Lecture 15

Particle Detectors

At the output of the accelerator, one has a beam of high energy particles. A typical experiment would then consist in sending the beam against a target (a' la Rutherford) and study the nature and the properties of new particles produced in the collisions. Alternatively, a more modern technique involves two counter-rotating particle beams contained within the accelerator ring. The beams are made to collide head-on with each other at some specific location within the ring. In either case, the collision points are surrounded with arrays of particle detectors, capable of identifying the individual particles produced in the interactions.

How can we detect subatomic particles, so small that in some case we don't even know how small they are ? The answer is that we do not "see" the particles directly, but we observe their effects as they track their paths through matter. The most fundamental rule of particle detection is the following: it is relatively straightforward to detect charged particles, since, as they cross a given medium, they interact with the atomic electrons. When doing so, they either give them enough energy to free them from their atom, or they might just excite them to a higher orbit. In the first case, the passage of the particle will generate a trail of free-electrons/ion pairs along its trajectory; in the second, it will be signaled by a small emission of radiation (e.g. in the visible spectrum), as the electrons fall back to the lower orbits.

Several techniques have been developed to detect either the ion trails or the small pulses of radiation. The situation is completely different when one tries to detect an uncharged particle. Typically, neutral particles can be detected only when they collide with a charged particle (e.g. a proton inside a nucleus), and one then detects the scattered proton.

Historically, the first particle detector was the serendipitous photographic film in Becquerel's drawer. Ionizing radiation, i.e. charged particles, can initiate the chemical reactions involved in the photographic process, the same way that light does when hitting the photographic plate. Until recently, photographic techniques were one of the standard tools to detect and record the tracks of sub-atomic particles, but currently they have been replaced by purely electronic techniques. The most commonly technique used nowadays is based on the same principle as the Geiger Counter, here is its basic principle of operation :

a certain volume of gas is enclosed within a sealed cylindrical container, and a thin wire is stretched along the center of the cylinder. The wire is kept at a positive high voltage, and it is connected to a very sensitive amplifier. When a charged particle crosses the volume of the detector, it leaves a trail of free electrons and ions along its path. The free electrons rush towards the positively charged wire, and in doing so they free even more electrons within the gas volume. This small "electron avalanche", when reaching the wire, induces a small electric pulse : the amplifier receives the pulse and magnifies it to a manageable level.

Modern particle detectors consist, among other components, of large arrays, in numbers exceeding hundreds of thousand, of state of the art "Geiger Counters", each one recording one point along the particles trajectories. Particle velocities are measured by determining the bending of the trajectories inside strong magnetic fields, and their energies are measured by stopping the particle within a thick absorber and recording the total deposited energy.

The overall dimensions required of particle detectors scale with the energy of the particles to be detected, and so does the number of individual detector channels required to provide full information on the event under study. Sophisticated detectors placed around the interaction regions of modern particle colliders have reached the dimension of a few-story building, and their operation and maintenance involves the work of several hundred physicists.

In a typical collision between high energy particles, the initial kinetic energy materializes itself into as many as hundreds of new particles, and detectors are capable of monitoring and analyzing up to several millions such interactions per second. These performances, unimaginable until a few years ago, have been made possible by outstanding progress in the miniaturization and speed of modern micro-electronics.

The Standard Model of Particle Physics.

The progress of the research effort, both experimental and theoretical, in the study of elementary particles at accelerators of ever increasing energy, has produced a very interesting, and rather surprising, description of nature at its most fundamental level. Our current understanding of the subatomic world is summarized in what is called "the Standard Model of Elementary Particles". Here are its major ingredients:

• The most useful way to classify the most elementary constituents of matter is based on whether they are or are not affected by the nuclear strong force. In this light , we will see that the universe is made of hadrons, that feel the strong force, and leptons, that don't.
• For every particle, there is a corresponding antiparticle. Even though, in principle, there is nothing special about antiparticles, one particular aspect of antimatter has always created a certain amount of interest, both in science and in science fiction : a particle and its antiparticle can annihilate each other, with a complete transformation of mass into energy.
• The interactions among elementary particles (and consequently, among any object in the universe) are controlled by the effects of four fundamental forces, Gravity, ElectroMagnetism, Strong Nuclear and Weak Nuclear. Forces are transmitted from on object to another by the exchange of a special category of elementary particles.

Leptons.

In spite of what the book says, the term lepton does not stand for "weakly interacting", but for "light weighted". This term goes back to the days when the only known particles not participating in the strong interactions had masses much smaller than the strongly interacting ones. The term has stuck, even though we now know about the existence of non-strongly interacting particles that are heavier than the protons.

The best known representative of the lepton family is the electron. Electrons, as we by now well know, are negatively charged particles, almost 2000 times lighter than protons (m_e = 0.511 MeV, m_p = 938 MeV). Even though they play an extremely fundamental role in the properties and composition of matter, electrons do not participate in the making of the nuclei.

We also know that electrons come into play in some aspect of nuclear instability. We have in fact learnt that neutrons are not stable, but a free neutron will decay, with a half-life of several minutes, into a proton and an electron (this is the so-called $\beta$-decay, which is also responsible for the $\beta$ radiation emitted by some unstable isotopes).

When we first introduced $\beta$-decay, we had also mentioned that another particle intervenes, the neutrino $\nu$, so that the complete expression for neutron decay is

$n \rightarrow p e \nu$

The existence of this extra particle was first hypothesized to explain an apparent non-conservation of energy in the neutron decay, since the measured mass and energies of the proton and electron were not enough to account for the whole mass of the initial neutron. Eventually, it was suggested that the missing energy was carried by an udetected, neutral particle, named the neutrino. It then took many more years (from the 30's to the 50's) for the neutrino to be detected, or, more precisely, to detect some process uncontroversially caused by the interactions of neutrinos with matter.

