The Standard Model (SM) of elementary particle physics is a theory that bun-dles all known elementary particles and defines how these interact with each other. This model grew from a combination of known fundamental physics, new experimental observations and the need for simplification and unifica-tion. More specifically, it originated from the attempt to unify the electroweak theory, which itself is a unification of the mathematics describing electro-magnetism and the weak force, and the theory of quantum chromodynamics (QCD), which describes the strong nuclear force. The framework was cast in its final form in the mid-1970s and thus comprises three of the four fun-damental forces: the electromagnetic (EM) force, and the weak and strong nuclear forces. The fourth force, gravity, is not included in this Standard Model. The lack of a theory unifying all four forces, often solemnly referred
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2 CHAPTER 1. NEUTRINOS: FROM STANDARD TO STERILE to as the Theory of Everything, is one of the biggest unsolved problems in theoretical physics. For the study of elementary particles, however, gravity is of so little effect that this force can be neglected in almost every particle physics experiment.
Figure 1.1:The buildup of matter. [1]
1.1.1 Particles
Let us take a step back and first have a look at the elementaryparticles. They are dubbed elementary, to stress the fact that as far as we know, they are not divisible into smaller pieces. They thus are both the building blocks of the Standard Model and of the world as we know it.
Figure 1.1 shows how ordinary matter - an atom - is built up out of a cloud of electrons and a core - or nucleus - of protons and neutrons, which in turn
1.1. THE STANDARD MODEL 3 exist of closely packed quarks. In this atom, the electron and the up and down quarks areelementaryparticles.
Both the electron and quarks belong to the class of fermions, particles with half-integer spin1. The class of fermions can be divided in two groups, where the up and down quarks in the atom are part of a larger group ofquarks, and the electron is part of a second group calledleptons. The fermions can also be classified in three generations (across lepton and quark groups), which are all identical except for the particle masses. Each generation combines an electri-cally charged lepton [e;µ;τ], an electrically neutral lepton [νe;νµ;ντ], called neutrino, and two quarks [(u, d); (c, s); (t, b)], as illustrated in the first three columns of figure 1.2 (top). The particles of the first generation are stable and they build up all matter, as it was described above. The higher generation particles are created in high energy processes and can have a relatively long lifetime, but most of them eventually decay to lower mass particles of the first generation.
Next to the fermions, there is a second type of particles, called (gauge) bosons, that have integer spin. Each of these fundamental particles is linked to a particular fundamental force, as a consequence of which they are also often referred to as force carriers. The photons (γ) carry the electromagnetic force, the W and Z+/Z− mediate the weak force, and the gluons (g) are the carriers of the strong force. They are illustrated in the fourth column of figure 1.2 (top). Following this principle, it can be assumed that also the grav-itational force acts via a corresponding boson. This hypothetical ”graviton”, however, has not been found yet.
In 2012, an additional boson, that had been predicted in the 1960’s by Robert Brout and Franc¸ois Englert [3] and independently also by Peter Higgs [4, 5], was discovered [6, 7]. This Brout-Englert-Higgs-boson is the carrier of the Higgs-field that drives the mechanism through which the elementary parti-cles obtain their mass.
1.1.2 Particle interactions
The Standard Model does not only describe what matter is made of, it also, and maybe more importantly, tells us how the various elementary particles interact. The three forces between SM particles allow three types of interac-tions.
Thestrong interactionis responsible for quarks binding together to form hadrons, such as protons and neutrons. As a residual effect, it creates the nuclear force that binds the latter particles to form atomic nuclei. Theweak
1”Spin” is a quantum number that refers to a particle’s intrinsic angular momentum.
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Figure 1.2: The Standard Model of particle physics (top) and the fundamental inter-actions between the Standard Model particles (bottom). Adapted from [2].
1.1. THE STANDARD MODEL 5 interactionacts on the nucleus of atoms, mediating some forms of radioactive decay. Theelectromagnetic forcegoverns electric and magnetic fields. These fields are responsible for the attraction between orbital electrons and atomic nuclei and thus hold atoms together. On a larger scale, this also provides the chemical bonding between atoms.
As mentioned already, for each of these forces working on the level of elementary particles, there is at least one corresponding boson that medi-ates the particle interactions. These bosons are the quanta of the force they are related to and the elementary forces can be mathematically described by quantum fields. All elementary particles have specific properties or quan-tum numbers linked to these fields and those quanquan-tum numbers govern how particles behave in the related interactions:
• The electromagnetic interaction works on particles that carry an electro-magnetic charge,Q. It ischargeas we most commonly know it. The value Qcan be positive or negative and can have different magnitudes. It is a conserved quantity.
• The weak interaction works on particles via their weak isospin, T. For a fermion, the weak charge depends on its chirality.2 The third com-ponent of the weak isospin, T3, is conserved by all weak, strong and electromagnetic interactions.3
• The strong interaction works via the color charge, which can take the values blue, redor green. The opposite ”negative” charges are antiblue, antired or antigreen. All quarks come in any of the three colours. The leptons have no colour charge and thus they cannot interact via the strong force.
Figure 1.2 (bottom) gives a schematic overview of the possible interactions, and table 1.1 summarizes the quantum numbers of the SM fermions. Each fermion has a corresponding antifermion, i.e. a particle of the same mass, but with opposite quantum numbers.
2Chirality is a quantum mechanical property, related to Dirac fields. A particle’s chirality can be positive (+1) or negative (-1). [8]
3Weak isospin and electromagnetic charge are combined in a property calledweak hyper-charge:YW=2(Q−T3), in the unified framework of electroweak theory.
6 CHAPTER 1. NEUTRINOS: FROM STANDARD TO STERILE Table 1.1: The fermions in the Standard Model and their quantum numbers related to the three fundamental interactions.
Fermions Generation1 2 3 EM charge (e) left-hd. right-hd.Weak isospin Colour charge
Leptons νe νµ ντ 0 1/2 — —
e µ τ -1 0
Quarks ud cs bt +2/3-1/3 1/2 00 r, g, b