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# From precision physics to the energy frontier with the Compact Linear Collider

## Abstract

The Compact Linear Collider (CLIC) is a proposed high-luminosity collider that would collide electrons with their antiparticles, positrons, at energies ranging from a few hundred giga-electronvolts to a few tera-electronvolts. By covering a large energy range and by ultimately reaching collision energies in the multi-tera-electronvolts range, scientists at CLIC aim to improve the understanding of nature’s fundamental building blocks and to discover new particles or other physics phenomena. CLIC is an international project hosted by CERN with 75 institutes worldwide participating in the accelerator, detector and physics studies. If commissioned, the first electron–positron collisions at CLIC are expected around 2035, following the high-luminosity phase of the Large Hadron Collider at CERN. Here we survey the principal merits of CLIC, and examine the opportunities that arise as a result of its design. We argue that CLIC represents an attractive proposition for the next-generation particle collider by combining an innovative accelerator technology, a realistic delivery timescale, and a physics programme that is highly complementary to existing accelerators, reaching uncharted territory.

## Main

The discovery of the Higgs boson at the Large Hadron Collider (LHC) in 20121,2 was an important milestone in high-energy physics. It completes a puzzle that scientists have been working on for decades: the Standard Model of particle physics. However, it is known that there must be physics beyond the Standard Model (BSM), for example to account for dark matter and the matter–antimatter asymmetry in the Universe. In the absence of clear guidance towards the scale of BSM physics from the LHC and other experiments to date, plans are already underway to prepare for the next-generation project in high-energy physics.

Among the various proposals for future particle colliders, the Compact Linear Collider3,4,5,6 is currently the only mature lepton-collider project aiming for energies of several tera-electronvolts (TeV). The advantage of CLIC as the next-generation collider following the High-Luminosity LHC (HL-LHC) is that it gives access to two complementary search paths for new physics. The first path focuses on studying known Standard Model processes with unprecedented precision to search for deviations from the predicted behaviour. Such deviations would represent indirect evidence of BSM physics. The second path employs direct searches for new physics phenomena such as the production of new particles. The clean environment of electron–positron collisions is favourable, both for the detection of even tiny deviations of the expected Standard Model properties and for the detection of rare new signals5. Combined, these results from CLIC would provide important guidance for the wider endeavour of particle physics.

The LHC accelerates and collides protons — composite particles made of quarks and gluons, which each carry a varying fraction of the proton’s energy. The complex internal structure of the proton limits knowledge of the individual quarks or gluons de facto participating in the collisions, complicating interpretation of the data. In addition, proton–proton collisions produce high rates of background events induced by strong interactions between quarks and gluons. Interesting interactions need to be filtered from these background events using triggers. Electrons and positrons, on the other hand, are elementary particles, meaning that the colliding system is well defined in terms of particle type, energy and polarization and does not suffer from large backgrounds. In addition, the generally lower cross sections in electron–positron collisions combined with instantaneous luminosities similar to those at the LHC lead to a lower event rate. These characteristics and the low duty cycle of linear colliders make a trigger-less detector readout possible at CLIC. Radiation levels are significantly lower at electron–positron colliders, relaxing constraints in terms of radiation hardness in detector design. Linear colliders such as CLIC provide high levels of electron–beam polarization at all energies, which, for example, might help to characterise newly discovered particles or processes in detail.

Reaching TeV-scale energies in an electron–positron collider is a challenging endeavour. In ring-shaped particle accelerators, such as the LHC, the circulating charged particles lose a fraction of their energy via synchrotron radiation when their trajectories are bent by magnetic fields. The resulting energy loss scales with the fourth power of the energy/mass ratio. Electrons, almost 2,000 times lighter than protons, are therefore especially prone to synchrotron radiation. Linear colliders, where synchrotron radiation is naturally avoided, provide an efficient solution for reaching high electron–positron collision energies.

