The fastest, cheapest particle physics path to a Higgs factory

Deep underground, this tunnel is part of interior workings of the Large Hadron Collider (LHC), where protons pass each other at 299,792,455 m/s while circulating in opposite directions: just 3 m/s shy of the speed of light. Particle accelerators like the LHC consist of sections of accelerating cavities, where electric fields are applied to speed up the particles inside, as well as ring-bending portions, where magnetic fields are applied to direct the fast-moving particles toward either the next accelerating cavity or a collision point.

This reconstruction of particle tracks shows a candidate Higgs event in the ATLAS detector at the Large Hadron Collider at CERN. Note how even with the clear signatures and transverse tracks, there is a shower of other particles; this is due to the fact that protons are composite particles, and due to the fact that dozens of proton-proton collisions occur with every bunch crossing. At higher energies, discoveries that don’t appear at lower energies become possible. Modern particle detectors are like a layer-cake, with the ability to track the particle debris in order to reconstruct what happened as close to the collision point as possible.

The first robust, 5-sigma detection of the Higgs boson was announced a few years ago by both the CMS and ATLAS collaborations. But the Higgs boson doesn’t make a single ‘spike’ in the data, but rather a spread-out bump, due to its inherent uncertainty in mass. Its mass of 125 GeV/c² is a puzzle for theoretical physics, but experimentalists need not worry: it exists, we can create it, and now we can measure and study its properties as well. Direct detection was absolutely necessary in order for us to be able to definitively say that.

The observed Higgs decay channels vs. the Standard Model agreement, with the full suite of Run 1 data from ATLAS and CMS included. The agreement is astounding, and yet frustrating at the same time, as no evidence for either a second Higgs boson or for a non-Standard Model Higgs boson has yet arisen.

A series of infrastructure upgrades, some of which have already taken place and others which are still to come later this decade, will transform the LHC into the HL-LHC: the high luminosity LHC. It will be capable of collecting superior amounts of high-quality data, each year, as was taken over the LHC’s first decade of life, from 2008-2018. However, to learn more about the Universe at a fundamental level, a machine fundamentally capable of probing what the HL-LHC cannot will need to be built.

The rest masses of the fundamental particles in the Universe determine when and under what conditions they can be created, and also relate to how long they can survive after their creation during the hot Big Bang. The lessons learned from our experiments and observations enable us to determine what sort of collider should be designed to produce large numbers of each species of particles, with the next major goal being to build a “Higgs factory” for studying the Higgs boson precisely.

The cross-section for producing a Higgs boson (plus other particles) through various production channels at a lepton-antilepton collider, with an electron-positron collider being the leading option. The enormous yellow peak corresponds to producing a Z-boson and a Higgs boson together: the most prolific production channel, which peaks at 216.3 GeV of energy: the Higgs boson mass plus the Z-boson mass.

The Future Circular Collider (in blue) would overlap slightly with the current Large Hadron Collider, but requires an additional ring (and tunnel) somewhere upward of 80 km in circumference: dwarfing the LHC’s current 27 km circumference. Bigger tunnels and stronger magnets are needed for a more energetic hadron collider, with the FCC proposing ~16 T magnets, approximately double the LHC’s current magnet strength.

This interior view of the Large Hadron Collider shows the outside of the accelerator where the particle beam passes through, where it receives electric “kicks” to accelerate it and collimation “squeezing” from bending magnets. With ~7-8 tesla electromagnets, it can achieve collision energies of ~14 TeV; stronger magnets (and/or a larger radius for the ring) are needed for higher energies.

This superconducting magnet from the National High Magnetic Field Laboratory can achieve sustained fields of 32 T, or about four times the field strength of the magnets currently powering the LHC. This magnet first came online in 2017, and won the R&D 100 award in 2022.

Although there are many novel proposals for new particle colliders, including in China, at CERN, and at Fermilab, the question of whether to build a circular machine, a linear lepton collider, or to pursue a novel muon collider all remain options on the table. In an ideal world, we’d get a linear machine to study the Higgs and the electroweak phase transition with great precision, and then a circular machine to collide hadrons at even higher energies. But funding, political realities, and popular opinion will also play a major role in determining what decisions get made.

This set of radiofrequency cavities within a linear accelerator in Australia consist of a very intricate electromagnetic setup. These cavities can accelerate electrons and/or positrons by up to about 30 MeV of energy for each meter of length. Unless this value can be increased substantially, a very long linear collider (of nearly 10 km) will be needed to reach the desired energies to produce a Higgs factory.

Relativistic electrons and positrons can be accelerated to very high speeds, but will emit synchrotron radiation (blue) at high enough energies, preventing them from moving faster. This synchrotron radiation is the relativistic analog of the radiation predicted by Rutherford so many years ago, and has a gravitational analogy if you replace the electromagnetic fields and charges with gravitational ones. Protons emit just one ten-trillionth of the synchrotron radiation that electrons do, and building LEP3 in the current LHC tunnel would struggle, but not prohibitively, to overcome this limitation of physics.

When two particles collide, there is the possibility of getting a large number of “daughter” particles out. However, when those two particles are electrons and positrons (or any lepton-antilepton combination) of equal energies but opposite momenta, the opportunity to produce a combination of particles with the exact combined rest mass of the collision energy increases greatly. This strategy is why an electron-positron machine is so attractive as a candidate for, for example, a Higgs factory.