a long-lived neutralino.This allows us to probe neutralino masses up to above 200 GeV, as will be shown in Sec.4.

This work is organized as follows.We introduce the RPV-MSSM model basics and benchmark scenarios in Sec.2.The simulation procedure is explained in Sec.3 together with the description of the event selections.Numerical results are presented in Sec.4 andwe conclude with a summary and conclusions in Sec.5.Additionally, in AppendixA, we describe our reinterpretation of the LHC monolepton search in the context of the RPV-MSSM.

2 Model and benchmark scenarios

In the RPV-MSSM, the MSSM is supplemented with the following RPV superpotential Weinberg (1982); Hall and Suzuki (1984)

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WRPV=∑iμi⁢Li⁢Hu+∑i,j,k(12⁢λi⁢j⁢k⁢Li⁢Lj⁢Ekc+λi⁢j⁢k′⁢Li⁢Qj⁢Dkc+12⁢λi⁢j⁢k′′⁢Uic⁢Djc⁢Dkc),subscript𝑊RPVsubscript𝑖subscript𝜇𝑖subscript𝐿𝑖subscript𝐻𝑢subscript𝑖𝑗𝑘12subscript𝜆𝑖𝑗𝑘subscript𝐿𝑖subscript𝐿𝑗subscriptsuperscript𝐸𝑐𝑘subscriptsuperscript𝜆′𝑖𝑗𝑘subscript𝐿𝑖subscript𝑄𝑗subscriptsuperscript𝐷𝑐𝑘12subscriptsuperscript𝜆′′𝑖𝑗𝑘subscriptsuperscript𝑈𝑐𝑖subscriptsuperscript𝐷𝑐𝑗subscriptsuperscript𝐷𝑐𝑘W_{\text{RPV}}=\sum_{i}\mu_{i}L_{i}H_{u}+\sum_{i,j,k}\left(\frac{1}{2}\lambda_%{ijk}L_{i}L_{j}E^{c}_{k}+\lambda^{\prime}_{ijk}L_{i}Q_{j}D^{c}_{k}+\frac{1}{2}%\lambda^{\prime\prime}_{ijk}U^{c}_{i}D^{c}_{j}D^{c}_{k}\right),italic_W start_POSTSUBSCRIPT RPV end_POSTSUBSCRIPT = ∑ start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT italic_μ start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT italic_L start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT italic_H start_POSTSUBSCRIPT italic_u end_POSTSUBSCRIPT + ∑ start_POSTSUBSCRIPT italic_i , italic_j , italic_k end_POSTSUBSCRIPT ( divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_λ start_POSTSUBSCRIPT italic_i italic_j italic_k end_POSTSUBSCRIPT italic_L start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT italic_L start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT italic_E start_POSTSUPERSCRIPT italic_c end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_k end_POSTSUBSCRIPT + italic_λ start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_i italic_j italic_k end_POSTSUBSCRIPT italic_L start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT italic_Q start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT italic_D start_POSTSUPERSCRIPT italic_c end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_k end_POSTSUBSCRIPT + divide start_ARG 1 end_ARG start_ARG 2 end_ARG italic_λ start_POSTSUPERSCRIPT ′ ′ end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_i italic_j italic_k end_POSTSUBSCRIPT italic_U start_POSTSUPERSCRIPT italic_c end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT italic_D start_POSTSUPERSCRIPT italic_c end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_j end_POSTSUBSCRIPT italic_D start_POSTSUPERSCRIPT italic_c end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_k end_POSTSUBSCRIPT ) ,(1)

where Qisubscript𝑄𝑖Q_{i}italic_Q start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT, Dicsuperscriptsubscript𝐷𝑖𝑐D_{i}^{c}italic_D start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_c end_POSTSUPERSCRIPT, Uicsuperscriptsubscript𝑈𝑖𝑐U_{i}^{c}italic_U start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_c end_POSTSUPERSCRIPT, and Lisubscript𝐿𝑖L_{i}italic_L start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT, Eicsuperscriptsubscript𝐸𝑖𝑐E_{i}^{c}italic_E start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_c end_POSTSUPERSCRIPT are chiral superfields and i,j,k=(1,2,3)𝑖𝑗𝑘123i,j,k=(1,2,3)italic_i , italic_j , italic_k = ( 1 , 2 , 3 ) are generation indices.The μisubscript𝜇𝑖\mu_{i}italic_μ start_POSTSUBSCRIPT italic_i end_POSTSUBSCRIPT, λi⁢j⁢ksubscript𝜆𝑖𝑗𝑘\lambda_{ijk}italic_λ start_POSTSUBSCRIPT italic_i italic_j italic_k end_POSTSUBSCRIPT, and λi⁢j⁢k′subscriptsuperscript𝜆′𝑖𝑗𝑘\lambda^{\prime}_{ijk}italic_λ start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_i italic_j italic_k end_POSTSUBSCRIPT couplings violate lepton number (L𝐿Litalic_L) while the λi⁢j⁢k′′subscriptsuperscript𝜆′′𝑖𝑗𝑘\lambda^{\prime\prime}_{ijk}italic_λ start_POSTSUPERSCRIPT ′ ′ end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_i italic_j italic_k end_POSTSUBSCRIPT couplings violate baryon number (B𝐵Bitalic_B).If all the RPV terms in Eq.(1) are present and unsuppressed, they would allow for a proton decay rate not compatible with current bounds on the proton lifetime111See Ref.Chamoun etal. (2021) for a recent study on constraints on RPV couplings from experimental and lattice results of nucleon decays..Therefore, we will consider the scenario where baryon-number-violating couplings (λi⁢j⁢k′′subscriptsuperscript𝜆′′𝑖𝑗𝑘\lambda^{\prime\prime}_{ijk}italic_λ start_POSTSUPERSCRIPT ′ ′ end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_i italic_j italic_k end_POSTSUBSCRIPT) are vanishing or negligible.This can be justified, e.g., by imposing a baryon triality B3subscript𝐵3B_{3}italic_B start_POSTSUBSCRIPT 3 end_POSTSUBSCRIPT discrete symmetryIbanez and Ross (1992); Dreineretal. (2012b).From the remaining L𝐿Litalic_L-violating terms in Eq.(1), the second trilinear term(L⁢Q⁢Dc𝐿𝑄superscript𝐷𝑐LQD^{c}italic_L italic_Q italic_D start_POSTSUPERSCRIPT italic_c end_POSTSUPERSCRIPT) allows for the superpartners to be singly produced at the LHC.In this work we will focus on the L⁢Q⁢Dc𝐿𝑄superscript𝐷𝑐LQD^{c}italic_L italic_Q italic_D start_POSTSUPERSCRIPT italic_c end_POSTSUPERSCRIPT term assuming all the other RPV couplings are zero. The Yukawa couplings generated by this operator are

