Searching for Quirks at LHCb

Abstract

Quirks are heavy particles connected by a flux tube from a hidden confining force that remain weakly constrained in large regions of their parameter space. This flux tube acts as a string that, at short enough distance, stretches as the quirk pair separates, then pulls the pair back together leading to interesting dynamics. We propose a novel search using the LHCb Vertex Locator (VELO), whose forward geometry and software-based trigger are uniquely suited to detecting the characteristic back-to-back, planar hit patterns produced by quirk pairs with little transverse recoil. Using detailed simulations of the VELO geometry, together with simple geometric selections, we present different sensitivity projections, demonstrating that LHCb can probe parameter regions inaccessible to existing ATLAS and CMS searches and offering a powerful, complementary path toward discovering quirks.

Figures (1)

• Figure 4: Example trajectories of quirk-antiquirk pairs in the VELO. Three VELO stations, centered at the origin of the $x$ and $y$ axes and shown as a series of colored rectangles parallel to one another and perpendicular to the $z$-direction, are included for reference in each case. The experimental phenomenology of quirks at collider experiments is defined by the macroscopic properties of the infracolor string connecting the pair, which, as explained, depends critically on the confinement scale $\Lambda$ relative to the quirk mass $m_Q$. Consequently, the search strategy at the LHC must vary across the parameter space, leveraging different measurements and types of searches to place bounds on these exotic states. In Reference Farina:2017cts, the authors reinterpret existing LHC analyses within the quirk parameter space. When $\Lambda$ is relatively small, the string-like force between quirks has minimal influence, and their behaviour resembles that of HSCPs. Because HSCP searches are highly sensitive, they impose stringent constraints on quirks in this regime. For larger values of $\Lambda$, monojet searches, which rely on detecting missing energy and initial-state radiation, can be adapted to constrain quirks. However, these searches face challenges from significant backgrounds and reduced signal rates, resulting in weaker constraints. The reinterpretation draws on HSCP searches performed by CMS CMS:2016ybj and monojet searches conducted by ATLAS ATLAS:2016bek. Reference Knapen:2017kly presents an alternative method for detecting quirks in regions where HSCP searches are less effective. This strategy focuses on identifying pairs of hits in the tracker that are aligned within the same plane (similar to the picture depicted in Figure \ref{['fig:quirks']}), referred to as co-planar hits. To ensure sufficient triggering efficiency, the method requires the presence of a high-$p_T$ jet from initial-state radiation. Additionally, the event selection process includes a cut-off on the quirk–anti-quirk separation distance, limiting it to $1$ cm to control the background. While this cut-off helps reduce background, it also diminishes sensitivity for intermediate values of $\Lambda$. The quirk pair may also lose substantial energy through ionisation and eventually come to rest within the detector. During idle periods of the LHC (no active collisions), these quirks can annihilate, producing distinctive signals. Such events are constrained by searches for stopped Long-Lived Particles (LLPs) or those occurring out of time (OoT). Reference Evans:2018jmd proposes optimisations of the CMS analysis for OoT particles CMS:2017kku to achieve similar or better sensitivity compared to the co-planar hits approach. Another intriguing proposal, discussed in Reference Feng:2024zgp, involves using delayed or slow-moving tracks in conjunction with the FASER2 detector. Although future FASER2's capabilities may allow it to match or surpass the OoT strategy in sensitivity, this approach is not discussed further since FASER 2 is not an approved experiment yet. The most relevant projected bounds discussed in this section are shown in Figure \ref{['fig:existing']}, assuming a total integrated luminosity of $425~\text{fb}^{-1}$. This corresponds to the full dataset expected from ATLAS and CMS by the end of Run 3. From the figure, we observe that despite existing limits (HSCPs and monojets) and proposed searches (co-planar hits, OoT), there remain weak constraints in the mid-$\Lambda$ range. In this regime, the LHCb experiment has the potential to set competitive bounds due to its unique detector capabilities. Projected constraints on quirks compared to expected LHCb sensitivity. The corresponding integrated luminosities are $425~\text{fb}^{-1}$, $10~\text{fb}^{-1}$ and $300~\text{fb}^{-1}$ for the ATLAS/CMS Run 3, LHCb 2026 and LHCb ultimate datasets, respectively. Bounds are showed at 95% CL. The LHCb sensitivity is obtained with a toy simulation of the VELO detector reproducing LHCb running conditions.The LHCb experiment can be used to provide a unique, complementary approach in the search for quirks. LHCb has transitioned into a general-purpose detector in the forward region, having conducted several searches for LLPs LHCb:2021dyuLHCb:2020akwLHCb:2020ysnLHCb:2019vmcLHCb:2017trqLHCb:2017xxnLHCb:2016inzLHCb:2016buhLHCb:2016awgLHCb:2014osdLHCb:2014jgs. It is also essential to note that LHCb is expected to continue data-taking in the high luminosity LHC (HL-LHC) phase (Upgrade II). The ultimate integrated luminosity target for this phase is approximately $300~\text{fb}^{-1}$LHCb:2018coe. For the immediate future, specifically for 2026, we assume an integrated luminosity of roughly $10~\text{fb}^{-1}$, comparable to the successful $11.8~\text{fb}^{-1}$ of proton-proton collision data actually collected during the 2025 run LHCb-Outreach:2025run. From 2022 onwards, the LHCb trigger operates as a High Level Trigger (HLT), fully software-based and divided into two levels: HLT1 and HLT2. The HLT1, performing a rapid partial reconstruction step, is GPU-based Aaij:2019zbu. Events passing through HLT1 are buffered on disk for subsequent filtering and storage at HLT2. At HLT2, given the buffered events, the reconstruction attains the same quality as offline. Importantly for LLP reconstruction, with this new trigger system full event information is available for decision-making in every event. Moreover, a flexible reconstruction step takes place, which can be adapted to search for non-standard LLP signatures, such as quirks. While the strict latency constraints of the online trigger ($30~\text{MHz}$ throughput) limit the complexity of Machine Learning (ML) algorithms that can be deployed during the initial real-time selection, the system's architecture offers a critical workaround. Because the trigger buffers selected events to disk, heavy and sophisticated ML algorithms, which would be too slow for the live data stream, can be trained for and applied to these stored events during offline analysis. This allows for the identification of complex quirk signatures that would otherwise be missed by standard low-latency triggers. The search for quirks at LHCb that we propose utilises the VELO Akiba:2024now, a high-precision tracking detector located close to the LHC interaction point, designed to reconstruct primary and secondary vertices with exceptional accuracy. It consists of 52 modules of pixel sensors, aligned along the LHC beam pipe, spanning approximately $-300~\text{mm}$ to $750~\text{mm}$. To ensure complete angular coverage and hermeticity, the stations on the opposite sides of the beam are slightly shifted relative to each other along the beam axis ($z$-direction). This staggering allows the two halves of the detector to overlap when moved into the closed data-taking position without mechanical interference, effectively eliminating any gaps in acceptance. The VELO provides precise three-dimensional hit information, with a single-hit spatial resolution of $\mathcal{O}(10~\mu\text{m})$Buchanan:2022iib. A key feature of the VELO is its lack of a magnetic field, which significantly simplifies quirk trajectories.Characteristic kinematic features of quirk hits in the VELO detector, simulated with $m_Q=1200$ GeV and varying $\Lambda$ (left) and $\Lambda = 1100$ eV and varying $m_Q$ (right). An electric charge of $Q_E -1$ is assumed. The panels show: a) the number of reconstructed hit pairs per event; b) the azimuthal difference $\Delta\phi$ between paired hits; c) the radial difference $\Delta r$ between paired hits; and d) the maximum $\Delta\phi$ variation across different modules. Note that the geometric correlations (b, c, d) remain mostly stable across the parameter space. The distributions are obtained with a toy simulation of the VELO detector reproducing LHCb running conditions.Projected VELO detection efficiency across the quirk parameter space ($m_Q$ vs. $\Lambda$). Left: Average number of reconstructed hit pairs per event. Right: Fraction of events satisfying the selection criterion of at least 5 reconstructed hit pairs. The efficiencies are obtained with a toy simulation of the VELO detector reproducing LHCb running conditions.We propose that LHCb searches for quirk--anti-quirk pairs moving predominantly along the beam axis with minimal transverse recoil. To evaluate the feasibility of this search, we simulate quirk trajectories using a standalone code that generates hits according to the precise VELO geometry Coco:2683878, explicitly accounting for the single-hit