# Searching for Long-Lived BSM Particles at the LHC

Post-publication activity

Curator: Marie-Hélène Genest

## Long-lived particles: what are they and where could they come from?

By definition, a long-lived particle (LLP) is an unstable particle with a sizeable lifetime. The definition of sizeable, in turn, will depend on the experimental apparatus,  as it should be long enough to allow for the distance between the LLP production and decay points to be observable. In the Large Hadron Collider (LHC) experiments, LLPs could be produced in the proton-proton (p-p) collisions and manifest themselves in the detectors via their late decay, leading to a signature of visible particles which do not originate from the nominal interaction point. For a given proper decay lifetime $$\tau$$ (the lifetime as measured in the particle rest frame) and an initial number of particles $$N_0$$, the expected number of particles surviving after a time $$t$$ measured in the rest frame follows an exponentially decreasing probability function$N(t) = N_0e^{-t/\tau}$

As high-energy collisions can lead to large relativistic boosts of the produced particles,  if these are light compared to the collision energy, the displacement $$L$$ corresponding to the proper lifetime can be enhanced in the laboratory frame$L = \gamma\beta c\tau$

where $$\gamma = 1/(1-\beta^2)^{1/2}$$ is the Lorentz factor and $$\beta=v/c$$ is the ratio of the particle's velocity $$v$$ to the speed of light $$c$$.

The fraction of decays in the various detector systems will thus change with the lifetime and boost, and multiple types of searches might be needed to cover the various signatures, as will be described below.

For a particle to have a long lifetime, the decay must be suppressed, which can happen through two mechanisms: small couplings to decay mediators or a suppressed decay phase space. These mechanisms are at play even in the Standard Model (SM), which contains multiple LLPs, such as charged pions ($$\tau_{\pi^{\pm}}=26$$ ns), muons ($$\tau_{\mu}=2.2$$ $$\mu s$$) or neutrons ($$\tau_{n}=880$$ s). It is therefore not unexpected that they could also be at play in theories beyond the SM (BSM), and there are indeed many BSM models predicting LLPs.

The small-coupling case can happen for example if the interaction violates an approximate symmetry which would otherwise forbid the decay to take place, or if there is a small mixing with SM particles. This can happen in dark/hidden-sector theories, i.e. BSM theories in which the postulated new particles are not charged under the usual SM interactions but communicate with the SM only through a new mediator which is heavy and/or only weakly coupled to the SM. An example of this mechanism arises in some dark-photon ($$A'$$) theories. In this scenario, the hypothetical massive vector boson $$A'$$, which could mediate the interactions of dark matter particles, couples to the SM through a mixing with the SM photon with strength $$\epsilon$$ - for small values of this mixing parameter, the dark photon $$A'$$ becomes long lived.

A long lifetime through this mechanism can also happen if the mediator of the decay is very massive, thus reducing the effective coupling. This happens for example in some supersymmetric (SUSY) theories. In these theories, every fermion of the SM has a new scalar particle counterpart, and every boson - a new fermion; the Higgs sector is also enlarged and the supersymmetric partners of the gauge and Higgs bosons can mix, creating charged and neutral states called charginos and neutralinos, the lightest neutralino often being stable and a suitable dark-matter candidate. As the superpartners do not have the same masses as their SM counterparts, SUSY is not an exact symmetry and must be broken. For split SUSY models, the scalar partners of the SM fermions are very heavy, $$O(10^{2-3})$$ TeV, while the fermionic partners of the SM bosons are at a mass scale accessible at the LHC. The superpartner of the gluon, the gluino ($$\tilde{g}$$), could then be pair-produced in the p-p collisions, but its decay, into a pair of quarks and the lightest neutralino ($$\tilde{\chi}$$) through a virtual squark production ($$\tilde{q}^*$$) , would be suppressed ($$\tilde{g}\rightarrow\tilde{q}^*\bar{q}\rightarrow\tilde{\chi}q\bar{q}$$). This long-lived gluino, as it carries colour charges, would hadronise with SM particles into a so-called R-hadron before decaying.

