Exploring the Supersymmetric Grand Unified Theories with Gauge Mediation at the Future Proton-Proton Colliders and Hyper-Kamiokande Experiment

The universe we see around us is built on a foundation of particles and forces that physicists have spent decades trying to understand. At the heart of this understanding is the Standard Model, a successful theory that describes how matter behaves, yet it leaves some profound questions unanswered. One of the most persistent mysteries is why the forces of nature, which act differently at low energies, might have been unified into a single force at the very beginning of the universe. This idea, known as Grand Unification, suggests that at incredibly high energies, the distinct forces we observe today merge into one. To make this picture complete, many physicists turn to a concept called supersymmetry. This theory proposes that every known particle has a heavier, invisible partner. These partners could solve deep mathematical problems in physics and provide a candidate for dark matter, the invisible substance that holds galaxies together. However, despite years of searching, no one has ever found these partner particles, leaving scientists to wonder if they are simply too heavy to be seen with current technology or if they exist in a form we have not yet imagined.

A team of researchers has taken a fresh look at this puzzle by combining the ideas of Grand Unification and supersymmetry with a specific mechanism for how these heavy partners might acquire their mass. They focused on a scenario called gauge mediation, where the mass of these new particles is transmitted through the fundamental forces of nature, much like a message passed through a chain of people. The researchers asked a critical question: if these particles exist, where should we look for them? They calculated that the answer depends entirely on the energy scale at which the forces of nature unify. By running detailed computer simulations of how these particles would behave and evolve from the earliest moments of the universe down to the present day, they mapped out two distinct possibilities. Their work suggests that we do not need to choose between looking for these particles in a massive new particle collider or in a giant underground tank of water; the universe might offer us a way to find them in both places, depending on the specific energy scale involved.

The team's simulations revealed a clear dividing line based on the energy scale of unification. If this unification happens at an energy level below a specific threshold, the theory predicts that the heavy gauge bosons responsible for the unification would be light enough to cause protons to decay within a timeframe that the next generation of underground experiments can detect. Specifically, if the unification energy is less than or equal to 0.84 times 10 to the 16th power GeV, the proton would have a lifetime of roughly 5 times 10 to the 34th power years. This is a timescale that the upcoming Hyper-Kamiokande experiment, a massive detector currently being prepared in Japan, is designed to probe. In this scenario, the experiment would look for the rare moment when a proton, the stable building block of every atom, spontaneously breaks apart into a positron and a pion. Finding this decay would be a direct confirmation of the theory, proving that the forces of nature were once unified.

On the other hand, if the unification energy is higher than that threshold, the story changes completely. In this higher-energy regime, defined as MGUT ≥ 0.84 × 10^16 GeV, the lightest neutralino is the Next to the Lightest Supersymmetric Particle (NLSP), which subsequently decays into a gravitino. The researchers found that in this case, the heavy partners of the quarks and gluons, known as squarks and gluinos, would have masses that are surprisingly within reach of future particle accelerators. Their calculations show that the gluino, a partner to the gluon, would have a mass no greater than 8.64 TeV, while the squarks, partners to the first two generations of quarks, would be capped at 11.82 TeV. These numbers are crucial because they fall well within the discovery potential of the proposed 100 TeV proton-proton colliders, such as the Future Circular Collider or the Super Proton-Proton Collider. Unlike the proton decay search, which looks for a single rare event, these machines would smash protons together with such force that they could create these heavy particles directly, allowing scientists to observe their decay patterns and measure their properties.

The study also explored the relationships between the masses of these various particles, revealing a structured pattern that depends on the underlying parameters of the theory. The researchers found that the masses of the colored particles, like the gluinos and squarks, are tightly linked to the energy scale at which supersymmetry is broken. When the unification scale is high, the entire spectrum of these new particles shifts to lower masses, making them easier to produce in a collider. Conversely, when the unification scale is lower, the particles become heavier, pushing them beyond the reach of colliders but bringing the proton decay signal within reach of underground detectors. This creates a complementary picture where the two experimental approaches cover different parts of the theoretical landscape. The team also examined the behavior of other particles, such as the sleptons and the Higgs boson, finding that their masses are similarly constrained by the same rules. For instance, the lighter stop quark, a partner to the top quark, would have an upper mass limit of about 11.66 TeV in the high-energy scenario, while the pseudoscalar Higgs boson would be accessible up to masses of around 10 TeV in the same region.

What makes this work particularly significant is that it provides a roadmap for the next generation of physics experiments. Instead of searching blindly, scientists now have a clear set of targets. If the Hyper-Kamiokande experiment detects proton decay, it will confirm that the unification scale is low and that the gauge mediation mechanism is at work. If that signal does not appear, the focus can shift immediately to the 100 TeV colliders, where the search for gluinos and squarks up to the specific mass limits identified by the researchers will become the priority. The discovery of any of these particles would be a monumental step forward, offering a glimpse into the messenger scale where the message of symmetry breaking is sent, and the effective scale where the breaking actually happens. It would also allow physicists to trace the evolution of the forces through the history of the universe, confirming how the soft terms that give particles their mass change as the energy drops. Ultimately, this research bridges the gap between the invisible world of high-energy theory and the tangible reality of experimental observation, showing that whether the answer lies in the silence of a deep underground tank or the roar of a future collider, the universe is ready to be understood.