In circular accelerators, the ultimate collision energy is reached by passing the beam through few acceleration units, at each turn increasing the particle energy by a small amount. In a linear accelerator, however, the full collision energy must be delivered to the particles in a single passage through the accelerator. In this case, the accelerator needs to be equipped with many acceleration structures distributed along its length. In order to keep the scale of a high-energy linear collider project within reasonable limits in terms of length and cost, very high acceleration gradients are required.

## An innovative acceleration technology to reach multi-TeV energies

CLIC is proposed to be built and operated in three stages with increasing collision energy and luminosity, providing collisions in a wide range of centre-of-mass energies from 350–380 GeV up to 3 TeV (ref. 4). Figure 1 shows the CLIC acceleration concept, a two-beam acceleration unit, as well as the footprint of the different CLIC stages for a possible implementation at CERN near Geneva in Switzerland.

The ability of CLIC to reach TeV energies in a compact and cost-effective way is one of its most important design features and unique among the proposed concepts for future electron–positron colliders. Here, the compactness refers to the length of the accelerator complex. It is made possible by a novel two-beam acceleration technology, illustrated in Fig. 1, which enables efficient acceleration of the colliding beams using normal conducting accelerating structures that achieve an acceleration gradient of ~100 MV m–1 (ref. 4). The radio-frequency pulses needed to accelerate the main beams are generated by decelerating a second, high-intensity electron drive beam in dedicated power-extraction structures. An animation of the CLIC accelerator concept can be found at https://go.nature.com/2SyT12u.

Detailed simulation studies have concluded that the optimal collision energy for the first stage of CLIC is 380 GeV (ref. 7), giving access to both precision Higgs-boson and top-quark physics with a targeted integrated luminosity of 1 ab−1 (ref. 3). Neither of these particles has previously been studied in electron–positron collisions. The two-beam accelerating scheme allows for a well-defined upgrade path towards multi-TeV collision energies4; the two higher energy stages at 1.5 TeV and 3 TeV would accumulate 2.5 ab−1 and 5 ab−1 of integrated luminosity, respectively3; see Box 1 for further details. A clear advantage of the staged programme of CLIC is its flexibility: the collision energy or schedule of operation can be adapted in light of any indication of new physics. Note further that — in contrast to circular colliders — the luminosity at a linear collider increases with centre-of-mass energy, making high-energy operation at CLIC particularly advantageous.

First collisions at CLIC could be realised as early as 20353, allowing continued exploration of the electroweak energy scale at the end of the high-luminosity phase of the LHC programme8. With a foreseen schedule of 7–8 years of operation per stage and an additional 2 years of construction and commissioning between stages, CLIC is expected to operate for about 30 years until the early 2060s.

Technical development, optimization and system tests of the accelerator design have resulted in significant progress in recent years. Major investments have been made in the high-power 12 GHz radio-frequency (X-band) linear-collider technology, which is the main pillar of the two-beam acceleration scheme. Long-term operation of accelerating gradients exceeding 100 MV m–1 has been routinely demonstrated in test stands at CERN, KEK and SLAC4. Further, the ambitious luminosity goals of CLIC put stringent requirements on alignment and stability as well as on the quality of the nanometre-sized beams. The required beam quality has been successfully demonstrated in several modern synchrotron light facilities4. The growing use of CLIC-like technology in accelerator projects, for example, light sources, worldwide is particularly important when moving towards industrialisation of the production of CLIC accelerator components.

## A multi-purpose detector for precision physics

The Compact Linear Collider features an advanced detector concept, illustrated in Fig. 2, for high-precision measurements and searches for physics beyond the Standard Model6,9. Modern detector technologies, profiting in particular from the rapid advancement in the silicon industry, as well as detector designs adapted to the favourable experimental conditions at CLIC allow for a highly granular detector system with superior measurement precision, compared to the detectors implemented in the current LHC experiments.