The suppressed decay phase space can happen if the mass difference between the decaying particle and its decay products is small, in a so-called compressed mass spectrum. This can happen in the anomaly-mediated SUSY breaking models, for which the masses of the lightest chargino and neutralino differ only by loop-level corrections of $$O(160)$$ MeV: the lightest chargino, which decays into the lightest neutralino and a charged pion in this case, hence becomes long-lived as the decay phase space is suppressed.

## Signatures of long-lived particles at the LHC

Figure 1: Overview of some LLP signatures in the various sub-dectors of a generic detector like ATLAS, shown in the transverse plane with respect to the beam line: the collision takes place in the center and the particles will cross in turn the inner tracking detector (in green), the electromagnetic and hadronic calorimeters (in turquoise and blue) and the muon spectrometer (in grey). The dotted lines show invisible particles, the full lines represent tracks, and the shaded areas are calorimeter energy deposits. The represented signatures (see the text) are from the top and in a clockwise fashion: a disappearing track, a kinked track, a non-pointing photon, an emerging jet, a heavy charged LLP going through the detector, a displaced hadronic jet in the calorimeter, the same in the muon spectrometer, a displaced electron, a displaced muon pair, a displaced electron pair and finally, a displaced hadronic jet in the inner detector. (Credit: Heather Russell, under the Creative Commons Attribution-NonCommercial 4.0 International License).

In a general-purpose detector like ATLAS or CMS, the particles produced in the collisions at the LHC will move away from the interaction point, first going through the inner tracking detector and, energy and lifetime permitting, the electromagnetic and hadronic calorimeters and finally, the muon spectrometer. The signature will thus not only depend on the lifetime of the particle, but also on its nature and hence on its possible interactions with the various sub-detectors. Some examples are described below and graphically shown in Figure 1.

In the inner tracking detector A displaced vertex (DV) signature can arise when an LLP decays to several charged particles in the inner tracking detector (ID) volume, leading to tracks whose intersection is not compatible with the primary vertex of the event, where the p-p collision took place, but instead form a DV at the position of the LLP decay. Another, more exotic, signature from LLPs in the ID is the so-called disappearing track signature, which can be produced if a charged LLP decays into an invisible state and a charged particle which has too little energy to be seen in the detector. Such is the case in the compressed supersymmetric model discussed above in which an LLP chargino, produced in the p-p collision and recorded as a track in the first layers of the inner detector, eventually disappears by decaying into an almost mass-degenerate invisible neutralino and a very low-energy charged pion which is not seen. A charged LLP could also decay into an energetic charged particle, which does not follow the direction of its LLP parent, and an invisible state; in this case, the track initiated by the LLP does not disappear but appears to abruptly change direction, thus giving a kinked track signature. Another LLP signature in the ID would be that of a track that is associated to an otherwise well-reconstructed lepton (electron or muon) but which would be displaced, i.e. with a larger than usual impact parameter with respect to the primary vertex, if this lepton comes from an LLP decay. As a final example, the LLP could be a high-mass charged particle (for example an R-hadron as discussed before) which would have, even at high energy, a low velocity compared to the speed of light. Even in the case in which the lifetime of such a particle would allow it to cross the full detector before decaying, it could leave a distinctive signature in the ID in the form of an abnormally large ionisation loss, dE/dx. Its low velocity could also be measured through time-of-flight techniques, which could combine the ID information with information from the muon spectrometer if the particle goes through all the detector volume, or with timing information from the calorimeters.

In the calorimeters The decay of LLPs can involve the production of hadronic jets, if their decay products involve SM quarks and/or gluons. Such jets could be identified in the detectors in various ways. If the decay happens in the calorimeter, the formed jets will be displaced, possibly exhibiting an atypically large ratio of energy deposited in the hadronic calorimeter with respect to that deposited in the electromagnetic calorimeter, and a lower number of associated tracks in the ID. In some dark QCD models, dark quarks, from a hidden sector, are produced in the collisions and then hadronise in the dark sector to form dark hadrons; these dark hadrons are invisible to the detector until some of them decay back to SM particles, such as SM quarks. In such a case, the initially formed dark jet would gradually become visible in the detector, as the LLPs inside it start to decay, leading to a possible emerging jet signature: multiple DVs in the ID associated with a jet in the calorimeters. If on the other hand the jet is coming from a massive neutral LLP decay in the calorimeter, it can lead to a delayed jet signature: the timing of the calorimeter is then used to measure the time of the jet with respect to the expected arrival time for a massless particle coming from the interaction point. Besides timing information, the geometrical segmentation of some calorimeters can also be used to recover some information: an example is to look for non-pointing photons, that is photons identified in the electromagnetic calorimeter whose flight direction does not coincide with the direction from the primary vertex. Such a signature could happen for example in some supersymmetric models in which a heavy neutralino LLP decays into a gravitino, which is invisible to the detector, and a Higgs boson which subsequently decays into two non-pointing photons.