LRPV=λi⁢j⁢k′(ν~i⁢Ld¯k⁢Rdj⁢L+d~j⁢Ld¯k⁢Rνi⁢L+d~k⁢R∗ν¯i⁢Rcdj⁢L−e~i⁢Ld¯k⁢Ruj⁢L\displaystyle L_{\text{RPV}}=\lambda^{\prime}_{ijk}\left(\tilde{\nu}_{iL}\bar{%d}_{kR}d_{jL}+\tilde{d}_{jL}\bar{d}_{kR}\nu_{iL}+\tilde{d}^{*}_{kR}\bar{\nu}^{%c}_{iR}d_{jL}-\tilde{e}_{iL}\bar{d}_{kR}u_{jL}\right.\ \ \ italic_L start_POSTSUBSCRIPT RPV end_POSTSUBSCRIPT = italic_λ start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_i italic_j italic_k end_POSTSUBSCRIPT ( over~ start_ARG italic_ν end_ARG start_POSTSUBSCRIPT italic_i italic_L end_POSTSUBSCRIPT over¯ start_ARG italic_d end_ARG start_POSTSUBSCRIPT italic_k italic_R end_POSTSUBSCRIPT italic_d start_POSTSUBSCRIPT italic_j italic_L end_POSTSUBSCRIPT + over~ start_ARG italic_d end_ARG start_POSTSUBSCRIPT italic_j italic_L end_POSTSUBSCRIPT over¯ start_ARG italic_d end_ARG start_POSTSUBSCRIPT italic_k italic_R end_POSTSUBSCRIPT italic_ν start_POSTSUBSCRIPT italic_i italic_L end_POSTSUBSCRIPT + over~ start_ARG italic_d end_ARG start_POSTSUPERSCRIPT ∗ end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_k italic_R end_POSTSUBSCRIPT over¯ start_ARG italic_ν end_ARG start_POSTSUPERSCRIPT italic_c end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_i italic_R end_POSTSUBSCRIPT italic_d start_POSTSUBSCRIPT italic_j italic_L end_POSTSUBSCRIPT - over~ start_ARG italic_e end_ARG start_POSTSUBSCRIPT italic_i italic_L end_POSTSUBSCRIPT over¯ start_ARG italic_d end_ARG start_POSTSUBSCRIPT italic_k italic_R end_POSTSUBSCRIPT italic_u start_POSTSUBSCRIPT italic_j italic_L end_POSTSUBSCRIPT
−u~j⁢Ld¯k⁢Rei⁢L−d~k⁢R∗e¯i⁢Rcuj⁢L)+h.c.\displaystyle\left.-\tilde{u}_{jL}\bar{d}_{kR}e_{iL}-\tilde{d}^{*}_{kR}\bar{e}%^{c}_{iR}u_{jL}\right)+h.c.- over~ start_ARG italic_u end_ARG start_POSTSUBSCRIPT italic_j italic_L end_POSTSUBSCRIPT over¯ start_ARG italic_d end_ARG start_POSTSUBSCRIPT italic_k italic_R end_POSTSUBSCRIPT italic_e start_POSTSUBSCRIPT italic_i italic_L end_POSTSUBSCRIPT - over~ start_ARG italic_d end_ARG start_POSTSUPERSCRIPT ∗ end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_k italic_R end_POSTSUBSCRIPT over¯ start_ARG italic_e end_ARG start_POSTSUPERSCRIPT italic_c end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_i italic_R end_POSTSUBSCRIPT italic_u start_POSTSUBSCRIPT italic_j italic_L end_POSTSUBSCRIPT ) + italic_h . italic_c .(2)

The fourth term in Eq.(2), which includes a charged slepton, allows for the neutralinos to be produced at the LHC together with a prompt charged lepton, as shown in Fig.1.

Searching for light neutralinos with a displaced vertex at the LHC (1)

As it will be explained in Sec.3, this prompt lepton will be used as a trigger in the proposed search.We consider χ~10superscriptsubscript~𝜒10\tilde{\chi}_{1}^{0}over~ start_ARG italic_χ end_ARG start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 0 end_POSTSUPERSCRIPT to be the lightest supersymmetric particle, so it can only decay through the RPV terms, with a total decay width proportional to the λi⁢j⁢k′superscriptsubscript𝜆𝑖𝑗𝑘′\lambda_{ijk}^{{}^{\prime}}italic_λ start_POSTSUBSCRIPT italic_i italic_j italic_k end_POSTSUBSCRIPT start_POSTSUPERSCRIPT start_FLOATSUPERSCRIPT ′ end_FLOATSUPERSCRIPT end_POSTSUPERSCRIPT couplings squared,

Γχ~10∝mχ~105⁢(λi⁢j⁢k′mf~2)2,proportional-tosubscriptΓsubscriptsuperscript~𝜒01superscriptsubscript𝑚subscriptsuperscript~𝜒015superscriptsuperscriptsubscript𝜆𝑖𝑗𝑘′superscriptsubscript𝑚~𝑓22\Gamma_{\tilde{\chi}^{0}_{1}}\propto m_{\tilde{\chi}^{0}_{1}}^{5}\left(\frac{%\lambda_{ijk}^{{}^{\prime}}}{m_{\tilde{f}}^{2}}\right)^{2},roman_Γ start_POSTSUBSCRIPT over~ start_ARG italic_χ end_ARG start_POSTSUPERSCRIPT 0 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT end_POSTSUBSCRIPT ∝ italic_m start_POSTSUBSCRIPT over~ start_ARG italic_χ end_ARG start_POSTSUPERSCRIPT 0 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 5 end_POSTSUPERSCRIPT ( divide start_ARG italic_λ start_POSTSUBSCRIPT italic_i italic_j italic_k end_POSTSUBSCRIPT start_POSTSUPERSCRIPT start_FLOATSUPERSCRIPT ′ end_FLOATSUPERSCRIPT end_POSTSUPERSCRIPT end_ARG start_ARG italic_m start_POSTSUBSCRIPT over~ start_ARG italic_f end_ARG end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT end_ARG ) start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT ,(3)

where mf~subscript𝑚~𝑓m_{\tilde{f}}italic_m start_POSTSUBSCRIPT over~ start_ARG italic_f end_ARG end_POSTSUBSCRIPT is the mass of the corresponding sfermion mediating the decay.Consequently, for small enough RPV couplings (and mχ~10subscript𝑚superscriptsubscript~𝜒10m_{\tilde{\chi}_{1}^{0}}italic_m start_POSTSUBSCRIPT over~ start_ARG italic_χ end_ARG start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 0 end_POSTSUPERSCRIPT end_POSTSUBSCRIPT) the neutralino will be long-lived.The decay products of this long-lived neutralino (shown in Fig.1) will be identified as displaced tracks from a common origin, i.e., a displaced vertex (DV).

