Probing the nucleon axial form factor via the $\vec{e}^{\,+} + {}^2\text{H} \rightarrow \bar{\nu}_e + p + p$ reaction below the pion-production threshold

Neutrinos are ghostly particles that zip through the universe, rarely stopping to interact with anything. When they do collide with matter, they often do so by swapping a charge, a process known as a charged-current interaction. To understand these collisions, scientists rely on a mathematical map called the axial form factor. This map describes how the internal structure of a proton or neutron changes when it is hit by a neutrino. While scientists know the value of this map at a single, specific point with great precision, the shape of the map at low energies remains a blurry, uncertain region. This uncertainty is a major problem for massive experiments like DUNE, which aim to study how neutrinos change their identity as they travel long distances. If the map is wrong, the entire experiment's ability to measure the universe's fundamental properties is compromised.

For decades, scientists have tried to pin down this blurry region using neutrino beams, but the results have been inconsistent and difficult to interpret. A new theoretical study suggests a different path forward, one that turns the problem on its head. Instead of firing neutrinos at a target, the researchers propose using a beam of positrons—the antimatter twins of electrons—captured by a simple nucleus of deuterium. Deuterium is a heavy version of hydrogen, consisting of just one proton and one neutron bound together. When a polarized positron hits this nucleus, it transforms into an antineutrino and knocks the two protons apart. By carefully measuring the energy and angles of these flying protons, scientists can reconstruct the details of the interaction with a clarity that neutrino experiments cannot achieve.

The researchers, led by a team at the Jagiellonian University in Poland, built a sophisticated computer model to simulate this process. They used a framework that respects the laws of relativity, ensuring that their calculations hold true even at high speeds. Before applying their model to the positron scenario, they tested it against real-world data from electron-scattering experiments. The model proved highly accurate, successfully reproducing the complex patterns of how electrons bounce off deuterium nuclei. This validation gave the team confidence to predict what would happen when positrons, rather than electrons, were used as the probe.

Their calculations focused on a specific energy range, below the threshold where the collision would create pions, which are unstable particles that would clutter the data. They found that at a positron energy of 130 million electron volts, the reaction produces a clean signal. The team then simulated how the results would change if the underlying map of the proton's structure were slightly different. They discovered that the reaction is incredibly sensitive to these changes. In the region where current neutrino experiments have uncertainties as high as 100 percent, this new method could reduce the error margin to just a few percent. The sensitivity is so high that even small variations in the theoretical map would cause noticeable shifts in the number of protons detected and the angles at which they fly.

The study also addressed the practical realities of building such an experiment. The researchers calculated how the detection of the two protons would be affected by the limits of real-world detectors. If a detector cannot see protons moving very slowly, it would miss a significant portion of the events, because the two protons are always produced in pairs. If one is too slow to be seen, the other is lost from the data set as well. However, the team showed that with a detector capable of seeing protons with energies as low as 10 million electron volts and covering a wide range of angles, the experiment would remain robust. They concluded that the upcoming upgrade to the positron beam at the Jefferson Lab in Virginia would provide the perfect environment to perform this measurement.

This work does not claim to have solved the mystery of the axial form factor, but it offers a clear and viable path to doing so. By simulating the reaction with high precision, the authors have demonstrated that a positron-capture experiment could provide the definitive data needed to refine our understanding of the proton's structure. This would not only resolve long-standing inconsistencies in neutrino physics but also provide a crucial benchmark for testing predictions from lattice quantum chromodynamics, a method used to calculate the properties of matter from first principles. The paper suggests that the tools to make this leap are already within reach, waiting for the right experimental conditions to be met.