Low-energy Muon-Nucleon scattering experiment: LUNE (White Paper)

The proton, the tiny, positively charged core of every atom, is not a solid, unchanging marble. It is a bustling, dynamic system made of even smaller particles called quarks, held together by a force so strong it is called the strong interaction. For decades, scientists have tried to measure the exact size of this proton, specifically its electric charge radius, which describes how far its electric charge spreads out in space. This measurement is crucial because it serves as a fundamental ruler for understanding how matter is built. However, a significant mystery has emerged: when scientists measure the proton's size using electrons, they get one answer, but when they use muons—a heavier cousin of the electron—they get a slightly different, smaller answer. This discrepancy, known as the "proton radius puzzle," suggests that our current understanding of the laws of physics might be incomplete, or that there are subtle effects in the way these particles interact that we have not yet accounted for.

To solve this puzzle and explore the deeper structure of matter, a new international collaboration called LUNE has proposed a dedicated experiment at the High-Intensity Heavy-ion Accelerator Facility (HIAF) in China. This facility is designed to produce beams of muons with a wide range of energies, a capability that is unique in the world. The LUNE team has outlined a comprehensive plan to use these muon beams to bombard hydrogen and other atomic nuclei, observing how the muons scatter off them. By doing so, they aim to measure the proton's size with unprecedented precision, investigate how the proton's internal structure changes under different conditions, and search for entirely new particles that lie beyond our current understanding of physics.

The heart of the LUNE proposal is a two-stage plan that matches the capabilities of the accelerator as it grows. The first stage focuses on the most immediate and critical question: the size of the proton. The researchers plan to fire a beam of muons at a target made of polyethylene, a plastic rich in hydrogen atoms. As the muons hit the protons inside the hydrogen, they will bounce off at various angles. By measuring the angle and energy of the scattered muons with extreme precision, scientists can calculate the proton's charge radius. The paper suggests that with the high intensity of the HIAF beam and a specially designed detector, LUNE could determine the proton's radius with an accuracy of about one percent. This level of precision is vital because it will allow scientists to see if the difference between the electron-based and muon-based measurements is real, or if it stems from subtle experimental errors or theoretical oversights.

A key feature of the LUNE experiment is its ability to use both positive and negative muons. While electrons are always negatively charged, muons come in two varieties, much like the positive and negative charges of a battery. This duality allows the team to study a specific quantum effect called two-photon exchange. In the standard view of particle scattering, a single particle of light, or photon, is exchanged between the muon and the proton. However, in reality, two photons can be exchanged simultaneously. This effect is tiny but becomes significant when measuring with high precision. Because positive and negative muons interact differently with these two-photon exchanges, comparing the results from both beams allows scientists to isolate this effect. This is something that cannot be done with electron beams alone, as electrons only come in one charge. By carefully measuring these differences, the experiment aims to refine our understanding of the electromagnetic force and ensure that the measurement of the proton's size is not skewed by these complex interactions.

Beyond the proton, the experiment will also look at other light atomic nuclei, such as deuterium, which consists of one proton and one neutron. Just as there is a puzzle with the proton, there are similar discrepancies in the measurements of the deuterium's size. LUNE plans to use muon beams to scatter off deuterium targets, providing an independent check on these measurements. The team also intends to study how muons interact with heavier nuclei, like carbon or lead. These interactions are complicated by the strong electric fields of the heavy nuclei, which can bend the path of the incoming muon before it even hits a target particle. By comparing how positive and negative muons are deflected by these fields, the researchers hope to better understand and correct for these distortions, leading to more accurate measurements of nuclear structure.

As the facility matures, the second stage of the LUNE program will expand its scope to explore the three-dimensional structure of the proton and neutron. While the first stage treats the proton as a whole object to measure its size, the second stage will look inside, mapping how the quarks and gluons are arranged in space and how they move. This involves firing higher-energy muons at the targets and observing the debris of the collision. When a muon hits a proton at high energy, it can knock out a quark, causing the proton to break apart and produce a shower of new particles. By tracking these particles, scientists can reconstruct the internal landscape of the proton, seeing how the quarks are distributed not just in terms of their momentum, but also in terms of their position. This is akin to creating a detailed map of the proton's interior, revealing how the spin of the proton is built from the spins and orbital motions of its constituent parts.

The paper also highlights the potential for LUNE to discover new physics. The high-intensity muon beam can be directed at heavy metal targets to search for hypothetical particles that interact very weakly with ordinary matter, often referred to as "dark sector" particles. If these particles exist, they might be produced when a muon interacts with a nucleus and then decay into pairs of electrons or photons that the detector can spot. Because the muon beam is so intense and the detector is so sensitive, LUNE could probe regions of parameter space that are inaccessible to other experiments, potentially uncovering new forces or particles that could explain mysteries like dark matter.

To achieve these goals, the researchers have designed a sophisticated detector system tailored to the specific needs of muon scattering. The detector is built in layers, starting with a target where the collisions happen, followed by a series of tracking chambers that record the path of every particle that flies out. These tracking chambers are made of silicon pixels, which are incredibly thin and precise, allowing the team to measure the angle of the scattered muons with a resolution better than one-thousandth of a degree. This precision is essential because the size of the proton is determined by how the scattering angle changes at very small angles. Behind the trackers, the detector includes magnets to bend the paths of charged particles, allowing their momentum to be calculated, and calorimeters that measure the energy of the particles. The design is modular, meaning it can be upgraded as the accelerator improves, ensuring that the experiment remains at the cutting edge of physics for years to come.

The authors of the paper emphasize that their proposed detector is based on technologies that have already been proven in other experiments, which reduces the risk of failure and keeps costs manageable. They have run extensive computer simulations to test their design, and the results show that the detector should perform exactly as needed to achieve the one-percent precision goal for the proton radius. These simulations also predict that the experiment will collect enough data to make statistically significant measurements of the proton's form factors, the two-photon exchange effects, and the structure of light nuclei. The team is confident that with the high-quality muon beams available at HIAF, they can provide a definitive answer to the proton radius puzzle and open new windows into the fundamental nature of matter.

In summary, the LUNE white paper presents a clear and ambitious roadmap for a new era of muon-scattering physics. It proposes using a unique combination of high-intensity muon beams and a precision detector to measure the size of the proton with a level of accuracy never before achieved. By comparing positive and negative muons, the experiment will isolate subtle quantum effects that have long been a source of uncertainty. As the project moves from the first stage of measuring the proton's size to the second stage of mapping its internal structure, it promises to deepen our understanding of how the universe is built from the smallest scales up. The work represents a convergence of nuclear physics, particle physics, and accelerator technology, offering a unique opportunity to test the limits of our current theories and potentially discover new phenomena that lie just beyond our reach.