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A schematic depiction of pair production of dark quarks forming two emerging jets. Shown is an $x-y$ cross section of a detector with the beam pipe going into the page. The approximate radii of the tracker and calorimeter are also shown. The dark mesons are represented by dashed lines because they do not interact with the detector. After traveling some distance, each individual dark pion decays into Standard Model particles, creating a small jet represented by solid colored lines. Because of the exponential decay, each set of SM particles originates a different distance from the interaction point, so the jet slowly emerges into the detector.

Graphical representation of the dark QCD model. Baryon and dark matter asymmetries are shared via a mediator $X_d$ resulting in an asymmetry in the stable dark baryons $p_d$, $n_d$. The symmetric relic density is annihilated efficiently into dark pions, which eventually decay into SM particles. The DM number density is naturally of the same order as that of baryons, so the correct DM relic density is obtained when the dark baryon masses are in the 10~GeV range.\\

Left: Feynman diagrams for the pair production of $X_d$ at hadron colliders. Right: Tree level cross section for $X_d$ pair production at the LHC.

Left: Feynman diagrams for the pair production of $X_d$ at hadron colliders. Right: Tree level cross section for $X_d$ pair production at the LHC.

Distribution of transverse decay distances of individual dark pions for model A (left) and model B (right) at LHC14 (the benchmarks are defined in Sec.~\ref{sec:benchmarks}). The green curve shows the average transverse laboratory frame decay length $\beta_T \gamma_T c\tau_{\pi_d} = (p_T/m_{\pi_d}) c \tau_{\pi_d}$. Dashed lines indicate the approximate regions covered by the tracker (50~mm - 1000~mm) and calorimeters (1000~mm - 3000~mm).

Distribution of transverse decay distances of individual dark pions for model A (left) and model B (right) at LHC14 (the benchmarks are defined in Sec.~\ref{sec:benchmarks}). The green curve shows the average transverse laboratory frame decay length $\beta_T \gamma_T c\tau_{\pi_d} = (p_T/m_{\pi_d}) c \tau_{\pi_d}$. Dashed lines indicate the approximate regions covered by the tracker (50~mm - 1000~mm) and calorimeters (1000~mm - 3000~mm).

Distribution of transverse decay distances of individual dark pions for model A (left) and model B (right) at LHC14 (the benchmarks are defined in Sec.~\ref{sec:benchmarks}). The green curve shows the average transverse laboratory frame decay length $\beta_T \gamma_T c\tau_{\pi_d} = (p_T/m_{\pi_d}) c \tau_{\pi_d}$. Dashed lines indicate the approximate regions covered by the tracker (50~mm - 1000~mm) and calorimeters (1000~mm - 3000~mm).

Difference between a displaced dijet signature from the decay of a heavy long-lived particle and the emerging jet signature.

$p_T$ distributions of the hardest emerging (solid, blue) and hardest QCD (dashed, red) jet in each signal event, as well as for the hardest jet in the background QCD sample (dotted, green). Emerging jets have $r=3$ mm, $n=0$, and $p_T^{\rm min} = 1$ GeV. These events pass all the kinematic cuts described in the text, and the signal events have at least two emerging jets. The left plot is for model A, while the right for model B.

Breakdown of the composition of the different ways that QCD can produce emerging jets. The left plots show the distribution of transverse decay radius of the earliest decaying neutral hadron within the jet. The histograms are stacked based on the quark content of the decaying neutral hadron, with strange, charm, and bottom going from bottom to top. The top (bottom) plot require $\leq 0$ (2) prompt charged tracks in the jet, and throughout we require all tracks to have $p_T > 1$ GeV. The right plots are jets with no displaced charged tracks at all and again $\leq 0$ (2) prompt charged tracks on the top (bottom). These jets are composed of photons, neutrons, neutral strange hadrons, and in the bottom plot, one or two prompt tracks. The right plots categorize these jets by which of the three types of displaced neutral categories carry the most $p_T$. The ``none'' category in the bottom plot is for jets where all the energy is in the one or two prompt tracks. All of the jets displayed must pass the kinematic cuts described in the text and in Tab.~\ref{tab:cut-flow4}.

Fraction of signal events in model A (top) and model B (bottom) which have at least one (left) or two (right) emerging jets with $p_T^{\rm min} = 1$ GeV as a function of $r$, the transverse distance. Within each plot, the curves are a maximum of 0, 1, and 2 tracks with transverse origin less than $r$ going from bottom to top. A vertical line is put at the proper lifetime of the particular model. All events must pass the kinematic preselection cuts.

Fraction of 4-jet QCD events that have at least one emerging jet as a function of the radius, $r$. These events have the kinematic cuts already applied, see text. From bottom to top, the lines are emerging jets with at most 0, 1, and 2 tracks inside of the radius $r$. The solid lines use the standard \textsc{Pythia} tune, while the dashed lines are the modified tune designed to increase the number of emerging jets in the sample~\cite{peter}.

Region of lifetime and mediator mass parameter space probed with 100~fb$^{-1}$ (top row) and 3000~fb$^{-1}$ (bottom row) at the 14~TeV LHC. For each model we show $2\sigma$ (dashed) and $5\sigma$ contours (solid) in the $M_X - c\tau_0$ plane, assuming a systematic uncertainty of 100\% on the background. The different colous correspond to requiring $E(1 {\rm \,GeV}, 0, 3 \,{\rm mm}) \geq 2$ (blue) and $E(1 {\rm \,GeV}, 0, 100 \,{\rm mm}) \geq 2$ (red).

