Design and beam-test characterization of the CRILIN semi-homogeneous crystal calorimeter

Imagine you are trying to take a photograph of a firework exploding in the night sky, but you have two major problems. First, the explosion happens incredibly fast, so fast that a normal camera would just see a blur. Second, the sky is already filled with thousands of tiny, glowing dust motes from other fireworks, making it hard to tell which spark belongs to the big explosion you are studying. This is the daily challenge for scientists building machines to study the universe's smallest particles, specifically in the upcoming generation of "lepton colliders." These are giant circular tracks where particles like electrons and muons smash into each other at nearly the speed of light. To understand what happens during the crash, scientists need detectors that can measure the energy of the debris with extreme precision, tell exactly when it arrived (down to a few billionths of a billionth of a second), and distinguish the main event from the background noise. If the detector is too slow or too confused, the physics secrets remain hidden.

Enter the CRILIN detector, a new kind of "camera" designed to solve these problems. Think of a traditional detector as a thick, heavy sponge that soaks up the energy of a particle crash. While sponges are good at soaking, they are often slow to dry and don't tell you exactly where the water went inside. CRILIN is different; it is built like a stack of transparent, high-speed ice cubes (made of a special crystal called lead fluoride, or PbF2). When a particle hits these cubes, it doesn't just heat them up; it creates a flash of light called Cherenkov radiation, similar to the sonic boom of a jet but made of light. Because this light happens almost instantly, the detector can act like a high-speed camera, snapping pictures of the particle shower as it develops layer by layer. The goal of the paper you are about to read is to see if a large, real-life version of this "ice-cube stack" actually works as well as the computer models predicted, and if it can measure energy and time with the precision needed for future physics experiments.

The Big Test: Building a Crystal Tower

The scientists behind this project, a team from various Italian research labs, decided to stop relying solely on computer simulations and build a massive prototype to test in the real world. They constructed a detector the size of a small suitcase, consisting of five layers of a 7-by-7 grid of lead fluoride crystals. That's 225 individual crystal "cells" in total, stacked up to a depth of about 22 radiation lengths (a fancy way of saying it's thick enough to stop even the most energetic electron showers).

Each of these 225 crystals is watched over by four tiny, super-sensitive light sensors called Silicon Photomultipliers (SiPMs). These sensors are like the eyes of the detector, capable of seeing single flashes of light. To keep the system fast and resistant to the harsh environment of a particle collider, the electronics that read the signals were placed far away from the crystals, connected by flexible cables. This is like having the camera sensor in the lens but the computer processing the image in a safe room down the hall, keeping the sensitive parts cool and protected.

The Beam Test: Shooting Crystals with Electrons

To see if their creation worked, the team took their detector to CERN in Switzerland, the home of the world's most famous particle accelerator. They set it up in a beamline where a stream of electrons was fired at the detector at different speeds, ranging from 10 to 120 GeV (giga-electronvolts, a unit of energy). They also fired muons (heavier cousins of electrons) at it to help calibrate the sensors.

The results were impressive. The detector proved it could act as a very precise stopwatch. For electrons with energies above 10 GeV, the team measured a time resolution of less than 50 picoseconds. To put that in perspective, a picosecond is to a second what a second is to about 32 years. At higher energies (above 60 GeV), the detector got even faster, reaching a resolution below 20 picoseconds. This is fast enough to distinguish between particles arriving at almost the exact same moment, a crucial feature for sorting out the "noise" in future colliders.

Measuring Energy: The Stochastic and Constant Terms

The team also checked how well the detector could measure the amount of energy in the crash. They found that the detector's accuracy is described by two main numbers: a "stochastic term" of about 6.58% and a "constant term" of 0.23%.

• The Stochastic Term: This is like the natural "fuzziness" of the measurement. It gets better as the energy gets higher, because more energy means more light flashes, which averages out the randomness.
• The Constant Term: This is the tiny bit of error that stays the same no matter how big the crash is. The team found this to be incredibly small (0.23%), meaning the detector is very stable.

One of the clever tricks the team used was looking at how the particle shower developed as it went deeper into the stack of crystals. Because the detector is sliced into layers, they could see if the shower started early or late in the stack. By using this "longitudinal information," they could make corrections for each individual event, significantly improving the accuracy of the energy measurement. It's like if you were guessing the weight of a watermelon by looking at it; if you could also see how deep the watermelon is, you could make a much better guess than just looking at its width.

The Verdict: A Successful Prototype

The paper concludes that the CRILIN design is a success. The large prototype they built works exactly as the simulations predicted. The combination of fast crystals, sensitive light sensors, and the ability to see the shower develop layer-by-layer allows for a detector that is compact, fast, and highly accurate.

The team measured a "light yield" (how much light is produced per unit of energy) of about 0.54 photoelectrons per MeV. While this might sound small, it is consistent across different types of particles and is sufficient for the detector to function effectively. The simulation, which included realistic details like electronic noise and the random nature of light detection, matched the real-world data almost perfectly, with a difference of less than 0.15%.

This work validates the entire chain of the CRILIN concept, from the mechanical design of the crystal stack to the complex software used to reconstruct the data. It suggests that this type of detector is a strong candidate for the next generation of particle colliders, where speed and precision are the keys to unlocking new physics. While the test was done without active temperature control (which caused some minor drifts in the data), the results are robust enough to show that with a proper cooling system in the final version, this technology could become a standard tool for exploring the universe's deepest secrets.