# Searching for Long-Lived Particles at the LHC

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## 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 the LLP to travel for an observable distance in a given detector before decaying. In the Large Hadron Collider (LHC) experiments, LLPs could be produced in the proton-proton 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 $$t$$ follows an exponentially decreasing probability function$N(t) = N_0e^{-t/\tau}$

As high-energy collisions can lead to large relativistic boosts, if the LLPs are relatively light, the displacement can also be further enhanced in the laboratory frame with respect to the rest-frame lifetime$L = \gamma\beta c\tau$

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 or a suppressed decay phase space. The former case can happen for example if the interaction violates an approximate symmetry which would otherwise forbid the decay to take place. The latter case can happen if the mass difference between the decaying particle and its decay products is small (a so-called compressed mass spectrum), or if the mediator of the decay is very massive. These mechanisms are at play even in the Standard Model (SM), which contains multiple long-lived particles, such as the B, D, or K mesons. It is therefore not unexpected that they could also be at play in theories beyond the SM.

## Signatures of long-lived particles at the LHC

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 other possible interactions with the various detectors. Some examples are described below and graphically shown in Figure 1 for a detector like ATLAS or CMS.

Figure 1: Overview of some long-lived particle signatures in the various subdectors of a generic detector like ATLAS or CMS: 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, calorimeter energy deposits. The signatures represented (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 the inner tracking detector Neutral LLPs decaying to some charged particles in the inner tracking detector (ID) could lead 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 displaced vertex (DV) which would indicate the position of the LLP decay. A charged LLP decaying in the ID could, on the other hand, give rise to an exotic disappearing track signature, if its decay products are an invisible state and a charged particle which has too little energy to be seen in the detector; such is the case in some supersymmetric models 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 soft 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. The ID track associated to an otherwise well-reconstructed lepton (electron or muon), could also appear 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 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 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.

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 decays happens in the calorimeter, the jets formed will be displaced, possibly exhibiting an atypically large ratio of energy deposited in the hadronic calorimeter with respect to the one 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. The geometrical segmentation of some calorimeters can also be used to recover some pointing information, and hence to look for non-pointing photons, that is photons identified in the electromagnetic calorimeter whose flight direction does not coincide with the primary vertex direction. This can also be complemented with further calorimeter timing information. Such a signature can happen for example in some supersymmetric models in which a heavy neutralino decays into a gravitino, which is invisible to the detector, and a Higgs boson which subsequently decays into two photons, which are non pointing.

In the muon spectrometer LLPs with large enough lifetimes could leave a signature of DV in the muon spectrometer, via the same mechanism as the DV signature in the ID. Displaced hadronic jets can also decay 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 signatures 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.(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 do start 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.

A 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 usual analyses, it may not be the case for some LLP searches for which they could remove a significant fraction of the signal candidates.

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

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). These can however be removed by fiducial cuts, 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. This does not mean that the LLP searches are necessarily generally background-free, but the sources of background are often more diversified, including rare mis-reconstructions 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, require data-driven techniques, e.g. using collisionless data containing only cosmic rays or unpaired proton bunches.

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 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 standard objects in order to make sure that the eventual signal events are picked up for further processing amongst the myriad of collisions. In some other situations, a dedicated trigger is needed, but can be devised in such a way as to collect these peculiar events without affecting the recording bandwidth significantly, given the relative rarity of their signature.

## An overview of current results

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)

## New and proposed dedicated detectors

While the ATLAS, CMS and LHCb detectors have all been used to search for LLPs, there is also ongoing work to propose, build prototypes of and even now exploit new LLP detectors at the LHC.

## References

J. Alimena et al, Searching for long-lived particles beyond the Standard Model at the Large Hadron Collider, Phys. G: Nucl. Part. Phys. 47 090501 (2020), arXiv:1903.04497

L. Lee, C. Ohm, A. Soffer and T. T. Yu, Collider Searches for Long-Lived Particles Beyond the Standard Model, Prog. Part. Nucl. Phys. 106, 210-255 (2019), arXiv:1810.12602

ATLAS Collaboration, Performance of the reconstruction of large impact parameter tracks in the inner detector of ATLAS, ATL-PHYS-PUB-2017-014, http://cds.cern.ch/record/2275635

ATLAS Collaboration, Summary Plots for Heavy Particle Searches and Long-lived Particle Searches - July 2022, ATL-PHYS-PUB-2022-034, http://cds.cern.ch/record/2815305

CMS Collaboration, Precision measurement of the structure of the CMS inner tracking system using nuclear interactions, JINST 13 (2018) P10034