In the muon spectrometer LLPs with large enough lifetimes could lead to a DV signature in the muon spectrometer, via the same mechanism as the DV signature in the ID. Very displaced hadronic jets can also appear in the muon spectrometer, leading to a possibly spectacular, multiple-track signature which is completely isolated from any activity in the ID or the calorimeters.

Some even more exotic signatures can happen for very long lifetimes, in models in which the LLPs would interact and come to rest inside the detector and decay at a later time, giving energetic events which are decorrelated in time from the collision activity in the detector, even possibly producing signal when the LHC is not running.

## Search strategies and unique difficulties

Figure 2: Reconstruction efficiency of tracks from displaced charged particles which come from the decay of an LLP at a radius $$r_{prod}$$ in the inner detector of ATLAS. The standard tracking algorithm, requiring some association of the tracks to the primary vertex, is quite inefficient for decays happening at large radii: the large-radius tracking algorithm is necessary to recover some efficiency for these LLP decays.(Credit: ATLAS Collaboration, ATL-PHYS-PUB-2017-014)

Given the atypical signatures expected, some of which were mentioned above, dedicated algorithms are often necessary to search for these objects in the detector. Large radius tracking is one such algorithm: after reconstructing the standard tracks which are pointing towards the primary interaction point, an additional algorithm running on the remaining unassociated hits in the ID can build a collection of tracks which originate at larger radius in the ID, and which are then used to search for DVs. Indeed, as can be seen in Figure 2, the standard tracking algorithm, which has constraints on the association of the tracks to the primary vertex, is not efficient for LLPs decaying at large radii in the ID, corresponding to longer lifetimes: the large radius tracking algorithm is necessary to have a non-negligible efficiency for these scenarios.

Figure 3: Example of a material map from CMS. (Credit: CMS Collaboration as published in JINST 13 (2018) P10034)

Great care must also be taken when using existing algorithms and analysis techniques, as standard procedures might be detrimental to some LLP searches. This can be the case for some event cleaning procedures for example, which are often undertaken in more standard analyses in order to avoid detector-related issues. In some recommended cleaning selections, events with atypical energy deposits in some detector parts, that could be due to electronic noise for example, are removed from the dataset. While these procedures usually have a negligible impact on the events targeted by standard analyses, i.e. those searching for the prompt decay of new particles, it may not be the case for some LLP searches for which they could remove a significant fraction of the signal candidates.

Standard Model processes can sometimes mimic the LLP signatures and might hence produce a large background to these searches. This is the case in the production of displaced vertices, which can frequently happen from the interaction of SM particles emitted from the collision point with the dense material of some detector parts (sensitive material, detector supports or services), such as photons converting into an electron-positron pair. These can however be removed by fiducial selections, that is by vetoing any DV that falls within a region compatible with the presence of such material, using the known material map of the detector, an example of which is shown in Figure 3. Applying selections on the mass of the DV can also help in that respect, and will also remove background from known low-mass SM resonances.