From the 27 flavor combinations of the λi⁢j⁢k′subscriptsuperscript𝜆′𝑖𝑗𝑘\lambda^{\prime}_{ijk}italic_λ start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_i italic_j italic_k end_POSTSUBSCRIPT couplings, the strongest sensitivity at the LHC will be for λi⁢11′subscriptsuperscript𝜆′𝑖11\lambda^{\prime}_{i11}italic_λ start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_i 11 end_POSTSUBSCRIPT (i=1,2𝑖12i=1,2italic_i = 1 , 2) as a result of the proton parton distribution functions and higher reconstruction efficiencies for electrons and muons compared to tau leptons.For concreteness, in this work we analyze the sensitivity of the LHC to λ111′subscriptsuperscript𝜆′111\lambda^{\prime}_{111}italic_λ start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT start_POSTSUBSCRIPT 111 end_POSTSUBSCRIPT, but the search strategy described in this work is expected to give similar constraints for λ211′subscriptsuperscript𝜆′211\lambda^{\prime}_{211}italic_λ start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT start_POSTSUBSCRIPT 211 end_POSTSUBSCRIPT.For simplicity, all the superpartners different from χ~10superscriptsubscript~𝜒10\tilde{\chi}_{1}^{0}over~ start_ARG italic_χ end_ARG start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 0 end_POSTSUPERSCRIPT and me~Lsubscript𝑚subscript~𝑒𝐿m_{\tilde{e}_{L}}italic_m start_POSTSUBSCRIPT over~ start_ARG italic_e end_ARG start_POSTSUBSCRIPT italic_L end_POSTSUBSCRIPT end_POSTSUBSCRIPT are taken to be heavy (10 TeV), so that they are effectively decoupled.Although this mass hierarchy may be difficult to achieve in a realistic model, this is a phenomenological consideration chosen to define our benchmarks, so the phenomenology at the LHC can be controlled by the following three parameters only:

λ111′,me~L,mχ~10.subscriptsuperscript𝜆′111subscript𝑚subscript~𝑒𝐿subscript𝑚subscriptsuperscript~𝜒01\lambda^{\prime}_{111},m_{\tilde{e}_{L}},m_{\tilde{\chi}^{0}_{1}}.italic_λ start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT start_POSTSUBSCRIPT 111 end_POSTSUBSCRIPT , italic_m start_POSTSUBSCRIPT over~ start_ARG italic_e end_ARG start_POSTSUBSCRIPT italic_L end_POSTSUBSCRIPT end_POSTSUBSCRIPT , italic_m start_POSTSUBSCRIPT over~ start_ARG italic_χ end_ARG start_POSTSUPERSCRIPT 0 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT end_POSTSUBSCRIPT .(4)

In Sec.4 we will present our numerical results with four benchmark scenarios of the selectron mass, me~Lsubscript𝑚subscript~𝑒𝐿m_{\tilde{e}_{L}}italic_m start_POSTSUBSCRIPT over~ start_ARG italic_e end_ARG start_POSTSUBSCRIPT italic_L end_POSTSUBSCRIPT end_POSTSUBSCRIPT: 1⁢TeV1TeV1\mbox{ TeV}1 TeV, 2.5⁢TeV2.5TeV2.5\mbox{ TeV}2.5 TeV, 5⁢TeV5TeV5\mbox{ TeV}5 TeV, and 7⁢TeV7TeV7\mbox{ TeV}7 TeV, while varying the mass of the lightest neutralino (mχ~10subscript𝑚subscriptsuperscript~𝜒01m_{\tilde{\chi}^{0}_{1}}italic_m start_POSTSUBSCRIPT over~ start_ARG italic_χ end_ARG start_POSTSUPERSCRIPT 0 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT end_POSTSUBSCRIPT) and λ111′subscriptsuperscript𝜆′111\lambda^{\prime}_{111}italic_λ start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT start_POSTSUBSCRIPT 111 end_POSTSUBSCRIPT freely.

3 Simulation and event selection

Inspired by the ATLAS 13-TeV SUSY search for displaced verticesAaboud etal. (2018b), we focus on a search strategy that identifies the χ~10subscriptsuperscript~𝜒01\tilde{\chi}^{0}_{1}over~ start_ARG italic_χ end_ARG start_POSTSUPERSCRIPT 0 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT decay products inside the inner tracker as displaced tracks, which can come from the hadronized quarks or the displaced electron from the neutralino decay.

We use the RPV-MSSM UFO model file implemented in Ref.RPV (2019), with flavor diagonal mixing matrices for sfermions. We also set the lightest neutralino to be a pure bino in the model spectrum.We simulate the process p⁢p→χ~10⁢e→𝑝𝑝subscriptsuperscript~𝜒01𝑒pp\rightarrow\tilde{\chi}^{0}_{1}eitalic_p italic_p → over~ start_ARG italic_χ end_ARG start_POSTSUPERSCRIPT 0 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT italic_e in MadGraph 5Alwall etal. (2011) at s=13𝑠13\sqrt{s}=13square-root start_ARG italic_s end_ARG = 13 TeV, and generate parton-level LHE events with displaced information. The decay widths of the selectron and the lightest neutralino are automatically computed by MadGraph 5.Figure2 shows the production cross section of p⁢p→χ~10⁢e→𝑝𝑝subscriptsuperscript~𝜒01𝑒pp\to\tilde{\chi}^{0}_{1}eitalic_p italic_p → over~ start_ARG italic_χ end_ARG start_POSTSUPERSCRIPT 0 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT italic_e for different values of λ111′subscriptsuperscript𝜆′111\lambda^{\prime}_{111}italic_λ start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT start_POSTSUBSCRIPT 111 end_POSTSUBSCRIPT as a function of the selectron mass, for a fixed neutralino mass of 100 GeV.For other neutralino mass values below ∼250similar-toabsent250\sim 250∼ 250 GeV, there are no appreciable differences, so we take only one benchmark neutralino mass of 100 GeV here.We note that for Figure2 and the remaining simulation,we set the kinematic cuts of pT≥10subscript𝑝𝑇10p_{T}\geq 10italic_p start_POSTSUBSCRIPT italic_T end_POSTSUBSCRIPT ≥ 10 GeV and |η|>2.5𝜂2.5|\eta|>2.5| italic_η | > 2.5 for the outgoing electron or positron at the generation level.

