Multiboson production at multi-TeV lepton colliders as complementary probes to rare Higgs decays

The universe is built on a set of fundamental rules that govern how particles interact, a framework physicists call the Standard Model. For decades, this theory has successfully explained almost everything observed in particle collisions, from the behavior of light to the forces holding atomic nuclei together. Yet, there is a lingering suspicion among scientists that this model is incomplete. It works well at the energies we can currently reach, but it struggles to explain why the universe has the specific properties it does, particularly regarding the mass of the Higgs boson, a particle discovered a decade ago that gives other particles their mass. If new, heavier particles exist beyond our current reach, they might subtly influence the behavior of the Higgs boson, leaving tiny fingerprints in how it decays or interacts. The challenge is that these fingerprints are often hidden in rare events or are so faint that they are easily drowned out by the noise of more common processes.

To find these hidden clues, scientists look at two main avenues. One is to produce a vast number of Higgs bosons and study their rare decay patterns with extreme precision, looking for even the smallest deviation from the expected behavior. The other is to smash particles together at incredibly high speeds, using the sheer energy of the collision to amplify any subtle effects from new physics. While the Large Hadron Collider has been the workhorse for the first approach, a new generation of machines is being proposed that would collide particles at energies far beyond what is currently possible. These future machines, specifically lepton colliders that smash electrons or muons together, offer a unique opportunity. Because these particles are fundamental and have no internal structure, the energy of the collision is used entirely to probe the laws of physics, rather than being wasted on breaking apart composite particles like protons. This allows researchers to test the limits of the Standard Model in a way that is both cleaner and more powerful than ever before.

A recent study by researchers at CERN and Italian institutions explores exactly how these future high-energy machines could reveal new physics. The team focused on a specific set of theoretical interactions that could modify how the Higgs boson turns into pairs of light particles, such as two photons or a photon and a Z boson. These rare decays are currently being measured at the Large Hadron Collider, and the High-Luminosity upgrade is expected to improve those measurements significantly. However, the researchers asked a different question: could the same new physics be detected more effectively by looking at the production of multiple heavy particles in a single collision, rather than just watching the Higgs decay? They investigated what would happen if they collided muons at a center-of-mass energy of 10 TeV, a scale far beyond current capabilities, and looked for the creation of two or three bosons—particles that carry the fundamental forces—along with Higgs bosons.

The researchers used a mathematical framework known as Effective Field Theory to model how new, heavy particles might influence these collisions without needing to know exactly what those heavy particles are. In this approach, the effects of unknown heavy physics are treated as small ripples in the known laws of nature. The study simulated the collisions and calculated how often specific events would occur if these ripples existed. They found that while the rare decays of the Higgs boson provide a very sensitive test, the production of multiple bosons at high energies offers a complementary and, in some cases, superior way to constrain these new effects. The key insight is that the influence of new physics often grows stronger as the energy of the collision increases. While the rate of rare Higgs decays is fixed by the mass of the Higgs itself, the rate of producing multiple bosons can surge dramatically as the collision energy rises, making the signal of new physics much louder against the background of standard processes.

The team analyzed several specific scenarios, including the creation of two bosons and the creation of three bosons. They discovered that the production of three bosons, a process that is naturally rarer and more complex, becomes the most powerful tool for discovery at these extreme energies. In their simulations, the sensitivity to new physics in these three-boson events grew so rapidly with energy that it surpassed the projected precision of the High-Luminosity LHC and even the future circular electron-positron collider known as FCC-ee. This is particularly true for processes involving three bosons, where the new physics effects are enhanced by the high energy of the collision, allowing the researchers to set limits on the scale of new physics that are competitive with the most powerful future proton colliders. The study showed that by combining the data from two-boson and three-boson production, scientists could close gaps in their understanding that would otherwise remain open, effectively ruling out certain combinations of new physics parameters that current methods might miss.

One of the critical aspects of this work was ensuring that the theoretical calculations remained valid at such high energies. The researchers had to verify that the energy of the collisions was not so high that it would break the assumptions of their mathematical model, which relies on the idea that the new particles are too heavy to be created directly. They found that for a collision energy of 10 TeV, the model holds up well, provided the new physics scale is not too low. This validation is crucial because it confirms that the predictions made for these future machines are reliable and that the potential to discover new physics is genuine. The study also highlighted that the production of a Higgs boson alongside a photon is a particularly clean channel for detection, as the background noise from standard processes is naturally low, making any deviation caused by new physics stand out clearly.

The findings suggest a shift in strategy for the search for new physics. Instead of relying solely on the precision of rare decay measurements, which are limited by the number of Higgs bosons that can be produced, the field could benefit immensely from pushing the energy frontier. The ability to produce multiple bosons at multi-TeV energies acts as a magnifying glass, turning faint theoretical signals into observable events. This approach does not replace the need for precision measurements at lower energies but rather complements them, offering a different perspective that can break through limitations where other methods stall. The researchers demonstrated that a 10 TeV muon collider would be a formidable tool in this regard, capable of probing the nature of the Higgs boson and the potential existence of new particles with a sensitivity that rivals or exceeds the most ambitious future projects currently on the drawing board.

Ultimately, the study provides a clear roadmap for how the next generation of particle colliders could operate. By focusing on the production of multiple bosons, scientists can leverage the full power of high-energy collisions to test the Standard Model in regimes where it is most likely to show cracks. The results indicate that the search for new physics is not just about building bigger machines to see more particles, but about using the energy of those machines to amplify the subtle effects of the unknown. As the field moves toward the design of these future facilities, the insights from this work will help prioritize which processes to measure and how to interpret the data, ensuring that the next breakthrough in our understanding of the universe is found in the right place.