The two innermost sub-detectors of the CLIC detector, both based on silicon-pixel technology, are essential for the measurement of charged particles: a light-weight vertex detector with very small pixels, optimised for the reconstruction of the particle trajectories and their origins (vertices), is surrounded by a large tracking detector, essential for accurate reconstruction of the charged particle momenta. The CLIC detector further comprises sampling calorimeters for electromagnetic and hadronic showers for the measurement of the particle energy. The detection layers of the high-granularity calorimeters are interleaved with dense absorber layers made of either tungsten or steel. The active calorimeter layers are equipped with silicon sensors for the electromagnetic and scintillator tiles coupled to silicon-photomultipliers for the hadronic calorimeter. These sub-detectors are located inside a superconducting solenoid magnet providing a magnetic field of 4 T, itself surrounded by a detector for muon identification, embedded in the magnet return yoke. The muon detectors are based on resistive plate chamber technology. In total, the CLIC detector comprises almost 19 billion readout channels. It is optimised for so-called particle flow analysis10 that improves the energy reconstruction of particle jets (narrow particle sprays originating from quarks or gluons), by combining measurements from all sub-detectors.

The CLIC detector concept was designed in view of physics performance and the experimental conditions6,9, and detailed detector simulations are being carried out covering a broad set of physics observables, using the full centre-of-mass energy range of CLIC5. These simulations are based on realistic modelling of the detector response and include overlay of beam-induced backgrounds at the level expected at CLIC. Such detector simulations are vital for a reliable estimation of the detector performance. The sub-detectors are adapted to the CLIC beam structure as described in Box 1.

Technology demonstrators are built and validated for the most challenging sub-detectors of the CLIC detector, such as the vertex and tracking detectors and calorimeters6. To validate the performance, for instance in terms of energy or position resolution and detection efficiency, prototypes are tested with particle beams. Figure 3a shows a silicon-pixel detector test chip designed in monolithic complementary metal-oxide semiconductor (CMOS) technology for the CLIC tracking detector.

The CLIC detector development is performed in collaboration with other projects studying future collider detector concepts as well as in dedicated detector research and development collaborations such as CALICE11 and FCAL12. Most recently one of the proposed linear collider calorimeter concepts was adapted for the HL-LHC; the calorimeter endcap upgrade of the CMS detector will employ highly granular sampling calorimeters13. A silicon sensor developed for the CMS upgrade is shown in Fig. 3b. Synergy exists between this detector concept and the calorimeters of the CLIC detector, for instance in view of detector calibration, integration and full system aspects.

## The CLIC physics programme

The CLIC programme offers two complementary paths for new physics searches. One path provides indirect access through precision measurements of already known processes and particles, such as the Higgs boson. The other path focuses on direct searches for new physics phenomena, such as the discovery of new particles.

The first stage of CLIC, with a centre-of-mass energy of 380 GeV, offers a precision physics programme focusing on measurements of the Higgs boson and the top quark5. Choosing 380 GeV as the first centre-of-mass energy gives simultaneous access to several Higgs-boson production processes as well as top-quark pair production7. Figure 4a shows the Standard Model cross sections for a number of additional processes at CLIC as a function of the collision energy.

The two main Higgs boson production channels at the first stage of CLIC are Higgsstrahlung, in which the Higgs boson is radiated from an off-shell Z0 boson (e+eZ0H), and Higgs-boson production via W+W fusion (e+eH νe$$\bar \nu$$e). The former is particularly interesting, because Higgs-boson candidate events can be identified in a model-independent way, solely via the properties of the Z0 boson recoiling against the Higgs boson, as shown in Fig. 4b — no assumptions on the Higgs-boson decay are necessary. Such a measurement is only possible at lepton colliders such as CLIC and for example allows a model-independent upper limit well below 1% to be set on the Higgs-boson decay to invisible particles.

