# A game of colliders: is CLIC the Tyrion Lannister of the future collider wars?

Despite the title, I have never seen a single Game of Thrones episode. I read the first of the books though some time ago, and while the book was interesting and catchy, everyone there was very but very bad and miserable, so I was not really motivated to proceed further. This said, I remember that Tyrion Lannister seemed at a first glance a character that might last a couple of chapters at most, specially given the low survival rate on the GoT universe. But apparently, at least from the Twitter spoilers, he was remarkably still around in the last episodes of the series. So all in all, his strategy was reasonably succesful: starting as an underdog, he became one of the dominant figures of the storyline, which is no small feat taking into account that terrible fire-breathing dragons were also involved. So Tyrion Lannister seemed to me to be a not too bad analogy to discuss some interesting recent developments about the future collider saga, namely the fact that the Compact Linear Collider (CLIC), which for a long time seemed not to be topping the bookies’ predictions , now appears to slowly but surely be gaining traction within the community. I will try to explain in this post why this might be the case.

What is CLIC? A nice summary of this future collider project can be found in the talk that Aidan Robson gave at the Nikhef Colloquium recently. CLIC would be a high-luminosity, multi-TeV electron–positron collider to be built at the CERN site which would operate in three phases. The first one, CLIC-1, would have a center of mass energy of 380 GeV and would focus on precision studies of the Higgs boson and the top quark, which are sensitive to potential new physics beyond the Standard Model (SM) via quantum corrections. Such program is to common to other proposed lepton colliders such as the International Linear Collider (ILC), the FCC-ee or the Chinese CepC. The key difference of CLIC is that it can be be upgraded to CLIC-2 (operating at 1.5 TeV) and then CLIC-3 (at 3 TeV), being thus the only lepton collider over the table that can reach the multi-TeV region. This offers significant advantages, both in terms of guaranteed deliverables (such as the measurement of the Higgs potential) as well as a marked increase in the reach for direct and indirect physics beyond the SM. Moreover, this upgrade program could be adjusted to other center of mass energies after stage-1, provided there is a good scientific motivation for that.

Indeed, one of the main physics goals of any future particle collider beyond the high-luminosity LHC should be the precise measurement of the Higgs self-coupling. The strength of the self-interactions of the Higgs boson plays a crucial role in the mechanism that drives electroweak symmetry breaking, and might be related to cosmological phenomena such as the matter-antimatter asymmetry or the phase transitions in the early universe. Some researchers are even proposing that the Higgs boson itself was the responsible for inflation. In this respect, the high-energy stages of CLIC offer the potential of measuring the Higgs self-coupling with a precision of a few percent . Lower energy lepton colliders, in particular the circular FCC-ee and CepC, would not be able to directly access this self-coupling via Higgs pair production though still they could be sensitive to it via quantum corrections to single Higgs production, emphasising the need for a global approach. Note that only for center of mass energies above 500 GeV is a lepton collider able to produce pairs of Higgs bosons at an appreciable rate.

CLIC would also be able to extend the HL-LHC reach for searches of new particles and interactions. In the context of such searches for potential new physics beyond the SM, it should be emphasised again that the distinction between direct (where one explicitly produces new heavy particles) and indirect (where quantum effects modify the properties of known particles) constraints is rather arbitrary. Indeed, with both types of searches one is being sensitive to kinematic regions never explored before, which is the main point of a search. To illustrate the potential of indirect searches at lepton colliders such as CLIC, in the figure below I show the expected bounds on the Wilson coefficients of specific dimension-6 operators of the Standard Model Effective Field Theory (the SMEFT) from future colliders, compared to the reach of the HL-LHC. Note from the right y-axis that these bounds can be interpreted as probing energies as high as 50 TeV, depending on the operator, which is much higher that the actual center of mass energy (3 TeV in stage-3 of CLIC). Here the SMEFT is the lower-energy effective theory of any ultraviolet completion of the Standard Model, and is written as a tower of higher-dimensional operators, $\mathcal{L}=\mathcal{L}_{\rm SM}+\sum_{i=1}^{N_{d6}}\frac{c_i}{\Lambda^2}\mathcal{O}_i$, with $\latex \Lambda$ is the scale of new physics where the effective theory approximation breaks down. This way, with precision measurements of “SM” processes, either at proton-proton or at lepton-colliders, we can thus be sensitive to energy scales way above those of which that probed by direct searches. For these kind of studies the very clean environment of electron-positron collisions, with a high signal to background ratio, is very beneficial.

Ok, so far so good. Now about the challenges: despite the very attractive scientific prospects, the main difficulties to be overcome by CLIC (partly shared with any other future collider proposal) are the costs and the energy footprint. In the table below I show an overview of the (approximate) costs of power consumption for different proposals for future colliders, as summarised in the documents for the European Strategy for Particle Physics update. Assuming that very rough conversion factor that 1 ILCU = 1 CHF = 1 \$ hold, then one sees that the costs for the various Higgs factories (ILC, CLIC-1, CEPC) are similar, with the exception of FCC-ee, which would be around a factor 2 more expensive. Note however that the FCC-ee cost includes also the costs of digging the 100 km tunnel.  If the FCC-hh is built afterwards, then its costing would be a further CHF17K, but if FCC-hh is built standalone. one needs to add the CHF7K for the tunnel. This implies that the costings for the FCC-ee and the FCC-hh become more attractive once they are considered as a joint facility, rather than as two single experiments, since then the tunnel digging costs are shared between the two of them. In other words, assuming that the FCC-hh is built afterwards (and this is a big if), then the costings of FCC-ee become comparable to those of CLIC stage-1, ILC250, and CepC.

