NNLL resummation for the production of four top quarks

In the vast, high-energy collisions that occur inside the Large Hadron Collider, particles smash together with such force that they briefly recreate conditions similar to those just after the birth of the universe. Among the countless interactions that happen in these moments, one stands out for its extreme rarity: the simultaneous creation of four top quarks. The top quark is the heaviest known elementary particle, and producing even a single pair of them is a difficult feat; creating four at once is a statistical anomaly that happens only a handful of times in a trillion collisions. Because this event is so rare and involves the heaviest particle in nature, it acts as a sensitive probe for the fundamental forces of the universe. It offers a unique window into how the top quark interacts with the Higgs boson, the particle responsible for giving other particles mass, and it serves as a strict test for theories that might extend beyond our current understanding of physics. If the laws of nature behave slightly differently than predicted, this rare four-quark event is one of the places where those deviations would most likely appear.

To study this elusive process, researchers at Nikhef and the University of Münster have developed a new, highly precise way to calculate what should happen when four top quarks are produced. In the world of particle physics, scientists use complex mathematical models to predict the outcome of collisions, but these models often struggle when the energy of the collision is just barely enough to create the heavy particles. In these "threshold" regions, standard calculations can become unreliable because they miss subtle, cumulative effects that occur when particles move slowly relative to one another. The team, led by Melissa van Beekveld, Anna Kulesza, Michele Lupattelli, and Tommaso Saracco, has refined their calculations to include these missing effects with unprecedented accuracy. They have combined the best existing fixed-order calculations with a sophisticated technique called threshold resummation, which effectively sums up an infinite series of small corrections that become important when the collision energy is tight. This approach allows them to predict the total number of four-top events and how their mass is distributed with a level of detail that was previously impossible.

The researchers applied their new method to the conditions of the Large Hadron Collider, specifically at a collision energy of 13.6 tera-electronvolts. When they analyzed their new, more complete predictions, they found a significant shift in the expected results compared to previous theoretical estimates. The total number of four-top events predicted by their new model is nearly 48 percent higher than the previous best estimate. This increase is not a sign of error in the old work, but rather a sign that the new method captures physical effects that were previously overlooked. Furthermore, the new calculations are much more stable; the range of uncertainty around the predicted number of events has shrunk considerably, giving physicists a clearer picture of what to expect. This stability is crucial because it means that if future experiments measure a number that differs from this new prediction, scientists can be more confident that the difference points to new physics rather than a flaw in the calculation itself.

Beyond the total count, the team also looked at the distribution of the mass of the four-top system. They found that the shape of this distribution changes noticeably when the new corrections are included. At the lower end of the mass range, the new prediction is about 30 percent higher than the old one, but this difference grows as the mass increases, reaching a 61 percent increase at the highest masses considered. This suggests that the way these heavy particles are produced at the very edge of what is energetically possible is more complex than previously thought. The researchers also noted that their results are beginning to settle into a stable pattern, meaning that adding even more layers of complexity to the calculation is unlikely to change the central prediction drastically. This convergence gives them confidence that they have reached a reliable description of the process.

The implications of this work extend to the ongoing experiments by the ATLAS and CMS collaborations, which have recently measured the rate of four-top production for the first time. The latest measurements from these experiments show a range of values, with ATLAS reporting a cross section of roughly 22.5 femtobarns and CMS reporting around 17.7 femtobarns. While this paper does not perform a direct comparison between these specific measurements and the new predictions, the new theoretical results provide a sharper benchmark against which to compare these experimental numbers in future studies. By reducing the theoretical uncertainty, the researchers have made it easier to tell if the experimental data agrees with the Standard Model or if it hints at something new. The team acknowledges that their work is preliminary and that further analysis is needed to fully map out all sources of uncertainty, including the effects of the top quark's mass and the internal structure of the proton. However, this step forward in precision represents a vital tool for the next generation of discoveries, turning a rare and chaotic collision into a clear signal for the laws of nature.