Already at the initial stage of CLIC, the Higgs-boson width and many Higgs-boson couplings including the Higgs-boson coupling to charm quarks — very difficult to observe at the LHC due to the large backgrounds — could be measured with percent-level precision14. The study of charm-quark jets at CLIC is facilitated by the excellent flavour-tagging capability of the CLIC detector as well as the low background levels. For specific Higgs-boson couplings such as the ones to bottom quarks, Z0 bosons and W bosons, CLIC would improve the precision significantly with respect to the HL-LHC. For instance, the accuracies of these couplings would improve by a factor of ~5 at the first CLIC stage, and by more than one order of magnitude in the full CLIC programme15.

Furthermore, the first CLIC stage allows for detailed measurement of top-quark pair production including a dedicated threshold scan at centre-of-mass energies around the onset for top-quark pair production at about 350 GeV (ref. 16) as shown in Fig. 4c. The top-quark mass is expected to be determined with a statistical uncertainty of 20 MeV at CLIC; the total uncertainty is 50 MeV and is dominated by current theory uncertainties16. The planned top-quark measurements further enable detailed studies of its electroweak couplings that are sensitive probes in the search for signs of new physics5.

Profiting from the increase of both the W+W-fusion cross section and the luminosity performance for increasing energies at linear colliders, the higher energy stages of CLIC at 1.5 TeV and 3 TeV would further improve the precision on the results discussed above and allow for detailed studies of rare Higgs-boson decays and additional Higgs-boson production channels14. The latter includes event topologies with multiple jets such as the associated production of top quarks and a Higgs boson (e+et$$\bar t$$ H), important for the accurate measurement of the top-Yukawa coupling. This also includes double-Higgs boson signatures, accessible mainly through W-boson fusion (e+eHHνe$$\bar \nu$$e) and the double Higgsstrahlung process (e+eZ0HH), from which the Higgs-boson trilinear self-coupling could be extracted at the 10% level17. In comparison, the HL-LHC will reach an accuracy of only 50% (ref. 18). In both cases the Standard Model Higgs self-coupling is assumed. The self-coupling determines the shape of the Higgs potential, providing important insight into the mechanism of electroweak symmetry breaking. The precision reached at CLIC is at the level of the typical deviations induced by many new physics models19.

The global impact of CLIC’s precision measurements programme on its reach for physics beyond the Standard Model is assessed within the so-called effective field theory framework. It efficiently allows knowledge from many different measurements at different energies to be combined and to be interpreted in terms of general new interactions added to the Standard Model. It also recognizes the added value and complementarity between lepton colliders and hadron colliders. Combining the CLIC input from electroweak (for instance W-pair and fermion-pair production), Higgs-boson and top-quark processes, measured at the three energy stages, yields a significant improvement in the precision of effective field theory parameters and a substantial gain in the energy reach for indirect measurements, going well beyond the physics reach of HL-LHC20. The staged programme of CLIC, covering one order of magnitude in collision energy, is particularly advantageous for those effective field theory operators whose contributions grow with energy. Detailed studies show that the physics programme of CLIC would extend the reach for certain new physics effects to scales beyond 100 TeV (ref. 20). This allows researchers to probe whether, for example, the Higgs boson has a substructure, and allows its dimension to be measured down to sizes of about 10–20 m, corresponding to an energy scale of almost 20 TeV (ref. 20). The size is more than 100,000 times smaller than the proton radius and smaller by a factor of approximately 4 than the HL-LHC reach20.

Direct discovery is often possible up to the kinematic limit of CLIC, for example half the centre-of-mass energy for pair-produced particles with electroweak-sized coupling strengths. CLIC’s discovery potential was benchmarked with signatures from individual models of wide interest, such as models with additional spin-0 particles besides the Standard Model Higgs boson or signatures with flavour-changing neutral currents5,21. For many of these models, CLIC provides competitive sensitivity in a shorter time frame than other collider proposals20.

For example, in super-symmetric extensions of the Standard Model, CLIC is especially competitive for electroweak states such as charginos, neutralinos and sleptons. This includes new particles with masses that are very close to each other in so-called compressed mass spectra which are difficult to observe at hadron colliders5,20.