Other LLP signatures are so unique that a very limited number of Standard Model processes, if any, can produce them. The fact that some LLP signatures are free from collision SM backgrounds can make them particularly interesting as the collected dataset increases in size. The sensitivity of standard searches, when they are not limited by systematic uncertainties, is roughly given by the ratio $$S/\sqrt{B}$$ where $$S$$ is the expected number of signal events and $$B$$ is the number of background events. As the collected dataset increases, so do S and B, at the same rate: the sensitivity thus increases proportionally to the square root of the dataset size. For searches in which the background is non existent, or unrelated to the collision rate, the sensitivity can grow more quickly, being directly proportional to the expected number of signal events. Even for these searches though, there can be sources of background, which are often more diverse in origin, including rare mis-reconstruction of objects or non-collision background which can be linked to noise in some parts of the detector, cosmic rays, or be induced by interactions of protons in the beam with collimators or with residual gas molecules in the beam pipes. Estimating the level of these backgrounds, which are difficult if not impossible to simulate reliably, requires designing background estimation methods which rely on samples in data selected to have little or no expected signal while being enriched in the background of interest (so-called data-driven techniques). For example, in order to estimate the number of cosmic-ray or beam induced events, one can measure the probability of mimicking the signal signature in an independent dataset which would be empty of signal contamination. Such a dataset could be a cosmic-ray dataset taken when there is no collisions in the first case, or a dataset corresponding to times in which only one proton bunch crosses the detector (called unpaired bunch) in the second case. The probability measured would then need to be applied appropriately to the dataset of the search in order to compute how many such background events are expected to pass the signal selection in the final analysis.

As with any other LHC analysis, a further hurdle in the search for LLPs is the trigger system which must pick interesting collision events in a short time, based on limited detector information. Indeed, of the 40 MHz of LHC p-p collisions, ATLAS and CMS store on disk for further offline analysis only about a kHz of p-p collisions due to bandwidth and storage restrictions; one must thus make sure that eventual signal events are picked up for further processing amongst the myriad of collisions. Depending on the nature of the LLP and on its production mechanism, the LLP can, in some models, be expected to be accompanied by other more standard, energetic objects in the detector, such as leptons, jets or missing transverse momentum. This can be especially helpful at the trigger level, as one can then rely on the presence of these objects in order to select the interesting events. In some other situations, a dedicated trigger is needed. The goal is then to devise it in such a way as to collect these peculiar events, by making a decision based on the available trigger information within the allocated trigger timescale and without affecting the recording bandwidth significantly. Given the relative rarity of the LLP signature, this can often be achieved but may require dedicated triggering algorithms without which the events would be lost. A particularly challenging scenario is one in which LLPs are very heavy: produced without a large boost, they could arrive too late in the detector to be considered by the triggering algorithms.

## Main LHC detectors

The scenarios described above and in Figure 1 focus mainly on a multipurpose general detector that is large, has an almost full coverage around the interaction point and is made of multiple subdetectors which can, together, cover a wide range of signatures, such as ATLAS or CMS. Indeed, CMS and ATLAS are sensitive to a large range of models and parameters, as shown in Figure 4 which gives an overview of excluded lifetimes for a selection of ATLAS analyses. Multiple models are given as examples in this Figure, such as supersymmetric scenarios, Higgs decays to LLPs such as dark photons, new long-lived scalar particles or long-lived heavy neutral leptons, and the exclusions span multiple orders of magnitude in lifetimes and masses, depending on the models.

Figure 4: Ranges of new particle lifetimes excluded at the 95% confidence level for a selection of ATLAS analyses. (Credit: ATLAS Collaboration, ATL-PHYS-PUB-2022-034)

The LHCb detector is also an excellent tool to search for LLPs: it was optimised to study b-hadrons, which are, in fact, SM LLPs whose identification often relies on the presence of a displaced vertex. Running at a lower instantaneous luminosity to avoid large pileup and only instrumented in the forward direction (i.e. in a rather small angle around the beam pipe), its coverage is unique and thus complementary to that of ATLAS and CMS, being able to probe lower masses with its forward acceptance and low-energy triggers, and lower lifetimes due to its excellent vertexing  capabilities and detector instrumented for decays with a larger forward boost. An example of unique coverage brought by the LHCb detector is shown in Figure 5, which shows the limits in the dark photon ($$A'$$) parameter space. The LHCb search looks for a dimuon displaced vertex which would come from the decay $$A'\rightarrow \mu\mu$$. As shown in the Figure, the LHCb coverage is unique amongst all experiments, probing the 200-350 MeV range for $$10^{-5} < O(\epsilon) < 10^{-4}$$.