Region of lifetime and mediator mass parameter space probed with 100~fb$^{-1}$ (top row) and 3000~fb$^{-1}$ (bottom row) at the 14~TeV LHC. For each model we show $2\sigma$ (dashed) and $5\sigma$ contours (solid) in the $M_X - c\tau_0$ plane, assuming a systematic uncertainty of 100\% on the background. The different colous correspond to requiring $E(1 {\rm \,GeV}, 0, 3 \,{\rm mm}) \geq 2$ (blue) and $E(1 {\rm \,GeV}, 0, 100 \,{\rm mm}) \geq 2$ (red).

Region of lifetime and mediator mass parameter space probed with 100~fb$^{-1}$ (top row) and 3000~fb$^{-1}$ (bottom row) at the 14~TeV LHC. For each model we show $2\sigma$ (dashed) and $5\sigma$ contours (solid) in the $M_X - c\tau_0$ plane, assuming a systematic uncertainty of 100\% on the background. The different colous correspond to requiring $E(1 {\rm \,GeV}, 0, 3 \,{\rm mm}) \geq 2$ (blue) and $E(1 {\rm \,GeV}, 0, 100 \,{\rm mm}) \geq 2$ (red).

Region of lifetime and mediator mass parameter space probed with 100~fb$^{-1}$ (top row) and 3000~fb$^{-1}$ (bottom row) at the 14~TeV LHC. For each model we show $2\sigma$ (dashed) and $5\sigma$ contours (solid) in the $M_X - c\tau_0$ plane, assuming a systematic uncertainty of 100\% on the background. The different colous correspond to requiring $E(1 {\rm \,GeV}, 0, 3 \,{\rm mm}) \geq 2$ (blue) and $E(1 {\rm \,GeV}, 0, 100 \,{\rm mm}) \geq 2$ (red).

$F$ distributions for model A (top), model B (middle), and QCD background (bottom). The left plots are the distribution of the highest and second highest $F$ values for jets in an event, where for model A (B) we have taken $r=100$ (3) mm, and for the background we show both. The right plot shows the fraction of events that have at least one jet with $F > $ 0.3, 0.5, or 0.7. All events must pass the kinematic cuts in Tab.~\ref{tab:cut-flow4}. Note that the signal plots use a linear scale while the background plots use a log scale, and the dashed lines in the bottom right plot are those using the modified \textsc{Pythia} tune.

Dark quark invariant mass distribution for different values of the cut-off $\Lambda$ at the 14~TeV LHC. The total integrated cross section for the process $pp \to \bar{Q}_d Q_d$ is $42$~fb for $\Lambda=5$~TeV and $2.5$~fb for $\Lambda=10$~TeV per dark quark flavor, for $N_d = 3$.

Left: Fraction of $Q_d \bar{Q}_d$ events with at least $N_{\pi_d}$ dark pions inside the LHCb detector. About 45\% of all events have at least one dark pion in LHCb, and almost 30\% have three or more. Right: Momentum distribution of dark pions in the LHCb detector.

Left: Fraction of $Q_d \bar{Q}_d$ events with at least $N_{\pi_d}$ dark pions inside the LHCb detector. About 45\% of all events have at least one dark pion in LHCb, and almost 30\% have three or more. Right: Momentum distribution of dark pions in the LHCb detector.

Multiplicity of charged tracks in $\pi_d$ decays, assuming 100\% decay to down quarks, and with the fragmentation process simulated using \textsc{Pythia}.

Pair production of squarks $\tilde{q}$ with subsequent decay into quarks $q$ and neutralinos $\chi_1$. The neutralino undergoes an $R$-parity violating three-body decay into a $uds$ final state, and has a macroscopic lifetime. Not shown is the corresponding diagram with initial state gluons.

Sensitivity of the emerging jets search for the RPV MSSM toy model, at the 14~TeV LHC. Contours are as in Fig.~\ref{fig:reachAB}. A common mass $M_{\tilde{q}}$ is assumed for first and second generation right-handed up-squarks, while all other MSSM particles are assumed to be heavy.

Sensitivity of the emerging jets search for the RPV MSSM toy model, at the 14~TeV LHC. Contours are as in Fig.~\ref{fig:reachAB}. A common mass $M_{\tilde{q}}$ is assumed for first and second generation right-handed up-squarks, while all other MSSM particles are assumed to be heavy.

Comparison of \textsc{Pythia} with (solid, blue) and without (dashed, red) running of the gauge coupling in the dark sector implemented. The left plot is the girth distribution (see Eq.~(\ref{eqn:girth})), while the right plot is the orphan $p_T$: the scalar sum of the $p_T$ of visible particles which are not clustered into a jet of $p_T > 200$ GeV. This is for model B events with $Z_d$ production so all jets originate from the dark sector.

Average dark meson multiplicity in $e^+ e^- \to Z_d^{*} \to \bar{Q}_d Q_d$ as a function of the center-of-mass energy $\sqrt{s}$. We compare the output of the modified \textsc{Pythia} implementation for $n_f = 7$ (blue circles) and $n_f = 2$ (red squares) to the theory prediction Eq.~(\ref{eqn:nmesontheory}), where we only float the normalization. The dark QCD scale and dark meson spectrum corresponds to benchmark model B.

Crude detector geometry we use: we model the calorimeter as a cylinder of radius 3 meters and height 6 meters. Particles that would decay inside the cylinder are decayed, while particles that would decay outside are left undecayed.

Decision tree for determining how to assess if a particle counts as displaced or not.

Error in opening angle introduced by displaced vertices. Our jet algorithm uses the momentum to determine the opening angle $\theta$, which overestimates the opening angle $\theta'$ seen by the actual calorimeter.

Girth distribution for signal vs. background. The background (green, dashed) in both plots is four jet QCD events passing the kinematic cuts of Tab.~\ref{tab:cut-flow4}, while the signal are model A (left, blue, solid) and model B (right, red, solid) in the $Z_d$ model only requiring that jets have $p_T > 200$ GeV.