Searching for light neutralinos with a displaced vertex at the LHC (2)

Events are further read within Pythia 8Sjöstrand etal. (2015) for showering and hadronization. We then perform a custom detector simulation within Pythia 8 for electrons, and displaced tracks and vertices. We start by selecting events triggering on a prompt, isolated electron with pT>25subscript𝑝𝑇25p_{T}>25italic_p start_POSTSUBSCRIPT italic_T end_POSTSUBSCRIPT > 25 GeV and with |η|<2.47𝜂2.47|\eta|<2.47| italic_η | < 2.47. Displaced vertices are then selected from tracks with a high transverse impact parameter, of |d0|>2subscript𝑑02|d_{0}|>2| italic_d start_POSTSUBSCRIPT 0 end_POSTSUBSCRIPT | > 2 mm and pT>1subscript𝑝𝑇1p_{T}>1italic_p start_POSTSUBSCRIPT italic_T end_POSTSUBSCRIPT > 1 GeV. Vertices are required to be within the inner tracker acceptance, with transverse decay positions rDVsubscript𝑟DVr_{\text{DV}}italic_r start_POSTSUBSCRIPT DV end_POSTSUBSCRIPT between 4 and 300 mm, as well as longitudinal distance |zDV|<300subscript𝑧DV300|z_{\text{DV}}|<300| italic_z start_POSTSUBSCRIPT DV end_POSTSUBSCRIPT | < 300 mm. Additionally, displaced vertices must have at least 5 tracks and have an invariant mass mDV≥10subscript𝑚DV10m_{\text{DV}}\geq 10italic_m start_POSTSUBSCRIPT DV end_POSTSUBSCRIPT ≥ 10 GeV (for which we assume all the tracks have the mass of the pion). These last two cuts define the region where signal is expected to be found free of Standard Model and instrumental background eventsAaboud etal. (2018b). In order to further characterize the detector response to displaced vertices within the above mentioned regions, we also make use of the parametrized vertex-level efficiencies provided by ATLAS in Ref.Aaboud etal. (2018b). A similar search for a long-lived right-handed neutrino in the context of a left-right symmetric model was performed in Refs.Cottin etal. (2019, 2018a).

Searching for light neutralinos with a displaced vertex at the LHC (3)

In figure 3 we show the overall selection efficiency of our DV strategy as a function of the neutralino mass, for three benchmark values of the slepton mass me~Lsubscript𝑚subscript~𝑒𝐿m_{\tilde{e}_{L}}italic_m start_POSTSUBSCRIPT over~ start_ARG italic_e end_ARG start_POSTSUBSCRIPT italic_L end_POSTSUBSCRIPT end_POSTSUBSCRIPT: 1, 2.5 and 5 TeV, and a fixed coupling, λ111′=10−2subscriptsuperscript𝜆′111superscript102\lambda^{\prime}_{111}=10^{-2}italic_λ start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT start_POSTSUBSCRIPT 111 end_POSTSUBSCRIPT = 10 start_POSTSUPERSCRIPT - 2 end_POSTSUPERSCRIPT.We observe that the larger is the slepton mass, the higher is the peak value in efficiency at a higher value of mχ~10subscript𝑚subscriptsuperscript~𝜒01m_{\tilde{\chi}^{0}_{1}}italic_m start_POSTSUBSCRIPT over~ start_ARG italic_χ end_ARG start_POSTSUPERSCRIPT 0 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT end_POSTSUBSCRIPT.The highest efficiency is achieved at values of the boosted decay length of the neutralino,

See Also
Dean’s List Students Named for Spring 2024

β⁢γ⁢c⁢τ=pmχ~10⁢ℏ⁢cΓχ~10,𝛽𝛾𝑐𝜏𝑝subscript𝑚subscriptsuperscript~𝜒01Planck-constant-over-2-pi𝑐subscriptΓsubscriptsuperscript~𝜒01\beta\gamma c\tau=\frac{p}{m_{\tilde{\chi}^{0}_{1}}}\frac{\hbar c}{\Gamma_{%\tilde{\chi}^{0}_{1}}},italic_β italic_γ italic_c italic_τ = divide start_ARG italic_p end_ARG start_ARG italic_m start_POSTSUBSCRIPT over~ start_ARG italic_χ end_ARG start_POSTSUPERSCRIPT 0 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT end_POSTSUBSCRIPT end_ARG divide start_ARG roman_ℏ italic_c end_ARG start_ARG roman_Γ start_POSTSUBSCRIPT over~ start_ARG italic_χ end_ARG start_POSTSUPERSCRIPT 0 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT end_POSTSUBSCRIPT end_ARG ,(5)

that lie within a certain optimal range (of order 𝒪𝒪\mathcal{O}caligraphic_O(cm)) corresponding to the ATLAS inner detector geometry and predict the largest decay probability inside the ATLAS fiducial volume.Here, p𝑝pitalic_p denotes the 3-momentum magnitude of the light neutralino.The neutralino boosted decay length is proportional to me~L4/mχ~106subscriptsuperscript𝑚4subscript~𝑒𝐿subscriptsuperscript𝑚6superscriptsubscript~𝜒10m^{4}_{\tilde{e}_{L}}/m^{6}_{\tilde{\chi}_{1}^{0}}italic_m start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT over~ start_ARG italic_e end_ARG start_POSTSUBSCRIPT italic_L end_POSTSUBSCRIPT end_POSTSUBSCRIPT / italic_m start_POSTSUPERSCRIPT 6 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT over~ start_ARG italic_χ end_ARG start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 0 end_POSTSUPERSCRIPT end_POSTSUBSCRIPT (see Eq.(3)).As a result, with λ111′subscriptsuperscript𝜆′111\lambda^{\prime}_{111}italic_λ start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT start_POSTSUBSCRIPT 111 end_POSTSUBSCRIPT fixed, the peak efficiency is obtained at a larger mχ~10subscript𝑚subscriptsuperscript~𝜒01m_{\tilde{\chi}^{0}_{1}}italic_m start_POSTSUBSCRIPT over~ start_ARG italic_χ end_ARG start_POSTSUPERSCRIPT 0 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT end_POSTSUBSCRIPT for a heavier slepton mass.Moreover, for heavier slepton and neutralino masses, the prompt electron tends to be harder, the displaced tracks have a larger transverse impact parameter as well as the transverse momentum, and the displaced vertices consist of a larger number of tracks and a heavier mDVsubscript𝑚DVm_{\text{DV}}italic_m start_POSTSUBSCRIPT DV end_POSTSUBSCRIPT; altogether these lead to a better overall efficiency at the peak.

