--- title: Semi-Visible Emerging Jets (SVEJ) url: https://www.emergentmind.com/topics/semi-visible-emerging-jets-svej type: topic --- # Semi-Visible Emerging Jets (SVEJ) Semi-visible emerging jets (SVEJ) are collider signatures arising in extensions of the Standard Model containing confining hidden sectors or Hidden Valley (HV) models coupled to the Standard Model via an $s$-channel mediator. In this scenario, dark sector hadronization produces a mixture of stable (collider-invisible) and long-lived but ultimately decaying (emerging) dark mesons within the same jet. By varying the proper lifetime $c\tau$ of the unstable dark bound states (“dark pions”), SVEJ interpolate continuously between the well-established regimes of semi-visible jets (prompt decays) and emerging jets (ultralong-lived decays). The SVEJ signature is characterized by multiple soft displaced vertices within a single jet cone, moderate missing transverse momentum, and a nontrivial fraction of the jet’s constituents arising from displaced decays inside the tracker. SVEJ provide experimental access to the $\mathcal{O}(1$–$10)$ mm proper lifetime regime, connecting and extending existing LHC searches for hidden-sector dark showers [2511.02918]. ## 1. Theoretical Framework and Model Structure The benchmark SVEJ scenario consists of a confining dark sector described by an $\mathrm{SU}(N_C)$ gauge theory with $N_F$ degenerate dark quark flavors $q_D$, each a Standard Model (SM) singlet. The only renormalizable portal to the SM is via an $s$-channel vector boson mediator (“dark $Z'$”), of mass $m_{Z'}$, with vector and axial couplings to both SM (light) quarks and dark quarks: \[ \mathcal{L} \supset \kappa_D\,Z'_\mu \left[ \bar q \gamma^\mu (\mathcal Q_V^{\rm SM} + \mathcal Q_A^{\rm SM} \gamma_5) q + \bar q_D \gamma^\mu (\mathcal Q_V^D + \mathcal Q_A^D \gamma_5) q_D \right] \] Below the dark confinement scale $\Lambda_D$, hadronization yields dark mesons: pseudo–Nambu–Goldstone bosons (dark pions, $\pi$) with $m_\pi \sim \mathcal{O}(\Lambda_D)$ and heavier vector resonances ($\rho$) with $m_\rho \gtrsim 2 m_\pi$. The decay phenomenology of these mesons is set by dark-sector flavor symmetries: flavor-diagonal pions can decay to SM $u\bar u$, $d\bar d$ pairs through $Z'$ exchange, while off-diagonal pions are (approximately) stable due to dark-flavor symmetry, yielding nontrivial missing energy. The $q_D\bar q_D$ pairs initiated in $pp\to Z'\to q_D\bar q_D$ undergo dark-sector showering and hadronization, producing $\mathcal{O}(10)$ dark pions per jet, with a visible (unstable) fraction $f_{\rm vis}$. ## 2. Phenomenological Definition and Signal Regimes SVEJ are defined as the intermediate regime where both stable and long-lived but unstable dark pions emerge inside a jet: - For $c\tau \ll 1$ mm, all dark pions decay promptly to SM hadrons, and the resulting jets are “semi-visible,” with moderate missing transverse momentum from stable pions. - For $c\tau \gg 1$ m, no decays occur inside the tracker; jets appear as emerging jets, or as missing transverse energy with only initial-state radiation. - For $c\tau \sim \mathcal{O}(1$–$10)$ mm, the SVEJ regime, a stochastic fraction of the unstable (diagonal) dark pions decay inside the tracker, leading to multiple spatially separated soft displaced vertices, while off-diagonal (stable) pions contribute to missing transverse momentum. By tuning $c\tau$, one interpolates smoothly between the two main regimes. The dark-pion decay length distribution in the laboratory frame is governed by: \[ L_{xy} = \beta_T \gamma\, c\tau \qquad \beta_T \gamma = \frac{p_T^\pi}{m_\pi} \] \[ \frac{dN}{dL_{xy}} \propto \exp\left[ -\frac{L_{xy}}{\beta_T\gamma\,c\tau} \right] \] SVEJ signatures are thus optimally probed when $c\tau \sim \mathcal{O}(1$–$10)$ mm, as the tracker geometry and acceptance favor displaced decays within the fiducial region. ## 3. Key Experimental Discriminants The identification of SVEJ relies on observables combining missing energy, jet structure, and displaced vertex information: - **Missing transverse momentum** ($E_T^{\rm miss}$): Arises from stable (invisible) dark pions. - **Jet $p_T$ sum ($H_T$)**: Scalar sum of jet momenta; provides overall event hardness. - **Prompt-track fraction (PTF)** in “fat jets”: Defined as $\sum_{i:\,|d_0|/\sigma_{d_0}<2.5} p_{T_i} / p_T^{\rm jet}$. Lower for jets with large emerging (displaced) components. - **Displaced-vertex (DV) observables**: - Number of vertices ($N_{\rm DV}$) per jet - Tracks per DV ($N_{\rm trk}$) - Invariant mass of the DV ($m_{\rm DV}$) - Angular opening of DV tracks ($\Delta R$) - Intervertex distance ($d_{vv}$) Optimal selection requires reconstructing multiple (≥3) displaced vertices within a large-$R$ jet, each with significant track multiplicity, sizable invariant mass, and substantial displacement from the interaction point. ## 4. Analysis and Search Strategy The SVEJ analysis strategy is designed to exploit maximal sensitivity to lifetimes $c\tau\sim\mathcal{O}(10)$ mm: ### (a) Trigger Selection Comparison of standard high-$E_T^{\rm miss}$ (MET), $H_T$, displaced-jet (DJ), and the dedicated ATLAS emerging-jet (EJ) triggers reveals the EJ trigger as optimal. For $m_{Z'}=2$ TeV, $\Lambda_D=8$–$50$ GeV, $c\tau=10$ mm: - $\epsilon_{\rm EJ} \simeq 0.55$–$0.61$ (trigger+preselection) - $\epsilon_{\rm MET} \sim 0.3$ - $\epsilon_{\rm DJ} \sim 0.1$–$0.4$ The EJ trigger requires a large-$R$ jet ($p_T>200$ GeV, $|\eta|<1.8$) with PTF$<0.08$. ### (b) Selection Cuts After trigger, events must contain $\geq3$ DVs satisfying: - $N_{\rm trk} \geq 3$ with $p_T>1$ GeV, $|\eta|<2.5$, $|d_0|>0.1$ mm - Vertex: $11$ mm from pixel layers - At least one track in each DV with $|d_0|>3$ mm - $m_{\rm DV}/\Delta R > 4$ GeV - $\sum p_T^{\rm DV} > 10$ GeV - $d_{vv} > 1.5$ mm between DVs Cumulative signal selection efficiency is $\epsilon_{\rm sel}\sim 0.27$–$0.36$ for $c\tau=10$ mm. ### (c) Reinterpretation with LLP Searches For longer lifetimes ($c\tau \sim 100$–$1000$ mm), existing LHC LLP searches are recast: - **ATLAS CalRatio**: Electromagnetic-to-hadronic energy ratios in the calorimeter; effective for decays in the HCAL ($c\tau\sim 100$ mm). - **CMS Muon-Displaced Shower**: Searches for hadronic showers in the muon endcap ($c\tau\sim 500$–$1000$ mm). ## 5. Sensitivity, Reach, and Experimental Limits Projected 95% C.L. upper limits for $pp\to Z'\to q_D\bar q_D$ depend sensitively on $c\tau$: | Analysis | Best sensitivity at $c\tau$ | $\sigma_{95\%}$ reach (for $m_{Z'}=2$ TeV) | |------------------|-----------------------------|---------------------------------------------| | SVEJ (proposed) | 10 mm | $\sim 0.1$ fb | | CalRatio | 100 mm | $1$–$10$ fb | | Muon-shower | 500 mm | intermediate | SVEJ searches are maximally sensitive at $c\tau\sim10$ mm ($\sigma_{95\%}\sim 0.1$ fb), with weaker reach for $c\tau \ll 1$ mm (prompt jets) and $c\tau \gg 100$ mm (decays outside tracker). In the $(\Lambda_D, m_\pi/\Lambda_D)$ plane for fixed $c\tau=10$ mm, SVEJ is sensitive down to sub-fb cross sections for $\Lambda_D \lesssim 20$ GeV, improving for higher $m_{Z'}$. ## 6. Systematic Uncertainties and Model Dependence The dominant systematic uncertainties impacting SVEJ search sensitivity include: - **Hadronization modeling**: Varying $\Lambda_D$ by a factor of three (at fixed $m_\pi, m_\rho$) can shift individual cut efficiencies by up to 20%, especially for $|d_0|>3$ mm and $m_{\rm DV}/\Delta R$. - **Detector-level effects**: Track impact-parameter and vertex-resolution, trigger turn-on behavior, and material vetoes introduce nontrivial uncertainties requiring full Geant4-based detector simulation and realistic reconstruction. - **Background estimation**: Fake displaced vertices from random track crossings, nuclear interactions, beam-halo, and cosmic rays must be estimated using data-driven control regions such as low $N_{\rm trk}$ vertices or $m_{\rm DV}/\Delta R$ sidebands. A *comprehensive tune* comparing different Hidden-Valley MC modules (e.g., Pythia 8, Herwig 7) is recommended for precision efficiency modeling. ## 7. Implications, Outlook, and Future Directions SVEJ searches demonstrably extend the LHC long-lived particle (LLP) search program to the $c\tau\sim\mathcal{O}(1$–$10)$ mm regime, a region not well covered by standard displaced-vertex or MET-based triggers. The SVEJ category provides a continuous experimental and phenomenological bridge between semi-visible and emerging jet signatures, probing theoretically motivated dark sectors with moderate lifetime and sub-fb cross section reach. Realizing the full potential of SVEJ searches requires: - Full experimental analyses with realistic detector simulation and control-region-based background constraints. - Dedicated triggering strategies (e.g., lowering PTF thresholds) to maximize efficiency for jets with soft displaced decays. - Detailed studies of hadronization and detector performance to control systematic uncertainties to the percent level. - Reinterpretation of existing and forthcoming displaced-jet and dark-shower analyses in the context of mixed stable/unstable dark meson ensembles. As experimental coverage of SVEJ parameter space expands, these searches will play a central role in constraining or discovering new confining dark sectors with nontrivial lifetime structure [2511.02918]. Source: https://www.emergentmind.com/topics/semi-visible-emerging-jets-svej