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Where the energy goes

Jul 08, 2023

Measuring the energies of high-energy elementary particles offers a gateway to new discoveries in particle physics. Sehwook Lee, John Hauptman and Richard Wigmans describe how recent developments in calorimeters are helping to advance the field

Particle physicists have been using calorimeters of one type or another for around 70 years. The basic principle of these workhorse instruments is straightforward: the idea is to measure the energies of elementary particles such as the electron, proton and neutron, as well as artificially produced ones such as pions and kaons, by sending them into a dense medium where they interact. Each interaction produces more particles at lower energies, which also interact with the medium, and the process continues until the original particle’s energy is fully exhausted. By interspersing the interaction medium with charge-sensing detectors and summing up the signals recorded, we can obtain a measurement of the initial particle’s total energy.

A particle “shower” induced by a high-energy electron is shown in the image above. Here, the charged particles of the shower (electrons and anti-electrons, or positrons) are made visible via a cloud chamber: a classic type of calorimeter called a sampling calorimeter. The development of these particle showers is highly random. The number of particles generated in the shower, N, is a direct measure of the energy, E, of the initiating particle. N follows a Poisson distribution so the random fluctuations in N are equal to √N and, therefore, the relative precision in N, which is the energy resolution, is √N/N. The energy resolution is a simple formula, σE/E ≈ k/√E. This cloud chamber calorimeter has k ≈ 85% when E is expressed in GeV units (for reference, the rest mass energy of a proton is about 1 GeV); for a modern electromagnetic sampling calorimeter, k is typically 10% or better.

Electron energies are easy to measure in calorimeters because these particles interact via the electromagnetic force, with only two simple allowed interactions. In contrast, particles subject to the strong nuclear force (such as protons, neutrons, pions and kaons – collectively known as hadrons) interact through a multitude of widely fluctuating mechanisms, with additional complications associated with breaking up nucleiand the energy expended for nuclear binding energies.

The tremendous complexity of a shower of hadrons is illustrated in figure 1, which shows the results of a simulation (created using the CERN code GEANT4) of a 500 GeV proton entering a copper absorber. Charged hadrons are shown in blue while electrons and positrons are in red. Visually, the intensity of the colour indicates the amount of energy lost by the particles and represents the signal generated by the calorimeter.

The particle interactions in showers such as this are a complex but highly important area of research in particle physics, and in the CERN R&D project RD52 we are studying them using a new type of calorimeter (full results from the project are available at, where one can view a collection of hadronic showers induced by protons in a copper absorber). These “dual-readout” instruments are made from copper or lead and interspersed with two types of optical fibres: scintillating fibres that sense all charged particles, and clear fibres in which Cherenkov light is generated predominantly by the electrons and positrons of the shower. These two very different signals from a shower are used in combination to extract a highly accurate measurement of hadron energies – including, most importantly, the energies of “jets” of particles resulting from the fragmentation of a quark or gluon produced in fundamental interactions such as those studied at CERN’s Large Hadron Collider and other facilities around the world.

A calorimeter specifically designed to measure these jets of particles is shown in figure 2. It consists of 1 mm-diameter fibres on 1.5 mm centres uniformly interspersed in a copper absorber. The size of this absorber is dictated by the characteristic interaction distances of electrons and hadrons. The distance over which an electron will interact and produce more particles is called the radiation length, and is around a centimetre for most metals (including copper). The corresponding distance over which a hadron will interact is known as the nuclear interaction length. This is considerably longer, typically 20–30 cm, and it takes several nuclear interaction lengths to fully absorb a hadronic shower. The difference is evident in the simulated shower in figure 1, which shows the blue charged hadrons travelling longer distances before interacting. The red-coloured electrons and positrons clearly interact on a much shorter scale. The salt-and-pepper red dots evident throughout the volume are electrons from Compton scattering of low energy (about 1 MeV) photons which have a minimum cross section to interact at this energy and therefore spread out spatially in the calorimeter.

The variation and complexity in the development of showers are challenging for calorimeters. Getting an accurate measure of the total energy requires us to measure each fluctuating component of a shower. The electromagnetic part consists of electrons and positrons and is measured by the Cherenkov light generated in the clear fibres. The charged hadrons are measured by the scintillation light generated in the scintillating fibres, and the neutrons from nuclear break-up are measured by the late-developing recoil protons from neutron-proton elastic scattering in the scintillating fibres.

This dual-readout approach has been thoroughly tested and yields energy resolutions near σE/E ≈ 30% /√E in both simulations and data. This means that the energy of 100 GeV jets can be measured with 3% precision, which is much better than achievable with currently available calorimeters. The main difficulty in constructing a calorimeter of this type is forming the copper absorber to the required precision: about 10 µm over a length of about 2.5 m. This spatial precision is needed in order to maintain a highly uniform (better than 1% when averaged over a cigar-shaped volume) distribution of the two fibre types relative to the absorber. Since the energy measurement depends critically on the light generated in the fibres, if a region of the calorimeter has 1% higher fibre density, then showers developing here will yield 1% more light. An ensemble of showers of the same energy will have a 1% wider signal distribution.

We have tested various methods of creating these copper absorbers, including rolling copper sheets, skiving, extruding, water-jet grooving, chemical etching and cutting with blades. Only the cutting procedure was successful, but it was also difficult and expensive. An industrial procedure involving rolling – perhaps with multiple rollings – might succeed, but in all our tests, rolling copper always resulted in highly warped sheets due to work hardening. Before we can really take advantage of our calorimeter’s improved performance, we need a better means to manufacture the copper sheets for large-scale tests.

Sehwook LeeJohn HauptmanRichard Wigmans