This last feature of high mass displaced vertices with higher number of tracks can also be seen in figure 4, which shows the DV efficiency as a function of the neutralino proper decay length, for representative benchmarks with fixed slepton masses, me~Lsubscript𝑚subscript~𝑒𝐿m_{\tilde{e}_{L}}italic_m start_POSTSUBSCRIPT over~ start_ARG italic_e end_ARG start_POSTSUBSCRIPT italic_L end_POSTSUBSCRIPT end_POSTSUBSCRIPT: 1, 2.5 and 5 TeV, and fixed neutralino masses, mχ~10subscript𝑚subscriptsuperscript~𝜒01m_{\tilde{\chi}^{0}_{1}}italic_m start_POSTSUBSCRIPT over~ start_ARG italic_χ end_ARG start_POSTSUPERSCRIPT 0 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT end_POSTSUBSCRIPT: 50, 100 and 150 GeV. Independent of the value of me~Lsubscript𝑚subscript~𝑒𝐿m_{\tilde{e}_{L}}italic_m start_POSTSUBSCRIPT over~ start_ARG italic_e end_ARG start_POSTSUBSCRIPT italic_L end_POSTSUBSCRIPT end_POSTSUBSCRIPT, the larger the neutralino mass, the higher is the peak efficiency in lifetime.

Searching for light neutralinos with a displaced vertex at the LHC (4)

With the above DV search strategy, we can then estimate 95%percent9595\%95 % confidence level (C.L.) exclusion limits under the assumption of zero background, in the RPV coupling and neutralino mass planes in the following section.

4 Results

Searching for light neutralinos with a displaced vertex at the LHC (5)

We proceed to calculate the sensitivity to the trilinear RPV coupling λ111′subscriptsuperscript𝜆′111\lambda^{\prime}_{111}italic_λ start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT start_POSTSUBSCRIPT 111 end_POSTSUBSCRIPT with our DV search strategy for long-lived light neutralinos at the ATLAS inner tracker detector. For simplicity, we will assume that the λ111′subscriptsuperscript𝜆′111\lambda^{\prime}_{111}italic_λ start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT start_POSTSUBSCRIPT 111 end_POSTSUBSCRIPT coupling is the only nonzero RPV coupling, and that the masses of the squarks are heavy enough to be outside of LHC range, except for the selectron mass, me~Lsubscript𝑚subscript~𝑒𝐿m_{\tilde{e}_{L}}italic_m start_POSTSUBSCRIPT over~ start_ARG italic_e end_ARG start_POSTSUBSCRIPT italic_L end_POSTSUBSCRIPT end_POSTSUBSCRIPT.

In figure 5 we show the expected sensitivity for light neutralinos with our DV search strategy for a luminosity of 3000 fb-1. The 95%percent9595\%95 % C.L. exclusion limits are displayed in the λ111′subscriptsuperscript𝜆′111\lambda^{\prime}_{111}italic_λ start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT start_POSTSUBSCRIPT 111 end_POSTSUBSCRIPT vs.mχ~10subscript𝑚superscriptsubscript~𝜒10m_{\tilde{\chi}_{1}^{0}}italic_m start_POSTSUBSCRIPT over~ start_ARG italic_χ end_ARG start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 0 end_POSTSUPERSCRIPT end_POSTSUBSCRIPT plane for selectron masses me~L=(1,2.5,5,7)subscript𝑚subscript~𝑒𝐿12.557m_{\tilde{e}_{L}}=(1,2.5,5,7)italic_m start_POSTSUBSCRIPT over~ start_ARG italic_e end_ARG start_POSTSUBSCRIPT italic_L end_POSTSUBSCRIPT end_POSTSUBSCRIPT = ( 1 , 2.5 , 5 , 7 ) TeV. This is so as we are assuming a zero background search and requiring three signal events.

In all benchmarks, the sensitivity is mostly limited by neutralinos decaying far away beyond the trackers (towards the lower left of the colored contours) and neutralinos decaying too promptly (towards the upper right of the colored contours). The reach in the neutralino mass is lower for higher selectron masses, as it is limited by production cross-section. With this DV search at 3000 fb-1, we are able to exclude λ111′subscriptsuperscript𝜆′111\lambda^{\prime}_{111}italic_λ start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT start_POSTSUBSCRIPT 111 end_POSTSUBSCRIPT values as low as ∼10−4similar-toabsentsuperscript104\sim 10^{-4}∼ 10 start_POSTSUPERSCRIPT - 4 end_POSTSUPERSCRIPT for mχ~10∼230similar-tosubscript𝑚superscriptsubscript~𝜒10230m_{\tilde{\chi}_{1}^{0}}\sim 230italic_m start_POSTSUBSCRIPT over~ start_ARG italic_χ end_ARG start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 0 end_POSTSUPERSCRIPT end_POSTSUBSCRIPT ∼ 230 GeV, and me~L=1subscript𝑚subscript~𝑒𝐿1m_{\tilde{e}_{L}}=1italic_m start_POSTSUBSCRIPT over~ start_ARG italic_e end_ARG start_POSTSUBSCRIPT italic_L end_POSTSUBSCRIPT end_POSTSUBSCRIPT = 1 TeV.