A wide range of dark matter models can be tested at CLIC, for instance through events with single photons and missing energy, a complementary approach to searches for mono jets and missing transverse energy at hadron colliders5,20. Searches for long-lived particles giving rise to disappearing tracks in the detector will also benefit from the clean environment at CLIC and the excellent tracking detectors. A particularly interesting example of a new particle that could be discovered at CLIC are long-lived Higgsinos with a mass of 1.1 TeV as predicted by certain models in which the Higgsino represents thermal dark matter5,20.

If new particles are found at the HL-LHC or CLIC, their properties (mass, coupling, quantum numbers) can be accurately measured at CLIC, also aided by the ability to polarise the electron beam5. Dedicated threshold scans can be integrated into the CLIC running scenario also for these newly discovered particles.

## Synergies with far-future accelerator technologies

The infrastructure for the next generation of linear colliders such as CLIC is also of interest for collider projects envisioned in the far future, for which new technologies such as dielectric-based acceleration or plasma wakefield-based acceleration may be available. For instance, in plasma wakefield-based acceleration, a region in a plasma is depleted of free electrons using a traversing particle drive beam, causing high electric fields to build up. Acceleration gradients reaching up to 50 billion volts per metre — 500 times larger than the CLIC gradient — have already been demonstrated over a metre using this technique22. Although further studies are needed for these technologies to reach the beam quality and power efficiency needed for particle physics, advances in this area could allow realisation of much more compact linear accelerator designs.

In the context of the CLIC project, these novel acceleration technologies are considered for application within and beyond the CLIC baseline programme3: an electron–positron accelerator reaching centre-of-mass energies of 10 TeV and beyond would become conceivable. Operation at 10 TeV allows for a significant improvement in the Higgs-boson self-coupling determination. At a few tens of TeV even triple-Higgs-boson production becomes accessible. Reaching high luminosities in such a collider would impose unprecedented requirements on the beamline alignment and stability — challenges for which CLIC operation will be an ideal testbed.

Special care is taken to ensure that the CLIC baseline infrastructure is compatible with the use of the novel technologies discussed above, for instance in terms of the beam crossing angle and the laser-straight accelerator layout3. A possible implementation at CLIC could include replacing parts or the full main linear accelerator with dielectric- or plasma-based acceleration units. Furthermore, the CLIC drive-beam complex could be adapted for use in a beam-driven plasma wakefield-based acceleration. The CLIC main linear accelerator injector complex, providing 9 GeV electrons and positrons, could be reused to inject directly into the new main linear accelerator.

If the initial stage of CLIC at 380 GeV is endorsed in the 2020 update of the European Strategy for Particle Physics, the next step towards realisation of CLIC will be a preparation phase aiming to produce a Technical Design Report (TDR) by 2025. Based on the rich and guaranteed 380 GeV physics programme — with first collisions in 2035 and lasting for about a decade — the physics and technology landscape can be re-evaluated to allow for a physics motivated decision on the subsequent large-scale particle-physics facility.

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## Acknowledgements

We would like to thank all members of the CLIC accelerator and CLIC detector and physics (CLICdp) collaborations, who perform detailed studies of the CLIC accelerator design, physics potential, detector design, and research and development on detector technologies. The CLIC project plans have recently been summarized in several comprehensive reports as input to the European Strategy for Particle Physics Update process (https://clic.cern/european-strategy). We gratefully acknowledge all contributors, authors and editors of these publications. In addition, we would like to thank K. Elsener, L. Linssen, A. Robson, P. Roloff, U. Schnoor, S. Stapnes and W. Wuensch who provided further essential input to this publication as well as M. Petrič, M. Vicente Barreto Pinto and M. Weber for their contributions to the figures of this publication.

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Correspondence to Eva Sicking.

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Sicking, E., Ström, R. From precision physics to the energy frontier with the Compact Linear Collider. Nat. Phys. 16, 386–392 (2020). https://doi.org/10.1038/s41567-020-0834-8

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