spatial resolution of approximately $10~\mu\text{m}$Buchanan:2022iib. Our study uses toy simulations based on reference points Farina:2017ctsKnapen:2017kly, with a SM-coloured quirk (see above). This choice was made to facilitate direct comparison with previous studies. The signal manifests as pairs of hits in consecutive $z$-layers of the VELO detector. Unlike conventional particle tracks, which originate from the primary vertex and propagate outwards, quirk hits may not necessarily appear at monotonically increasing radii in the forward layers. However, the signal topology is distinct: the quirk and anti-quirk are expected to leave hits in modules positioned on opposite sides of the beam pipe. To reconstruct these, we require pairs of hits located in modules facing each other (see again Figure \ref{['fig:quirks']}). Although the VELO modules are mechanically staggered (slightly offset in the $z$-direction), the radial difference $\Delta r$ between the paired hits is expected to be small; for our selection, we require this difference to be under $5~\text{mm}$. Furthermore, the azimuthal difference $\Delta \phi$ between the hits is expected to be very close to $180^{\circ}$ (back-to-back in the transverse plane), and the maximum variation in $\phi$ between pairs across different modules is minimal, indicating a planar trajectory. As shown in Figure \ref{['fig:all_draws']}, these geometric definitions, particularly the planarity and back-to-back correlation, remain stable across the quirk parameter space. While the geometric signatures are robust, the primary factor determining the selection efficiency is the total number of reconstructed hits per event. This quantity varies significantly depending on the quirk mass $m_Q$ and the confinement scale $\Lambda$, as illustrated in Figure \ref{['fig:maphits']}. Consequently, the hit multiplicity dictates the ultimate sensitivity of the search. The geometry of the VELO imposes natural constraints here: the sensors cover radial distances from $7$ to $40~\text{mm}$ from the beam pipe. For high $\Lambda$ values (tight confinement), the quirk and anti-quirk cannot be spatially resolved, while for very low $\Lambda$, the macroscopic separation may impede simultaneous reconstruction within the acceptance. As highlighted in Section \ref{['sec:exp_context']}, the upgraded LHCb trigger system offers a unique opportunity to accommodate these signatures. With full event information available at the software trigger level, flexible reconstruction strategies are feasible. We hypothesize that a trigger for quirks could be developed to collect data in 2026, based on simple, hit-level criteria, as those outlined above. This initial trigger would serve as a proof of concept, offering partial sensitivity and enabling refinements for Runs 4 and 5.To validate the robustness of this selection strategy against standard model processes, we performed a study using high-statistics samples of inelastic $pp$ collisions and $b\bar{b}$ events generated with Pythia 8 Sjostrand:2014zea, together with the same code that generates hits according to the VELO geometry used for signal. These samples were chosen to represent the dominant sources of combinatorial background and heavy-flavour activity in the forward region. The pivotal element of our proposed selection is the topological requirement that the characteristic pairs of back-to-back hits must appear in consecutive VELO stations. While random combinatorial associations or pile-up artifacts may occasionally mimic a single back-to-back pair, they lack the longitudinal coherence required to form a sequence across multiple adjacent $z$-layers. Our studies indicate that this strict geometric condition is highly effective: when applied to the simulated samples, the vast majority of background events are rejected, with only a handful of candidates surviving the initial filter. A second potential background arises from isolated photon conversions in the detector material, where the electron and positron hits are typically co-planar. To mitigate this, control channels in the data Alexander:2018png are used at LHCb to construct precise material maps that assist in rejecting such conversions. By vetoing track pairs that originate from known material dense regions (such as the RF foil or module supports), this background can be significantly suppressed. To eliminate any remaining candidates, we propose the use of sophisticated offline reconstruction techniques. Recently, ML approaches have been suggested as a powerful tool for reconstructing full quirk trajectories Sha:2024hzq. We anticipate that an offline ML-based tracking algorithm, trained on the specific output of the trigger selection, would provide the necessary