Figure 5 also compares our limits with current constraints from neutrinoless double beta decay searches at GERDA Agostini etal. (2020) and monolepton searches at ATLASAaboud etal. (2018a) with 36.1⁢fb−136.1superscriptfb136.1\,\mbox{fb}^{-1}36.1 fb start_POSTSUPERSCRIPT - 1 end_POSTSUPERSCRIPT of integrated luminosity. The neutrinoless double beta decay limits were obtained by comparing the theoretical calculations from Ref.Bolton etal. (2021) of the RPV SUSY contribution to 0⁢ν⁢β⁢β0𝜈𝛽𝛽0\nu\beta\beta0 italic_ν italic_β italic_β half-life, mediated by light neutralinos and selectrons222Figure 3 in Ref. Bolton etal. (2021) shows the calculation of the contribution of light neutralinos and selectrons to the 0⁢ν⁢β⁢β0𝜈𝛽𝛽0\nu\beta\beta0 italic_ν italic_β italic_β half-life for λ111′=10−3subscriptsuperscript𝜆′111superscript103\lambda^{\prime}_{111}=10^{-3}italic_λ start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT start_POSTSUBSCRIPT 111 end_POSTSUBSCRIPT = 10 start_POSTSUPERSCRIPT - 3 end_POSTSUPERSCRIPT and me~Lsubscript𝑚subscript~𝑒𝐿m_{{\tilde{e}}_{L}}italic_m start_POSTSUBSCRIPT over~ start_ARG italic_e end_ARG start_POSTSUBSCRIPT italic_L end_POSTSUBSCRIPT end_POSTSUBSCRIPT = 2 TeV (green dashed line). We have re-scaled these results for different values of λ111′subscriptsuperscript𝜆′111\lambda^{\prime}_{111}italic_λ start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT start_POSTSUBSCRIPT 111 end_POSTSUBSCRIPT and me~Lsubscript𝑚subscript~𝑒𝐿m_{\tilde{e}_{L}}italic_m start_POSTSUBSCRIPT over~ start_ARG italic_e end_ARG start_POSTSUBSCRIPT italic_L end_POSTSUBSCRIPT end_POSTSUBSCRIPT using the proportionality relation (T1/20⁢ν⁢β⁢β)−1∝|λ1112′/me~L4|2(T_{1/2}^{0\nu\beta\beta})^{-1}\propto|\lambda_{111}^{{}^{\prime}2}/{m_{\tilde%{e}_{L}}^{4}}|^{2}( italic_T start_POSTSUBSCRIPT 1 / 2 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 0 italic_ν italic_β italic_β end_POSTSUPERSCRIPT ) start_POSTSUPERSCRIPT - 1 end_POSTSUPERSCRIPT ∝ | italic_λ start_POSTSUBSCRIPT 111 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT start_FLOATSUPERSCRIPT ′ end_FLOATSUPERSCRIPT 2 end_POSTSUPERSCRIPT / italic_m start_POSTSUBSCRIPT over~ start_ARG italic_e end_ARG start_POSTSUBSCRIPT italic_L end_POSTSUBSCRIPT end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 4 end_POSTSUPERSCRIPT | start_POSTSUPERSCRIPT 2 end_POSTSUPERSCRIPT (see equation (4.5) in Ref. Bolton etal. (2021)). (see figure1 and rotate it by 90 degrees clockwise to visualize the Feynman diagram contributing to 0⁢ν⁢β⁢β0𝜈𝛽𝛽0\nu\beta\beta0 italic_ν italic_β italic_β decay) with the experimental current limits on the 0⁢ν⁢β⁢β0𝜈𝛽𝛽0\nu\beta\beta0 italic_ν italic_β italic_β half-life T1/2e⁢x⁢p>1.8×1026superscriptsubscript𝑇12𝑒𝑥𝑝1.8superscript1026T_{1/2}^{exp}>1.8\times 10^{26}italic_T start_POSTSUBSCRIPT 1 / 2 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT italic_e italic_x italic_p end_POSTSUPERSCRIPT > 1.8 × 10 start_POSTSUPERSCRIPT 26 end_POSTSUPERSCRIPTyr for the isotope 76Ge.

On the other hand, the monolepton limits are based on our reinterpretation of the ATLAS search described in AppendixA, which corresponds to the red solid curve in figure5. We obtain the limits by extracting a contour on the significance at 36.1⁢fb−136.1superscriptfb136.1\,\mbox{fb}^{-1}36.1 fb start_POSTSUPERSCRIPT - 1 end_POSTSUPERSCRIPT, i.e. Z36≡S/Bsubscript𝑍36𝑆𝐵Z_{36}\equiv S/\sqrt{B}italic_Z start_POSTSUBSCRIPT 36 end_POSTSUBSCRIPT ≡ italic_S / square-root start_ARG italic_B end_ARG, with S𝑆Sitalic_S the number of signal events after the monolopton cuts and B𝐵Bitalic_B the number of background events taken from the ATLAS search, at Z36=2subscript𝑍362Z_{36}=2italic_Z start_POSTSUBSCRIPT 36 end_POSTSUBSCRIPT = 2. The dashed red curve in figure5 is our projected limit for the same monolepton search but for a luminosity of 3000 fb-1. The contour is again obtained at Z3000=2subscript𝑍30002Z_{3000}=2italic_Z start_POSTSUBSCRIPT 3000 end_POSTSUBSCRIPT = 2 after re-scaling with Z3000≡3000/36.1⋅Z36subscript𝑍3000⋅300036.1subscript𝑍36Z_{3000}\equiv\sqrt{3000/36.1}\cdot Z_{36}italic_Z start_POSTSUBSCRIPT 3000 end_POSTSUBSCRIPT ≡ square-root start_ARG 3000 / 36.1 end_ARG ⋅ italic_Z start_POSTSUBSCRIPT 36 end_POSTSUBSCRIPT.

For higher selectron mass, the monolepton limits become less stringent, owing to the smaller production cross-sections. We also note a transition in the monolepton search sensitivity happening as the mass of the neutralino increases and ceases to be long-lived, see figure5. This is understood as follows. Monolepton searches are efficient, provided the electron pTsubscript𝑝𝑇p_{T}italic_p start_POSTSUBSCRIPT italic_T end_POSTSUBSCRIPT and the missing transverse momenta are high enough for the events to pass the cut on transverse mass (see AppendixA). When the mass of the neutralino is small enough for it to decay outside the detector, all of its momentum contributes to missing transverse momenta (as opposed to only a fraction when it has visible decay products inside the detector). As a result, missing transverse momenta is high enough for the event selections to be efficient when the neutralino is long-lived. For a more prompt neutralino, the monolepton signal efficiencies decrease, remaining constant for a large part of the neutralino masses thanks to the contributions to the missing transverse momenta coming from prompt activity.

5 Conclusions

In recent years, increasingly more searches for long-lived particles have been proposed and performed at the LHC and other experiments.In R-parity-violating supersymmetry (RPV-SUSY), the lightest neutralino is allowed to be light with mass in the GeV scale, as long as it decays via RPV couplings.Such a light neutralino also must be dominantly bino-like.If both the mass and the non-vanishing RPV couplings are small, the lightest neutralino is naturally long-lived.

