Semi-Visible Emerging Jets (SVEJ)

• SVEJ are collider signatures from confining hidden sectors where dark meson decays produce mixed visible and invisible jet constituents.
• They interpolate between prompt semi-visible jets and ultralong-lived emerging jets, with decay lengths of O(1–10) mm enabling clear displaced vertex detection.
• Search strategies leverage dedicated triggers and multi-vertex reconstruction to achieve sub-fb cross-section sensitivity in probing dark-sector models.

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 (Carrasco et al., 4 Nov 2025).

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: $1<r_{\rm DV}<300$ mm, $|z_{\rm DV}|<300$ mm; $>1$ 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 (Carrasco et al., 4 Nov 2025).