International Journal of Modern Physics A

High energy hadron colliders have been in the forefront of particle physics for more than three decades. At present, international particle physics community considers several options for a 100 TeV proton–proton collider as a possible post-LHC energy frontier facility. The method of colliding beams has not fully exhausted its potential but has slowed down considerably in its progress. This paper briefly reviews the accelerator physics and technology challenges of the future very high energy colliders and outlines the areas of required research and development towards their technical and financial feasibility.

We consider diverse examples of science goals that provide a framework to assess luminosity goals for a future 100-TeV proton–proton collider.

The scaling formulas in this paper — many of which involve approximation — apply primarily to electron colliders like CEPC or FCC-ee. The more abstract “radiation dominated” phrase in the title is intended to encourage use of the formulas — though admittedly less precisely — to proton colliders like SPPC, for which synchrotron radiation begins to dominate the design in spite of the large proton mass.

Optimizing a facility having an electron–positron Higgs factory, followed decades later by a p, p collider in the same tunnel, is a formidable task. The CEPC design study constitutes an initial “constrained parameter” collider design. Here the constrained parameters include tunnel circumference, cell lengths, phase advance per cell, etc. This approach is valuable, if the constrained parameters are self-consistent and close to optimal. Jumping directly to detailed design makes it possible to develop reliable, objective cost estimates on a rapid time scale.

A scaling law formulation is intended to contribute to a “ground-up” stage in the design of future circular colliders. In this more abstract approach, scaling formulas can be used to investigate ways in which the design can be better optimized. Equally important, by solving the lattice matching equations in closed form, as contrasted with running computer programs such as MAD, one can obtain better intuition concerning the fundamental parametric dependencies. The ground-up approach is made especially appropriate by the seemingly impossible task of simultaneous optimization of tunnel circumference for both electrons and protons. The fact that both colliders will be radiation dominated actually simplifies the simultaneous optimization task.

All GeV scale electron accelerators are “synchrotron radiation dominated”, meaning that all beam distributions evolve within a fraction of a second to an equilibrium state in which “heating” due to radiation fluctuations is canceled by the “cooling” in RF cavities that restore the lost energy. To the contrary, until now, the large proton to electron mass ratio has caused synchrotron radiation to be negligible in proton accelerators. The LHC beam energy has still been low enough that synchrotron radiation has little effect on beam dynamics; but the thermodynamic penalty in cooling the superconducting magnets has still made it essential for the radiated power not to be dissipated at liquid helium temperatures. Achieving this has been a significant challenge. For the next generation p, p collider this will be even more true. Furthermore, the radiation will effect beam distributions on time scales measured in minutes, for example causing the beams to be flattened, wider than they are high. In this regime scaling relations previously valid only for electrons will be applicable also to protons.

Extending the Standard Model with sterile (“right-handed”) neutrinos is one of the best motivated ways to account for the observed neutrino masses. We discuss the expected sensitivity of the Circular Electron Positron Collider (CEPC) for testing such extensions. An interesting scenario is given by symmetry protected seesaw models, which theoretically allow for sterile neutrino masses around the electroweak scale with up to order one mixings with the active (SM) neutrinos.

When the masses of the sterile neutrinos are well above the electroweak scale, they affect precision data via effective non-unitarity of the leptonic mixing matrix in a model independent way. The expected improvement of the electroweak precision observables from the CEPC may allow to test mixings between active and sterile neutrinos down to $\sim 5\times 10^{-3}$ (using currently discussed CEPC performance parameters).

For sterile neutrinos with masses around the electroweak scale, direct searches are possible. Such tests are given by the search for sterile neutrino decays at the $Z$ pole, by deviations from the SM cross section for four leptons at and beyond the $W$ threshold, and by Higgs boson production and decays. The expected sensitivities at the CEPC could reach down to mixings as small as $\sim 5\times 10^{-5}$.

In this write-up, we summarize the production of non-SM Higgses in the Type II Two Higgs Doublet Model at a 100 TeV $pp$ collider, as well as their decays. We present the reach for $pp\to bb{H}^0∕A\to bbtt$, $bb\tau \tau$ as well as $pp\to tb{H}^{\pm }\to tbtb$, $tb\tau \nu$ at the 100 TeV $pp$ collider and outline the possible search channels via Higgs exotic decays. We point out that a combination of these conventional channels potentially yields full coverage for $tan\beta$ and pushes the exclusion limits from the ${𝒪}(1)\mathrm{\text{TeV}}$ at the LHC to the ${𝒪}(10)\mathrm{\text{TeV}}$ at a 100 TeV $pp$ collider, whereas the exotic decays of a heavy Higgs into two light Higgses or one light Higgs plus one SM gauge boson provide alternative discovery channels.