## Calorimeters for High Energy Physics experiments – part 1 April 6, 2008

Posted by dorigo in physics.

Yesterday I discussed some of the most important features that characterize the detectors with which the Large Hadron Collider at CERN is equipped to study 14 TeV proton-proton collisions. There is one very important – I would say crucial – design requirement of these apparata that I left out of the discussion, however: the demand for high-resolution, full-containment calorimeters. That post was getting too long and out of its original scope, but today I will expiate, with a two-part discussion of these important devices.

Much of our present knowledge of particle physics has been reached, in the course of the last fifty years, through a continuous refining of techniques necessary to accelerate and detect charged particles. In particular, more and more effective means of detection and amplification of the weak signals released by matter traversed by ionized radiation have allowed more and more accurate measurements of position and momentum of the bodies produced in scattering experiments, allowing the identification of new states and the deduction of new laws. During the last thirty years, however, the need of precise measurements of trajectory has been joined by a concurrent need of energy measurements, by total absorption devices generically called calorimeters.

The convenience of the calorimetric approach to the analysis of particle collisions is due not only to the possibility to measure energy of particles regardless of their electric charge (calorimeters are in fact just as good at measuring charged and neutral particles), but most of all to the increase of available energy in the center-of-mass of collisions: and this, in turn, not so much for the consequent increase -approximately logarithmic with collision energy- of the number of produced particles, as for the presence, above a few tens of GeV of total energy, of hadron jets in the final state.

For hadron jets, which are due to the fragmentation of single energetic quarks or gluons emitted by the hard interaction, the calorimetric measurement is very effective: calorimeters measure the collective behavior of particles traveling along approximately the same path, and are thus naturally suited for the measurement of jets. Moreover, the increase of average energy of the produced particles that modern detectors have had to increasingly withstand makes calorimeters advantageous since their longitudinal dimensions have to increase, for a given measurement resolution, only with the logarithm of particle energy.

Logarithmic scaling

The reason for a logarithmic dependence is the exponential growth of the number of particles produced with the energy E of the incoming particle. To understand it, let us take a 4 GeV electro hitting an electromagnetic calorimeter element such as the bar of lead tungstate shown in the picture on the right (one of the bars with which the CMS electromagnetic calorimeter is built). At an average depth of one radiation length, the electron radiates a hard photon, on average sharing its original energy with it. About another radiation length further down (actually nine sevenths of it for photons, but let’s not be distracted by these details), the photon converts to an electron-positron pair of energy E/4=1 GeV; the latter travel one more radiation length and radiate further photons of energy E/8=0.5 GeV, and the process continues until photons and electrons reach a critical energy (which depends on the material, and is of the order of a few MeV in lead) below which they lose energy by other means, and the multiplication stops. The measurement unit here is the radiation length, which is very short (0.56cm in lead) in high atomic number elements: it may be defined as the average distance traveled in the material by a relativistic particle before radiating a hard photon. It is usually labeled as $X_0$, as in the picture below, where a photon incoming from the left splits in an electron-positron pair and a shower develops.

Because of the process outlined above, at a depth of X radiation lengths one finds on average $2^X$ particles produced by the incoming electron, each with energy $1/2^X E$: when this energy becomes equalto the critical energy $E_c$ one has N particles if $2^N = E/E_c$, so in total $N=ln(E/E_c)/ln 2$, and a logarithmic dependence of the longitudinal dimensions with energy fully contained in the device is indeed obtained.

If you compare the above scaling law with the one we discussed in the previous post for momentum measurement in a particle tracker – dimensions scaling with the square root of particle momentum – you realize that calorimeters win as momentum and energy increase: if a meter of tracker and a meter of calorimeter are enough to track with sufficient resolution and full containment a 10 GeV particle, for 400 GeV you need 6.5 meters of tracking and $ln(40)=3.8m$ of calorimeter to obtain the same performances.

Triggering is easy in a calorimeter

When comparing general bonuses of calorimeters with respect to particle trackers one also needs to mention the triggering capabilities of the two devices. In the study of phenomena of very small cross section, such as the production of Higgs bosons (say $pp \to ttH$, which has a cross section of one picobarn at LHC energy), one is required very high beam luminosities to produce enough of the searched bosons. For instance, if your collider has a luminosity of 0.01 pb/s, such as the LHC at design running, only one $ttH$ event is produced every 100 seconds.

In the face of that paucity of signal, one gets about 800 million uninteresting collisions per second, or 20 per every bunch crossing (a bunch crossing happens every 25 nanoseconds). However, only about 100 collisions per second can be stored to disk. The detector therefore needs to be read out and its information understood at blitzing speed, in order to decide whether a $ttH$ event might have been produced or not in each of the 40 million bunch crossings occurring every second.

