Exploring nucleon spin by Drell-Yan process

Inside every atom, protons and neutrons form the dense core of matter, yet they are not solid, unchanging spheres. Instead, they are dynamic bundles of smaller particles called quarks and gluons, constantly in motion. For decades, physicists have understood that the spin of a proton—the way it rotates like a top—is not just the sum of the spins of its three main quarks. A significant portion of this spin comes from the orbital motion of these quarks as they zip around inside the proton, and from the gluons that hold them together. To map this invisible internal landscape, scientists use high-energy collisions to probe the proton's structure. One of the most powerful tools for this is a process where two hadrons, such as protons or pions, smash together to create a pair of muons, which are heavy cousins of the electron. By studying how these muons fly apart, researchers can reconstruct the behavior of the quarks that created them, revealing details about how the proton's spin is assembled.

A recent presentation by Wen-Chen Chang at an international symposium on spin physics reviews how this collision process, known as the Drell-Yan process, is being used to test our understanding of these internal motions. The work focuses on two specific ways quarks move: their transverse momentum, which describes how they move side-to-side relative to the proton's direction, and their correlation with the proton's spin. In simpler terms, scientists are looking for patterns that show whether a quark's sideways movement is linked to the direction the proton is spinning. This is crucial because a fundamental theory in physics predicts that the relationship between spin and sideways motion should flip signs depending on whether the collision happens in a "space-like" or "time-like" environment. While previous experiments using electron beams had confirmed this flip for one type of motion, the Drell-Yan process offers a unique way to check if this rule holds true for other types of motion and to see if the same rules apply when protons are hit by other particles, like pions.

The presentation highlights recent findings regarding the Boer-Mulders function, a mathematical description of how quarks and gluons are correlated with the proton's spin. By analyzing data from past experiments where pion beams hit tungsten targets, researchers compared the observed patterns of muon pairs against complex computer calculations based on standard quantum theory. The results showed that while the standard theory could explain some of the data, it could not explain everything on its own. Specifically, the data revealed a distinct pattern in the angles at which the muons emerged that deviated from the pure theory predictions. This deviation suggests the presence of the Boer-Mulders effect. Furthermore, when combining these new findings with earlier results from electron scattering experiments, the evidence strongly supports the idea that the correlation between quark motion and spin reverses direction between the two different types of collisions. This confirmation is a vital step in proving that the laws governing the proton's interior are universal, regardless of how the probe is fired at it.

Beyond these confirmed findings, the paper looks forward to a new frontier: using the Drell-Yan process to study generalized parton distributions. These are more complex maps that describe not just how quarks move, but also where they are located inside the proton. While these maps have been partially drawn using electron beams, the paper proposes a novel method to complete the picture using pion beams at the J-PARC facility in Japan. The researchers have designed a plan to fire high-energy pions at protons and look for a very specific, rare event where a pion and a proton collide to produce a virtual photon that immediately decays into a muon pair, leaving the proton intact but changed into a neutron. This is an extremely difficult measurement because the signal is tiny compared to the background noise of other collisions. However, detailed simulations suggest that with a dedicated beamline and a specific detector setup, it is possible to isolate these rare events. The simulations indicate that running the experiment for about 50 days with a 15-GeV pion beam would generate enough data to distinguish between different theoretical models of the proton's internal structure.

The path to this new measurement involves a phased construction of a high-momentum pion beamline at J-PARC. Early tests have already successfully identified the secondary particles needed for the experiment, confirming that the beam intensity matches predictions. If successful, this experiment will provide the first direct look at the proton's structure through a time-like process using hadron beams, offering a complementary view to the space-like views obtained from electron scattering. By verifying that the same underlying rules apply in these different collision environments, physicists hope to finalize a comprehensive three-dimensional picture of the nucleon. This work does not just fill in missing data; it rigorously tests the fundamental symmetries of nature, ensuring that our understanding of how matter is built holds true across the different ways we choose to examine it.