Let me also emphasise however that the total costs of these facilities needs to the factored out by its total operation time: this is not a on-off payment but rather a long-term investment in cutting edge fundamental science and technology, with quantifiable returns on investment also in terms of spin-offs, education, and outreach. Another interesting number in this comparison is the power consumption required by these facilities: between stage-1 and stage-3, the power consumption of CLIC would increase by more than a factor 3, where its energy footprint would become comparable to that of the FCC-hh, the 100 TeV future hadron collider.

What is then the gist of the matter? Why, given that its physics potential is comparable or superior to that of other electron-positron high-energy colliders (in particular thanks to its higher in center of mass energy) and that the costs are not particularly worse, CLIC might seem to be the underdog in the future collider wars? One reason has to do with the long-term scientific strategy that CERN will select for its future. Certainly, there is a strong motivation for CERN to plan ahead such that there is a new collider operating on site once the HL-LHC program is completed around 2035. The question, of course, is what type of collider should that be. For example, the advocates of the circular project, FCC-ee, advocate strongly that this project could indeed start by 2035 (provided the construction of the 100 km tunnel starts around 2025) and moreover that it would naturally pave the way towards the 100 TeV hadron collider since the tunnel would already be in place (in the same way as LEP paved the way to the LHC, the argument follows). Most certainly CERN is not going to build two lepton colliders, so if one decides to follow this option (as opposed to say moving directly to a higher energy proton collider), then the choice would be between CLIC and FCC-ee. In this case, the main argument in favour of the FCC-ee as opposed to CLIC is that it facilitates the eventual construction of a 100 TeV (or higher) hadron collider. So CLIC advocates need to (scientifically) fight not only with the FCC-ee aficionados but also with those of the 100 TeV hadron collider.

This is, however, only a small part of the story, since also the role played by the Asian community will be crucial. In particular, whether or not the Japanese keep pushing the ILC project, in principle with the support of CERN (under active discussion now) and the Chinese move forward with their Higgs factory project CepC (increasingly likely) will affect any decision that CERN takes in this respect. It is clear that the chances of CLIC would increase if the ILC does not move forward, for example, specially since ILC is unlikely to be realised without CERN’s support. Note, in any case, that CLIC, in particular due to its unique reach into the multi-TeV regime, has from many points of view a complementary physics program to that of the Higgs factories. It is therefore a complicated discussion with many actors involved.

The question of the timescales is also of paramount importance in this discussion: as mentioned above, ideally one would like the next collider to start operation as soon as HL-LHC is completed (if built on the CERN site) or as soon as possible if it is built in some other location, in Asia for example. According to the timeline below, both CLIC and the ILC could start operation as soon as 2034, with CepC even a few years earlier. FCC-ee would start shortly afterwards, but with as many attractive features as it has, it would also delay the start of the CERN’s 100 TeV hadron collider by up to around 2060 at the earliest. Even by the standards of high energy physics, this is perhaps planning far too long in the future: I will be lucky to be around to see the first 100 TeV collisions, though perhaps I will have uploaded my brain to the cloud by then ;). This is thus another important factor to take into account in the discussion for future colliders: is it wise to plan ahead that far in the future? Maybe, I don’t have the answer for this question. In this context, another of the selling points of CLIC is that its energy can be adjusted to tailor to any new developments on our field, for example, hints or even discoveries of new physics that might be provided by the HL-LHC or evidence for heavy dark matter particles. In this case these new insights could be use to tune the center of mass energy of CLIC after the initial (Higgs and top factory) stage to ensure a maximal scientific return.

What are then the next steps? If CERN wants to have a new particle collider operative by the time the HL-LHC program is completed, a decision about start digging tunnels (or replacing and producing magnets) needs to be made by 2025 at the latest. This means that the recommendations that will be provided by the current EPPSU, to be presented by 2020, will not be definitive but will anyway be very important to inform the 2025 decision. For example, a recommendation to invest in further R&D for the CLIC accelerator technologies could be understood as a sign that this machine could be the future of CERN. It is not written in stone that the high-energy frontier can only be reached by hadron collisions, and perhaps plasma wakefield acceleration or muon colliders will be the next big breakthrough in particle physics. In the meantime, we want a collider with a bullet-proof physics case, that combines guaranteed deliverables with a wide exploration potential and that is based on demonstrated reliable accelerator technologies. We also want to avoid duplications and overlaps and we should combine global efforts in HEP in an optimal way. The Strategy Group in charge of writing these recommendations has a challenging task in front of them, so we should all stay tuned for developments!

Correction: I fixed a mistake in the FCC tunnel costings, thanks to Aidan Robson for pointing this to me!