Measuring Dual-Superconductor Length Scales in the QCD Vacuum at HERA

Deep within the heart of every atom lies a hidden world where the rules of everyday matter dissolve into a seething sea of energy. This is the realm of quantum chromodynamics, the theory that explains how the smallest building blocks of the universe, quarks and gluons, stick together to form protons and neutrons. For decades, physicists have suspected that the empty space between these particles is not truly empty but acts like a special kind of fluid, one that behaves much like a superconductor. In a regular superconductor, electricity flows without resistance, but magnetic fields are pushed out and confined into tiny, narrow tubes. In this theoretical "dual superconductor" picture of the vacuum, the roles are reversed: magnetic fields are free, but the electric-like forces that hold quarks together are squeezed into tight, invisible tubes. These tubes are what keep quarks trapped inside particles, never allowing them to escape alone. To understand how this cosmic fluid works, scientists need to measure two specific distances that define its behavior: how far a force can penetrate into the vacuum before being blocked, and how quickly the vacuum fluid recovers after being disturbed. Until now, these distances could only be guessed at through complex computer simulations, leaving a gap between theory and the real, measurable universe.

A team of researchers at the Indian Institute of Technology Delhi has now bridged that gap by looking at the vacuum in a completely new way. Instead of relying solely on computer models, they turned to data collected at HERA, a massive particle collider that operated in Germany for many years. They focused on a specific type of collision where a high-energy photon, a particle of light, smashes into a proton and transforms into a heavy particle called a J/psi meson. In these collisions, the proton does not break apart; instead, it remains intact while the photon briefly creates a tiny, localized disturbance in the vacuum's fluid. The researchers realized that the shape of this disturbance, or "hotspot," acts as a direct fingerprint of the vacuum's properties. By analyzing the angles and energy of the particles flying out of these collisions, they could reconstruct the geometry of the vacuum's response to the impact.

The team tested a specific mathematical shape, known as the Clem profile, which describes how a vortex behaves in a superconductor. They compared this shape against a vast collection of 104 data points from two major experiments at HERA, covering a wide range of collision energies and angles. The results were strikingly precise. The data fit the superconductor model perfectly, revealing that the vacuum behaves like a "type-II" superconductor, a state where the force-carrying tubes are stable and repel one another, much like magnets with the same pole facing each other. From this fit, the researchers extracted the two fundamental lengths that characterize the vacuum. They found that the force penetrates the vacuum to a depth of 0.19 femtometers, a distance so small it is a fraction of the width of a proton. They also measured the size of the core where the vacuum is disturbed, which comes out to 0.087 femtometers.

These measurements allow the scientists to calculate the mass of the particles that carry these forces. The penetration depth corresponds to a particle with a mass of about 1.03 billion electron volts, a value that matches remarkably well with previous computer calculations of the lightest "gluelump," a particle made entirely of the force-carrying gluons. The size of the core suggests a much heavier particle, roughly 2.3 billion electron volts, which is heavier than the lightest known glueball, a particle made of pure glue. The researchers also checked the strength of the force holding these tubes together and found it aligns with the known strength of the force that binds the atomic nucleus, provided they use a specific value for the interaction strength that matches other theoretical calculations.

The study also addressed a long-standing issue in how physicists model these collisions. Previous attempts to describe the shape of these hotspots assumed they were simple, smooth blobs, similar to a bell curve. However, those simple shapes failed to explain the data when the collisions were very energetic or the angles were sharp. The new study shows that the vacuum's response is far more complex, with a distinct core and a specific type of tail that stretches out. This new shape successfully describes the data across three decades of energy levels without needing to add extra, complicated layers of theory. The researchers found that the number of these hotspots inside a proton is likely around eight, though the data is not sensitive enough to pinpoint an exact number, suggesting a range between five and eighteen.

While the results are robust, the authors note that some details remain open for future investigation. For instance, they tested whether the hotspots repel each other as the theory predicts, but the current data is not precise enough to confirm or rule this out. They suggest that future experiments at the Electron-Ion Collider, a planned facility, could solve this by tagging the mass of the proton after the collision, which would separate the different types of fluctuations causing the data. For now, this work provides the first extraction of the vacuum's fundamental length scales from scattering data, confirming that the dual superconductor picture provides a model that well describes the observed transverse profile of the proton's gluon distribution. The vacuum is not a passive stage for particle physics; it is an active, structured medium with its own distinct dimensions and properties, waiting to be mapped one collision at a time.