Figure 5: Limits in the dark photon ($$A'$$) parameter space of the $$\gamma-A'$$ mixing parameter $$\epsilon$$ versus the dark photon mass. The LHCb LLP coverage, based on a displaced signature of $$A'\rightarrow \mu\mu$$, is displayed by the two excluded islands in the middle of the plot. LHCb offers a unique coverage amongst all experiments, probing the 200-350 MeV range for $$10^{-5} < O(\epsilon) < 10^{-4}$$. (Credit: LHCb Collaboration, Phys. Rev. Lett. 124 (2020) 041801).

## Current and proposed dedicated detectors

Besides these large, general detectors, other detectors specialising in LLP detection have been installed or proposed at the LHC, usually instrumenting service areas which may not be used otherwise. These detectors, further away from the interaction points where the collisions take place, can often benefit from existing passive or active shielding, possible complementary collision information from their associated general-purpose detector, a dedicated design and a good positioning to reconstruct LLPs in a lower background environment.

Figure 6: FASER projected sensitivity to dark photons, compared to other experiments, such as MATHUSLA.(Credit: FASER Collaboration, https://faser.web.cern.ch/)

Such is the case for FASER, which has been installed in an unused tunnel 480 meters away from the ATLAS interaction point and which has started taking data in LHC Run-3. The idea is to look for long-lived light particles produced in meson decays in the very forward region of LHC collisions which is not instrumented in ATLAS. While the proton beam will follow the curved LHC path and most of the other SM particles emitted in the forward region will be absorbed by the 100 meters of rock and concrete between ATLAS and FASER, the neutral, weakly-interacting particles produced in the collisions will travel straight towards FASER and could decay inside its cylindrical decay volume (radius of 10 cm, length of 1.5 meters) into an electron-positron or a photon pair. These particles would then pass through a strong magnetic field, a spectrometer and a calorimeter, allowing their identification. One scenario FASER can probe is the production of dark photons, see Figure 6. In front of the main FASER detector an emulsion/tungsten neutrino detector is placed, called FASER$$\nu$$.

Another recently installed detector is SND@LHC: similarly to FASER, it probes the forward region of the ATLAS detector, being located at the same distance of 480 meters away from the interaction point, on the other side. Differently from FASER though, the detector is slightly off-axis with respect to the beam inside ATLAS, thus providing a complementary coverage. The detector, 1-meter wide and 2.6-meter long, is shielded by about 100 meters of rock, has an active scintillator veto, a vertex detector and electromagnetic calorimeter made of emulsion/tungsten and scintillating fibers and a muon spectrometer and hadronic calorimeter made of scintillator and iron. While being primarily intended to study neutrinos coming from the collisions, like FASER$$\nu$$, it can also be used to look for long-lived, feebly-interacting particles scattering or decaying in the detector volume.

Larger versions of both FASER and SND@LHC are proposed as part of the Forward Physics facility (FPF). The proposed FPF would be a new underground cavern hosting forward experiments which would be shielded by concrete and rock and located a few hundreds of meters away from the ATLAS interaction point. Another recently proposed forward detector is FACET, which would complement the CMS detector in the very forward region in view of the high-luminosity phase of the LHC (HL-LHC).

Instead of looking for LLPs produced in the decay of light SM particles such as mesons in the very forward region, detectors can also be placed in a transverse way, close to the surface, enhancing the lifetime sensitivity of searches for LLPs produced in the decay of heavy particles such as the Higgs boson. This is the case for the MATHUSLA project, which proposes to place a large (100 m large x 100 m long x 25 m high) detector close to the surface, above the CMS interaction point, looking for decays of LLPs produced in the p-p collisions but escaping CMS as they have very long lifetimes. It would consist in multiple layers of tracking detector to search for decays inside a 20-meter-high air-filled decay volume. Most of the background from SM particles would be absorbed by the O(100-m) overhead rock on the way to MATHUSLA, except high-energy muons coming from the interaction point (which can be vetoed through a scintillator layer at the entrance of the detector) or from cosmic rays (which can be identified and removed based on their direction of propagation inside the multiple tracking layers). A test stand installed above the interaction point of ATLAS as a proof of concept was operated in 2018. If approved, this experiment could be installed to take data during the HL-LHC. The projected sensitivity to a Higgs decaying to two long-lived scalars X is shown in Figure 7, showing its complementarity to the ATLAS dectector at longer lifetimes.