It should not be a surprise that neutrinos are so difficult to detect : not only they are neutral and they have an extremely small, possibly zero, mass, but also they do not feel the strong force. How then do they interact with matter at all? Study of $\beta$-decay processes and of neutrino interactions revealed that another type of force, the so called weak nuclear force exists at the subatomic level. This force, much weaker than the the strong and the electro-magnetic force, intervenes, among other things, to induce $\beta$-decay and to control the interactions of neutrinos.

A neutrino, affected only by the weak force, can traverse any amount of material as if it was travelling through vacuum. One can calculate that, in order to have a high probability of stopping a neutrino, one would need an absorber of the thickness of one billion (10⁹) meters !!!

How can then one detect such an elusive particle ? The answer is: by having a very very large amount of them. If one neutrino interacts, in the average, in one billion meters of material, then there is a good probability that, if I have one billion neutrinos, one of them will interact in one meter of material.... This is how neutrinos were originally discovered, by monitoring the expected very high neutrino flux from a nuclear reactor in South Carolina, and observing the reaction :

$\nu + p \rightarrow e^{+} + n$

In addition to the electron and its neutrino, two more members of the lepton family, christened $\mu$ and $\tau$, were shown to exist: these particles have properties similar to the electron, except that they are heavier in mass, and are allowed to decay into lighter particles: the $\mu$ (or muon), for instance, decays into electron plus neutrinos. Both $\mu$ and $\tau$ come with their own neutrinos, so that the complete family of lepton is :

$(e,\nu_{e}) \hspace{1in} (\mu ,\nu_{\mu}) \hspace{1in} (\tau , \nu_{\tau})$

Presently, we believe that the leptons are "elementary" (in the sense that they are not made of some smaller unit), but this still leaves us with many unanswered questions:

Why does the electron have two heavy partners? Are there only three pairs of leptons (the likely answer is yes). Why three? What is the role of the neutrino? Are neutrino massless ?
Research is continuing in the attempt to answer these, and other questions that would bring, ideally, to the ultimate understanding of the world we live in.

Hadrons

The term "hadron" was introduced to represent particles affected by the strong force. The most familiar among these are obviously the proton and the neutron, but, with the advent of higher and higher energy accelerators, it was found that a very large collection (up to a few hundred) of strongly interacting particles existed, with properties obviously relating them to the familiar protons and neutrons. This particle explosion generated a fair amount of puzzlement for several years (how can so many particles all be fundamental?), until, in the attempts to create some order among the chaos, it was realized that there was a simple way to explain the multiplicity : in a way somewhat similar to the realization that all of the different chemical elements are in reality made of different combinations of a few fundamental building blocks, it was realized that all of the known strongly interacting particles could be accounted for as being formed by the combination of some more elementary unit.

The scientist who first came up with this explanation, Murray Gell-Mann, chose the name quarks for such fundamental particles, a whimsical name inspired by Joyce's "Finnegan's Wake" (in reality, another scientist had indipendently reached the same realization, and he had called the fundamental constituents aces; aces went away, and quarks remained...).

The existence of quarks was completely unexpected, and so was one of its more fundamental properties, i.e. the fact they they carry an electric charge smaller than the one carried by the electron. If we indicate the electron charge by e, then the quarks carry charges of $\pm 1/3$ and $\pm 2/3 e$ . This fact was hard to digest for a while: even though we have no knowledge of what the fundamental unit of electric charge should be, the universality of the electron (and proton, and all the other known elementary particles) charge in units of e had created the strong belief the e should be the basic quantum of charge.

But scientists should be (and usually are) open to revise their belief when faced with experimental and theoretical evidence, and nowadays the acceptance of the existence of quarks with fractional charges is universal (even though we have never seen, and we might never see, a free, fractionally charged quark).

What is then the relation between quarks and protons and neutrons (as well as the other hadrons)? Like leptons, quarks come in pairs, and the two members of the first doublet were called respectively up (charge 2/3 e) and down (charge -1/3 e). A proton is really a bound state of two "up" and one "down" quarks, while a neutron is made of two downs and one up (you can easily verify that this gives protons and neutrons the correct 1 and 0 charges). The $\beta$-decay of the neutron into a proton (plus electron and neutrino) should really be interpreted as a transition from an up to a down quark : an important facet of the quark theory is in fact that the weak interaction can transform a quark of a type into another.

In a way similar to the lepton family, it was found that also quarks come into three pairs, of increasing mass, which are unstable and will eventually decay into the fundamental up and down quarks. The three (and, most likely, no more than three) quark doublets are known as

(up, down) (charm, strange) (top, bottom)

Our observations have shown, and the theory explained, that quarks can form bound states either in triplets (as in the proton and the neutron) or in a quark-antiquark pair : these latter type of particles form the large family of mesons

As it is often the case in science, a new discovery answers many questions but creates many new ones: Why quarks? Why three doublets? Is it just an accident that leptons and quarks, currently the best candidates for the "ultimate building blocks", both come in three doublets? Is there any explanation for the mass scales of the fundamental quarks and leptons? etc...

One thing that we claim to understand about quarks is why it might not be possible to observe free quarks, but they can only appear in bound states. This is a consequence of the fact that, within its limited range, the strong force between two quarks grows with increasing separation between the two particles. As we try to pull two quarks apart from each other, we must supply more and more energy, until the energy is large enough to be equivalent to the mass of a new quark-antiquark pair, which will then pop into existence.

A useful image is to think of a quark and an antiquark being at the two ends of a piece of rubber band. I will never be able to have only "one end" of the band, if I stretch it, it will eventually break into two pieces (i.e., if I try to get a single quark, I end up with four, etc....).