discrimination power to suppress the background to mostly negligible levels. In the event of a signal discovery, these ML techniques would naturally extend to the characterisation of the particle, allowing for the estimation of the quirk mass and string tension. Further refinements to ensure signal purity include the use of the Ring Imaging Cherenkov (RICH) detectors Adinolfi:2012qfa. Similar to Heavy Stable Charged Particle (HSCP) searches at LHCb LHCb:2015ujr, we can require that the candidate tracks produce no corresponding signal in the RICH, consistent with slow-moving or highly ionising particles. Consequently, for the sensitivity estimates presented in this paper, we assume a background-free hypothesis. Finally, to address systematic uncertainties associated with material interactions and tracking efficiencies, we propose the use of control channels in data, such as photon conversions. By reweighting the trajectories of electron-positron pairs to resemble quirk signatures, we can validate the detector response. The successful application of such data-driven techniques has proven effective in reducing uncertainties in previous LLP searches at LHCb LHCb:2021dyuLHCb:2020akwLHCb:2020ysn.To estimate the physics reach of the proposed search, we define a statistical framework based on the signal efficiencies derived in Section \ref{['sec:analysis']}. We assume a hadronisation model where $30\%$ of quirks form charged particles, consistent with the benchmarks established in Reference Knapen:2017kly. For the interaction of these heavy charged states with the detector material, we adopt a simplified assumption of $100\%$ detection efficiency for quirks with electric charge $Q_E=\pm 1$, regardless of their mass. It should be noted that detailed material interaction studies, accounting for specific energy loss mechanisms, will be required to validate this assumption in a full experimental analysis. The signal yield is calculated based on the selection requirement of at least five VELO stations containing back-to-back hits at consistent $\phi$ angles. We assume that the combination of the strict geometric selection and the proposed offline ML filtering reduces the background contribution to negligible levels. Consequently, exclusion limits are set using the Feldman-Cousins method Feldman:1997qc at $95\%$ confidence level (CL). We provide sensitivity projections for two scenarios: an integrated luminosity of $10~\text{fb}^{-1}$, corresponding to the expected dataset for the 2026 run, and an ultimate scenario of $300~\text{fb}^{-1}$ representing the full HL-LHC dataset for LHCb. The resulting sensitivity contours in the $m_Q$--$\Lambda$ plane are summarised in Figure \ref{['fig:existing']}. These projections suggest that LHCb could achieve unprecedented sensitivity, covering significant portions of parameter space potentially inaccessible to other experiments, particularly in the $\Lambda \sim 1000$ eV region. The search proposed here for LHCb should remain robust for Run 4 and holds excellent prospects for Run 5 (Upgrade II), particularly given the enhanced timing capabilities of the future 4D VELO upgrade deAguiarFrancisco:2024bzg. In conclusion, the unique geometric configuration of the LHCb VELO, combined with a flexible software-based trigger, provides a powerful and distinct handle to explore uncharted regions of the quirk parameter space. This approach offers high complementarity to the central detector searches performed by ATLAS and CMS. We strongly encourage the development of dedicated trigger lines for these signatures during the remainder of Run 3 and for future data-taking campaigns at LHCb. Moving forward, further studies will be necessary to fully validate the background-free hypothesis, specifically through the implementation of full quirk trajectory reconstruction algorithms and the inclusion of particle identification information from the RICH subdetectors.We thank Fred Blanc and Stefania Vecchi for providing comments to our manuscript. The work of XCV, MFG and ANC is supported by the Spanish Research State Agency under projects PID2022-139514NA-C33, PCI2023-145984-2 and EUR2025-164824; by the “María de Maeztu” grant CEX2023-001318-M, funded by MICIU/AEI/10.13039/501100011033; and by the Xunta de Galicia (CIGUS Network of Research Centres and project 2025-CP119). The work of MFG is supported by Xunta de Galicia under Programa de axudas á etapa predoutoral Grant ED481A-2022. The work of ANC is supported by the Spanish Science Ministry through the FPU program (FPU24/01899). The work of YT is supported by the NSF Grant PHY-2412701. YT would also like to thank the Tom and Carolyn Marquez Chair Fund for its generous support. 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