A Pythia8 Tune for Open Charm and Beauty Production in Fixed-Target Collisions

High above the Earth, invisible particles rain down constantly, born when cosmic rays strike the atmosphere. Among these are neutrinos, ghostly particles that rarely interact with anything, yet they carry secrets about the universe's most violent events. To understand where these neutrinos come from, scientists must trace their origins back to the moment they were born: the decay of heavy particles like charm and beauty hadrons. These heavy particles are created when high-energy beams of protons or pions smash into a target, a process that happens not only in the upper atmosphere but also in specialized laboratories where researchers fire particle beams into dense blocks of matter. Predicting how many of these heavy particles are made, and exactly how they move after creation, is essential for calculating the flux of neutrinos that reach our detectors. If the predictions are off, the background noise in experiments searching for new, hidden particles becomes impossible to distinguish from a genuine discovery.

For decades, physicists have relied on computer simulations to model these collisions, using complex software that acts as a virtual laboratory. One such program, Pythia, has been the standard tool for decades, but it was originally tuned to match data from high-energy collisions at the Large Hadron Collider, where particles smash together at energies far beyond what fixed-target experiments can achieve. When scientists tried to use this standard setting to predict what happens in fixed-target experiments—where beams hit stationary targets at lower energies—the results were often wrong. The software tended to predict that the heavy particles would move too fast and be produced in greater numbers than what was actually observed in the data. This mismatch created a blind spot for experiments like SHiP, which are designed to hunt for rare, weakly interacting particles by analyzing the debris from a massive beam dump. Without a more accurate map of how heavy particles are born and behave in this specific energy range, the search for new physics is hampered by uncertainty.

To fix this, a team of researchers from Ghent University has developed a new set of instructions for the Pythia software, tailored specifically for the conditions found in fixed-target collisions. They call this new configuration FTFT. The team did not simply guess at the right settings; instead, they took a vast collection of real-world measurements from experiments conducted over the last forty years. These measurements came from beams of both protons and pions striking various metal targets, recording the speed and direction of the resulting charm and beauty particles. By feeding this historical data into their optimization tools, the researchers adjusted the internal knobs of the simulation until the virtual collisions matched the real ones. They focused on two main things: the shape of the particle distributions, such as how far forward the particles fly and how much sideways momentum they carry, and the total number of particles produced.

The results of this tuning were striking. The standard software settings, which work well for the highest energy collisions, failed to describe the fixed-target data, predicting a spectrum of particle speeds that was too aggressive. The new FTFT tune corrected this by altering how the simulation handles the breakup of heavy quarks into detectable particles and how multiple interactions occur within a single collision. The researchers found that the heavy particles in fixed-target collisions fragment differently than they do at the LHC, requiring a softer, more gentle breakup process in the simulation. They also had to adjust how the simulation scales with energy, moving the reference point from the massive energies of the LHC down to the range relevant for fixed-target beams. Once these shape parameters were locked in, the team applied a final scaling factor to match the total number of particles produced to the experimental measurements. For proton beams, the simulation needed to be boosted by a factor of roughly 2.5, while for pion beams, the boost was about 2.0. These factors account for the complex physics that the standard model misses at these energies.

For the even heavier beauty particles, the situation was slightly different. Because beauty production is so rare and difficult to measure in detail at these energies, the team could not tune the shape of the distribution. Instead, they simply applied a scaling factor to the total number of beauty pairs produced. Surprisingly, for beauty, the standard simulation was already quite close to the data, requiring only a tiny adjustment of about 4% for proton beams and 19% for pion beams. This suggests that the fundamental process of creating heavy beauty pairs is better understood than the process of creating charm particles in this regime. The new tune also addressed a specific puzzle regarding the charge of the particles. In collisions with pion beams, there is a known preference for producing negative charm particles over positive ones, a phenomenon driven by the internal structure of the pion beam itself. The standard simulation struggled to capture this asymmetry, but the new FTFT tune, by incorporating a specific set of rules for how pions are structured, brought the prediction much closer to reality, though a small discrepancy remained.

The implications of this work are immediate for the next generation of physics experiments. The SHiP experiment, which is currently being built to search for hidden particles, relies heavily on accurate predictions of neutrino backgrounds. The old simulations underestimated the production of charm particles, which meant the background estimates were likely too low. With the FTFT tune, the predictions for the neutrino flux and the background rates are now grounded in a model that has been rigorously tested against decades of data. This gives the SHiP team a much firmer foundation for their search, allowing them to distinguish between a background fluctuation and a true signal of new physics with greater confidence. Beyond SHiP, this tune is also relevant for understanding the prompt component of atmospheric neutrinos, which are produced when cosmic rays hit the Earth's atmosphere. Since these atmospheric showers involve many secondary collisions at energies similar to fixed-target experiments, the new tune offers a better way to model the heavy particles that contribute to the neutrino flux measured by telescopes.

The researchers are careful to note that while this tune is a significant improvement, it is not a final answer for all possible scenarios. The tuning was performed specifically for the energy range of 20 to 42 GeV, and the parameters were adjusted to fit the available data, which mostly concerns charm mesons. The behavior of charm baryons, which are heavier cousins of the mesons, was not constrained by the data and remains an area of uncertainty. Furthermore, the tune assumes that the production of these particles scales linearly with the size of the target nucleus, an assumption supported by existing data but one that could be tested further. Despite these limitations, the work represents a crucial step forward in bridging the gap between high-energy collider physics and the lower-energy fixed-target regime. By grounding the simulation in the reality of past measurements, the team has provided a tool that turns a source of uncertainty into a reliable predictor, ensuring that the search for the universe's hidden particles is guided by the most accurate map available.