In this work, we have proposed a search strategy based on an existing ATLAS 13-TeV SUSY search, and performed Monte-Carlo simulations to estimate the sensitivities at the high-luminosity LHC (HL-LHC) to such a light neutralino with a single RPV coupling switched on, λ111′subscriptsuperscript𝜆′111\lambda^{\prime}_{111}italic_λ start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT start_POSTSUBSCRIPT 111 end_POSTSUBSCRIPT.We consider on-shell production of an selectron from p⁢p𝑝𝑝ppitalic_p italic_p collisions via λ111′subscriptsuperscript𝜆′111\lambda^{\prime}_{111}italic_λ start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT start_POSTSUBSCRIPT 111 end_POSTSUBSCRIPT which then decays promptly into an electron and the lightest neutralino.The lightest neutralino travels a macroscopic distance before decaying into an electron and two quarks via the same RPV coupling and an off-shell selectron.Thus, this theoretical scenario comes with only three free parameters: the RPV coupling λ111′subscriptsuperscript𝜆′111\lambda^{\prime}_{111}italic_λ start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT start_POSTSUBSCRIPT 111 end_POSTSUBSCRIPT, the neutralino mass mχ~10subscript𝑚superscriptsubscript~𝜒10m_{\tilde{\chi}_{1}^{0}}italic_m start_POSTSUBSCRIPT over~ start_ARG italic_χ end_ARG start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 0 end_POSTSUPERSCRIPT end_POSTSUBSCRIPT, and the selectron mass me~subscript𝑚~𝑒m_{\tilde{e}}italic_m start_POSTSUBSCRIPT over~ start_ARG italic_e end_ARG end_POSTSUBSCRIPT.

For numerical results, we present plots of search efficiencies as functions of either the neutralino mass or its proper decay length, c⁢τ𝑐𝜏c\tauitalic_c italic_τ, as well as plots of final sensitivities in the plane λ111′subscriptsuperscript𝜆′111\lambda^{\prime}_{111}italic_λ start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT start_POSTSUBSCRIPT 111 end_POSTSUBSCRIPT vs.mχ~10subscript𝑚superscriptsubscript~𝜒10m_{\tilde{\chi}_{1}^{0}}italic_m start_POSTSUBSCRIPT over~ start_ARG italic_χ end_ARG start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT start_POSTSUPERSCRIPT 0 end_POSTSUPERSCRIPT end_POSTSUBSCRIPT for four benchmark selectron masses, me~Lsubscript𝑚subscript~𝑒𝐿m_{\tilde{e}_{L}}italic_m start_POSTSUBSCRIPT over~ start_ARG italic_e end_ARG start_POSTSUBSCRIPT italic_L end_POSTSUBSCRIPT end_POSTSUBSCRIPT: 1, 2.5, 5, and 7 TeV.Our final results show that for 1 TeV selectron mass, the proposed search at the HL-LHC can probe values of λ111′subscriptsuperscript𝜆′111\lambda^{\prime}_{111}italic_λ start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT start_POSTSUBSCRIPT 111 end_POSTSUBSCRIPT up to two orders of magnitudesmaller than current bounds from neutrinoless double beta decay experiments, as well as up to 40 times smaller than our recast of an LHC monolepton search with an integrated luminosity of 36.1 fb-1, projected to the final HL-LHC target, 3000 fb-1, for neutralino masses between 10 GeV and 230 GeV.However, for a heavy selectron of mass 7 TeV, our sensitivities are rather limited, and at most comparable with the bounds from neutrinoless double beta decay at mχ~10∼50similar-tosubscript𝑚subscriptsuperscript~𝜒0150m_{\tilde{\chi}^{0}_{1}}\sim 50italic_m start_POSTSUBSCRIPT over~ start_ARG italic_χ end_ARG start_POSTSUPERSCRIPT 0 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT end_POSTSUBSCRIPT ∼ 50 GeV.

We further note that while we have focused on the single coupling λ111′subscriptsuperscript𝜆′111\lambda^{\prime}_{111}italic_λ start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT start_POSTSUBSCRIPT 111 end_POSTSUBSCRIPT, our results are almost equally applicable to the same scenario but with another RPV coupling, λ211′subscriptsuperscript𝜆′211\lambda^{\prime}_{211}italic_λ start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT start_POSTSUBSCRIPT 211 end_POSTSUBSCRIPT, as at the LHC, we expect prompt muon efficiencies to be similar from that of electrons. For the case of a single coupling λ211′subscriptsuperscript𝜆′211\lambda^{\prime}_{211}italic_λ start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT start_POSTSUBSCRIPT 211 end_POSTSUBSCRIPT the limits from neutrinoless double beta decay do not apply.

Acknowledgements.

We thank Benjamin f*cks and Torbjörn Sjöstrand for useful discussions on the UFO implementation and Pythia 8, respectively.G.C. acknowledges support from ANID FONDECYT grant No. 11220237.G.C., J.C.H. and F.H.P. also acknowledge support from grants ANID FONDECYT No. 1201673 and ANID – Millennium Science Initiative Program ICN2019_044. J.C.H. acknowledges the financial support of DIDULS/ULS, through the project PTE202135.Z.S.W. is supported by the Ministry of Science and Technology (MoST) of Taiwan with grant number MoST-110-2811-M-007-542-MY3.N.A.N. was supported by ANID (Chile) under the grant ANID REC Convocatoria Nacional Subvención a Instalación en la Academia Convocatoria Año 2020, PAI77200092.We thank Wei Liu for pointing out an error in Figure2 in the previous version of the article.

Appendix A Reinterpretation of monolepton search

The ATLAS collaboration has presented a search for a monolepton signal based on ℒ=36.1ℒ36.1\mathcal{L}=36.1caligraphic_L = 36.1 fb-1 of statistics taken at s=13𝑠13\sqrt{s}=13square-root start_ARG italic_s end_ARG = 13 TeVAaboud etal. (2018a). We reinterpretthis existing prompt search for a new W′superscript𝑊′W^{\prime}italic_W start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT gauge boson decaying to an electron and a neutrino, W′→e⁢ν→superscript𝑊′𝑒𝜈W^{\prime}\rightarrow e\nuitalic_W start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT → italic_e italic_ν, in the context of our RPVsignal, e~→e⁢χ~10→~𝑒𝑒subscriptsuperscript~𝜒01\tilde{e}\rightarrow e\tilde{\chi}^{0}_{1}over~ start_ARG italic_e end_ARG → italic_e over~ start_ARG italic_χ end_ARG start_POSTSUPERSCRIPT 0 end_POSTSUPERSCRIPT start_POSTSUBSCRIPT 1 end_POSTSUBSCRIPT.