Figure 7: MATHUSLA projected sensitivity to a Higgs boson decaying to two long-lived scalars X, shown in the plane of the decay branching ratio versus the lifetime of X, showing its complementarity to the ATLAS detector at longer lifetimes.(Credit: MATHUSLA Collaboration, https://mathusla-experiment.web.cern.ch/node/9)

There is also a proposal to install a 10 x 10 x 10 m$$^3$$ detector, CODEX-b, about 25 meters away from the LHCb interaction point, in the old DELPHI experiment cavern, in view of HL-LHC. In this case as well, backgrounds would be reduced by an existing concrete wall, complemented by passive shielding and active vetos to be installed. In the baseline configuration, resistive-plate chambers (RPCs) would be used on each face of the cubic detector, which would be complemented by further RPCs inside the volume. The broad LLP search program of this experiment would benefit from the ability to combine information with the existing data stream of the LHCb detector. A demonstrator of smaller size (2 x 2 x 2 m$$^3$$), CODEX-β, should be installed in 2022-2023 and be operated during a part of Run-3, as a proof of concept.

An 18-meter diameter, 56-meter long shaft above the ATLAS experiment, which has been used for the ATLAS detector installation in the cavern but which is not used during normal LHC operation, could also be instrumented with RPCs to search for LLPs in view of the HL-LHC, as proposed in the ANUBIS project. This experiment could be combined with ATLAS information to veto and estimate the SM particle backgrounds, using timing information to reject cosmic rays which would travel in the opposite direction. A demonstrator, proANUBIS, should be installed during Run-3.

On a longer timescale, the AL3X project would aim to exploit the cavern and part of the current ALICE experiment, should its current heavy-ion program finish after Run-4. In this project, the current interaction point would need to be upgraded to run at the nominal HL-LHC luminosity and also to be moved, in order to allow LLPs to travel some distance before decaying in the detector. AL3X would be re-using the existing L3 magnet and ALICE time projection chamber, adding some shielding material in front.

While the dedicated detectors above are able to extend the coverage for neutral LLPs, MoEDAL+MAPP and milliQan are specifically designed to cover charged LLPs.

The MoEDAL experiment, which is installed in the LHCb cavern since Run-1, targets long-lived highly-ionising particles which would be produced in the collisions, such as hypothetical magnetic monopoles, or singly-charged massive LLPs, such as long-lived supersymmetric partners of the leptons. The detector consists of two parts which can passively record events during the runs and are then read out to look for signs of new physics. The first part is a plastic nuclear track detector, in which the passage of charged particles would be recorded as visible track damage. The second part is a magnetic monopole trapper made of nearly one ton of aluminium, which would, as its name indicates, capture magnetic monopoles. The scanning of the volume with a SQUID magnetometer would then reveal their presence. The experiment has placed stringent limits on these models, as shown in Figure 8. For Run-3, the detector is upgraded to MoEDAL-MAPP: the MAPP addition comprises two new detectors, one (MAPP-LLP) looking for LLPs decaying to charged particles, and the other one (MAPP-mQP) looking for millicharged LLPs, that is particles carrying a fractional electric charge as low as $$O(0.001e)$$.

Figure 8: Limits set by the MoEDAL experiment on the mass of the magnetic monopoles as a function of their magnetic charge, compared to some general-purpose detector results. (Credit: J. Pinfold @ Phil.Trans.Roy.Soc.Lond.A 377 (2019) 2161, 20190382 )

Millicharged LLPs are also the target of the milliQan experiment. After running a scintillation-bar prototype in 2018, two complementary, scintillation-based detectors will be used in Run-3, with a possible extension proposed for the HL-LHC. Installed in a drainage and observation gallery 70 meters underground and 33 meters away from the CMS interaction point, the detectors benefit from rock shielding. The projected sensitivity is shown in Figure 9. An upgrade, called FORMOSA, is also proposed as part of the FPF.

Figure 9: Existing sensitivity using the 2018 demonstrator and projected sensitivity to millicharged particles by the milliQan collaboration, compared to other experiments, shown in the plane of the charge versus the mass of the particles. (Credit: milliQan Collaboration @ Phys. Rev. D 104 (2021) 3, 032002 )

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