The trigger system takes care of that unforgiving task. However, calorimeters are much more suited for that task, since they are usually built with scintillators, which provide a very fast signal from the charged particles crossing them. Calorimeters give a response in a few nanoseconds, while trackers usually take as much as a microsecond to provide a signal. So calorimeters are very important in the online selection of events likely to originate from interesting processes.

Different kinds of Calorimeters

There exist many kinds of calorimeters, developed for different experimental layouts and requirements: homogeneous or sampling ones, compensated or weighted, electromagnetic or hadronic, scintillation or gaseous. The way they work is however always the same: in calorimeters, the energy of particles, be them electrically charged or neutral, is measured by having them interact with matter until they totally exhaust their kinetic energy. The energetic yield is minuscule in terms of macroscopic quantities such as temperature: for instance, the total absorption of a 100 GeV proton in a 10 kg block of iron causes the latter to raise its temperature by only 4×10^-12 degrees Celsius.

Only a small part of the energy released, however, is available for detection in the form of light emission -such as in scintillation counters- or in the form of a ionization measurable by means of suitable wire chambers filled with gas mixtures (argon-ethane, for instance). In both cases, one needs a so-called proportional regime, which guarantee the constancy of the ratio between detected signal and deposited energy. Moreover, it becomes mandatory a signal amplification: this can be achieved with photomultiplier tubes in the case of the about 10,000 photons produced by a plastic scintillator per each centimeter traversed by a minimum-ionizing particle, while high-gain amplifiers are needed in the case of the few pico-Coulombs of charge collected at the anode wire by the multiplication typical in proportional regimes (about 10,000×1) of the electrons freed in the gas by ionizing radiation.

(To be continued in part 2)

1. Myke - April 6, 2008

Well-done. I hope you will note the maximum attainable sensitivities of the various detector elements…

2. Myke - April 8, 2008

Supplementary question: how much does a bar (pictured) of lead tungstate cost?

3. dorigo - April 9, 2008

Hello Myke,

sorry for taking time to answer – and it is going to be incomplete anyway (I had other things to attend to which required more attention yesterday).

You ask about the sensitivities. It is a rather technical question if interpreted the way I do. Sensitivity is not just resolution: it has to do with efficiency, noise, acceptance. A number of issues. In any case:
– the tracker of CMS is made of silicon pixels (the three innermost layers, closer to the beam) and strips (the rest). It is a wonderful instrument from almost any point of view. Tracks will be reconstructed with high efficiency and small noise even in the high-luminosity conditions. The rationale of building a tracker with silicon rests in several advantages: speed of response, insensitivity to background levels, redundancy; but the final goal is a high accuracy in the measurement of impact parameter, that is the distance between the primary interaction vertex and the track trajectory. An impact parameter significantly different from zero tags a track coming from a secondary vertex, produced by a long-lived particle such as a tau lepton or a b-meson. On impact parameter the tracker sensitivity is of the order of a few tens of microns, depending on track geometry and momentum – quite appropriate to the task.
– the e.m. calorimeter has excellent energy and spatial resolution, to reconstruct the $H \to \gamma \gamma$ decay over huge QCD backgrounds. I do not remember actual numbers – I can dig them out if you insist – but it is of the order of 1% for a 100 GeV photon.
– the hadronic calorimeter is less good: lots of money went into the former two apparata, and the muon system cannot certainly be sacrificed… Jets are measured with a resolution which is worse than that of other recent HEP experiments, I think of the order of 130%/sqrt(E) – which means 13 GeV resolution for a 100 GeV jet. Again, I am quoting off the top of my head; I will come back and refine these numbers if they turn out to be unacceptably off. Jets, however, can be measured also with the tracker and e.m. calorimeter to some extent (there are methods to do that), and a big effort in CDF is trying to tackle that issue. The most pressing issue is the resolution on missing transverse energy, which is measured in the hadronic calorimeter and is critical to detect neutrinos or other non-interacting particles. This, in my opinion, is the weak spot of CMS.
– the muon system is redundant and composed of different systems. The spatial resolution is not an issue, because it exceeds the typical spread in position which results from multiple scattering in the large amount of material the muons have to traverse before reaching the chambers. Redundancy and fast self-triggering are the strong points of the system.

As for the cost of a crystal, I have no idea, but it is high.We are talking of small change if compared to the typical budget of NASA missions, but it did weigh in the total CMS budget.

Cheers,
T.

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5. Plato - April 15, 2008

Nice Posts Dorigo on the Calorimeters

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