For our recast, we first validated the W′superscript𝑊′W^{\prime}italic_W start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT Sequential Standard Model (SSM) signal modelAltarelli etal. (1989). The simulation for the W′superscript𝑊′W^{\prime}italic_W start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT signal was done with Pythia 8Sjöstrand etal. (2015) for both production and decay. We performed a custom detector simulation where electrons are reconstructed as an isolated prompt object within |η|<2.47𝜂2.47|\eta|<2.47| italic_η | < 2.47 with smeared momenta (idem as in Ref.Cottin etal. (2018b)). Missing transverse momenta, pTm⁢i⁢s⁢ssubscriptsuperscript𝑝𝑚𝑖𝑠𝑠𝑇p^{miss}_{T}italic_p start_POSTSUPERSCRIPT italic_m italic_i italic_s italic_s end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_T end_POSTSUBSCRIPT, is reconstructed from all visible physics objects (following Ref.Allanach etal. (2016), with a standard reconstruction that includes a vector sum of the pTsubscript𝑝𝑇p_{T}italic_p start_POSTSUBSCRIPT italic_T end_POSTSUBSCRIPT of jets, leptons and unclustered deposits of energy not associated to leptons and jets). Everything decaying outside the inner detector is considered stable. We consider a cylinder with inner detector dimensions radius r=1100𝑟1100r=1100italic_r = 1100 mm and length |z|=2800𝑧2800|z|=2800| italic_z | = 2800 mm, as in Ref.Allanach etal. (2016). The following cuts are applied:

  • •

    One electron with pT>120subscript𝑝𝑇120p_{T}>120italic_p start_POSTSUBSCRIPT italic_T end_POSTSUBSCRIPT > 120 GeV and transverse energy ET>4.5subscript𝐸𝑇4.5E_{T}>4.5italic_E start_POSTSUBSCRIPT italic_T end_POSTSUBSCRIPT > 4.5 GeV

  • •

    Missing transverse momenta pTm⁢i⁢s⁢s>65subscriptsuperscript𝑝𝑚𝑖𝑠𝑠𝑇65p^{miss}_{T}>65italic_p start_POSTSUPERSCRIPT italic_m italic_i italic_s italic_s end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_T end_POSTSUBSCRIPT > 65 GeV

  • •

    Transverse mass mT=2⁢pT⋅pTm⁢i⁢s⁢s⁢(1−cos⁡Δ⁢ϕ)>130subscript𝑚𝑇⋅2subscript𝑝𝑇subscriptsuperscript𝑝𝑚𝑖𝑠𝑠𝑇1Δitalic-ϕ130m_{T}=\sqrt{2p_{T}\cdot p^{miss}_{T}(1-\cos{\Delta\phi})}>130italic_m start_POSTSUBSCRIPT italic_T end_POSTSUBSCRIPT = square-root start_ARG 2 italic_p start_POSTSUBSCRIPT italic_T end_POSTSUBSCRIPT ⋅ italic_p start_POSTSUPERSCRIPT italic_m italic_i italic_s italic_s end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_T end_POSTSUBSCRIPT ( 1 - roman_cos roman_Δ italic_ϕ ) end_ARG > 130 GeV. Here pTsubscript𝑝𝑇p_{T}italic_p start_POSTSUBSCRIPT italic_T end_POSTSUBSCRIPT corresponds to the transverse momentum of the electron, pTm⁢i⁢s⁢ssubscriptsuperscript𝑝𝑚𝑖𝑠𝑠𝑇p^{miss}_{T}italic_p start_POSTSUPERSCRIPT italic_m italic_i italic_s italic_s end_POSTSUPERSCRIPT start_POSTSUBSCRIPT italic_T end_POSTSUBSCRIPT is the missing transverse momenta, and Δ⁢ϕΔitalic-ϕ\Delta\phiroman_Δ italic_ϕ is the azimuthal angle between these vectors.

A plot of the overall signal efficiency after all cuts as a function of W′superscript𝑊′W^{\prime}italic_W start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT mass is shown in the left frame of figure6, compared with the ATLAS auxiliary figure 6 from HepData. We also validate Table 1 of the ATLAS paperAaboud etal. (2018a), and extract the number of expected events from mTsubscript𝑚𝑇m_{T}italic_m start_POSTSUBSCRIPT italic_T end_POSTSUBSCRIPT distributions, which we generate for each mW′subscript𝑚superscript𝑊′m_{W^{\prime}}italic_m start_POSTSUBSCRIPT italic_W start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT end_POSTSUBSCRIPT mass point. These mTsubscript𝑚𝑇m_{T}italic_m start_POSTSUBSCRIPT italic_T end_POSTSUBSCRIPT distributions are given after all cuts in the ATLAS paper, so we reproduce these histograms in order to extract event level efficiencies. We calculate the signal efficiency (for a given mass benchmark) after integrating over the mTsubscript𝑚𝑇m_{T}italic_m start_POSTSUBSCRIPT italic_T end_POSTSUBSCRIPT bins defined by ATLAS. An example benchmark for mW′=2subscript𝑚superscript𝑊′2m_{W^{\prime}}=2italic_m start_POSTSUBSCRIPT italic_W start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT end_POSTSUBSCRIPT = 2 TeV is shown in the right frame of figure6. In general, most bins match within 30%percent3030\%30 %. The biggest discrepancy is found to be for the first mTsubscript𝑚𝑇m_{T}italic_m start_POSTSUBSCRIPT italic_T end_POSTSUBSCRIPT bin of [130-200] GeV for the mW′=4subscript𝑚superscript𝑊′4m_{W^{\prime}}=4italic_m start_POSTSUBSCRIPT italic_W start_POSTSUPERSCRIPT ′ end_POSTSUPERSCRIPT end_POSTSUBSCRIPT = 4 TeV benchmark, which reaches 55%percent5555\%55 %.

Searching for light neutralinos with a displaced vertex at the LHC (6)

Searching for light neutralinos with a displaced vertex at the LHC (7)

We implement the same above mentioned strategy to our RPV signal. As for calculating the monolepton exclusion in figure5, we take the background numbers directly from the ATLAS paperAaboud etal. (2018a), which are provided in HepData in bins of mTsubscript𝑚𝑇m_{T}italic_m start_POSTSUBSCRIPT italic_T end_POSTSUBSCRIPT. We note that monolepton searches have been reinterpreted in a similar way (but without considering detector effects) in Ref.Nemevšek etal. (2018) in the context of right-handed WRsubscript𝑊𝑅W_{R}italic_W start_POSTSUBSCRIPT italic_R end_POSTSUBSCRIPT bosons and heavy neutrinos.

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Searching for light neutralinos with a displaced vertex at the LHC (2024)

References

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