Drell-Yan lepton pair production from low to high transverse momentum

In the vast, high-energy collisions that occur inside particle accelerators, protons smash together with such force that they shatter into a spray of new particles. Among the most important of these collisions are those that produce a pair of leptons, a type of fundamental particle that includes electrons and muons. Physicists call this the Drell-Yan process. For decades, these events have served as a crucial laboratory for testing the Standard Model, the theory that describes how the universe's fundamental particles interact. By measuring the properties of the resulting lepton pairs, specifically how much sideways momentum they carry, scientists can probe the inner workings of the proton and search for signs of new physics. However, predicting exactly how these particles should behave has long been a challenge. Theoretical calculations are incredibly precise when the particles move slowly, but they become less reliable as the particles gain speed, while computer simulations used to model the experiments often lack the same level of precision as the best mathematical theories.

A team of researchers has now bridged this gap, creating a new method that combines the most advanced theoretical calculations with flexible computer simulations. Their work allows for a description of these particle collisions that is accurate across a wide range of speeds, from the slowest movements to the most energetic bursts. The team achieved this by taking a state-of-the-art theoretical prediction, which includes complex quantum effects calculated to an extremely high order of precision, and translating it into a format that can be used by standard computer simulations. They did this by extracting key statistical patterns from the theory and using them to adjust the weights of individual events in a simulation, ensuring the final result matches the theory without losing the detailed information about how many other particles are produced alongside the lepton pair.

The core of this achievement lies in how the researchers handled the low-speed region of the collisions. In this regime, the behavior of the particles is dominated by non-perturbative effects, meaning they cannot be calculated using standard step-by-step mathematical expansions. Traditionally, physicists had to fit their models to experimental data to account for these effects, which limited their ability to make truly predictive calculations. In this study, the team replaced that fitting process with a direct calculation from first principles. They used results from lattice quantum chromodynamics, a method that simulates the strong nuclear force on a grid of space-time points, to determine a specific component known as the Collins-Soper kernel. This kernel describes how the particles interact at a fundamental level, and by using a value derived from these simulations rather than from experimental fitting, the team made their prediction more robust and less dependent on prior measurements.

To make this high-precision theory usable for experimentalists, the researchers employed a technique based on information theory. They started with a standard computer simulation that already generated millions of collision events, but which lacked the ultimate precision of the new theory. Instead of trying to rewrite the entire simulation from scratch, they calculated a set of specific statistical moments—essentially average values and patterns related to the sideways momentum and the angle between the two leptons—from their precise theory. They then used a mathematical principle called maximum entropy to find the set of adjustments that would make the simulation match these moments while changing the original data as little as possible. This process resulted in a new set of weights for each event in the simulation. When applied, these weights transformed the simulation so that it reproduced the high-precision theory results with remarkable accuracy, while retaining the simulation's ability to describe complex details like the number of jets, or sprays of particles, produced in the collision.

The results of this method were tested against real data collected by the ATLAS experiment at the Large Hadron Collider. The researchers compared their new, reweighted simulation to the measured distribution of the lepton pairs' sideways momentum. In the region where the particles move slowly, up to about 10 gigaelectronvolts, the agreement between the theory and the data was excellent, with deviations of no more than 1.3 percent. As the momentum increased, the agreement remained strong, though the theoretical uncertainty grew slightly, reaching about 3.5 percent at the highest energies. Crucially, the team demonstrated that this method works not just for the momentum distribution, but also for other observables, such as the angle between the leptons and the number of additional jets produced. The simulation successfully preserved the complex correlations between these different features, which is essential for searching for new physics that might hide in the details of multi-particle events.

One of the most significant aspects of this work is that it provides a strictly positive weight for every event, meaning the simulation remains physically valid and can be used directly by experimental collaborations without the complications of negative probabilities that sometimes arise in high-precision calculations. The team also showed that their method is flexible enough to be applied to different types of initial simulations, including those generated by other popular software tools. By using only a small number of statistical moments to transfer the information from the theory to the simulation, they avoided the computational nightmare of trying to match every single detail of the theory directly. This approach allows the high-precision insights from the theory to be applied to the full, complex final state of the collision, including the production of up to six jets of particles.

The study also quantified the various sources of uncertainty in their prediction. They found that the largest remaining uncertainties come from the theoretical scales used in the calculation and the parton distribution functions, which describe the internal structure of the proton. The uncertainty introduced by the lattice QCD calculation of the Collins-Soper kernel was found to be small, contributing at most 2.6 percent in the lowest momentum bin and less than 1 percent at higher momenta. This confirms that the lattice approach is a viable and precise alternative to fitting parameters to data. The researchers also noted that the statistical uncertainty of their calculation is currently limited by the available computing power, suggesting that even more precise results could be achieved with greater resources.

Looking ahead, this technique opens the door for applying similar high-precision methods to other important processes, such as the production of W bosons, pairs of vector bosons, and the Higgs boson. By providing a way to incorporate the most advanced theoretical knowledge into the flexible framework of Monte Carlo simulations, the researchers have given experimentalists a more powerful tool for interpreting their data. The ability to test the Standard Model with such precision across the entire range of particle momenta, from the softest interactions to the most energetic collisions, represents a significant step forward in our understanding of the fundamental forces of nature. The code and methods developed in this work are publicly available, allowing other scientists to apply these improvements to their own analyses and further refine our picture of the subatomic world.