STANDARD MODEL class of “High Energy Physics Phenomenology” Mikhail Yurov Kyungpook National University November 15 th

Introduction The Standard Model (SM) of particle physics is a theory which describes the strong, weak, and electromagnetic fundamental forces, as well as the fundamental particles that make up all matter. It is a quantum field theory, and consistent with both quantum mechanics and special relativity. Almost all experimental tests of the three forces described by the Standard Model have agreed with its predictions. However, the Standard Model is not a complete theory of fundamental, primarily because it does not describe gravity.

Content of the Standard Model The Standard Model contains both fermionic and bosonic fundamental particles. Fermions are particles which possess half-integer spin and obey the Pauli exclusion principle. Bosons possess integer spin and do not obey the Pauli exclusion principle. Fermions are particles of matter and bosons are particles that transmit forces. In the SM, the theory of the electroweak interaction (which describes the weak and electromagnetic interactions) is combined with the theory of quantum chromodynamics. All of these theories are gauge theories, meaning that they model the forces between fermions by coupling them to bosons which mediate the forces. The Lagrangian of each set of mediating bosons is invariant under a transformation called a gauge transformation, so these mediating bosons are referred to as gauge bosons.

Bosons The bosons in the Standard Model are: Photons, which mediate the electromagnetic interaction. W and Z bosons, which mediate the weak nuclear force. Eight species of gluons, which mediate the strong nuclear force. Six of these gluons are labelled as pairs of "colors" and "anti-colors“. The other two species are a more complicated mix of colors and anti-colors. The Higgs bosons, which induce spontaneous symmetry breaking of the gauge groups and are responsible for the existence of inertial mass.

It turns out that the gauge transformations of the gauge bosons can be exactly described using a unitary group called a "gauge group". The gauge group of the strong interaction is SU(3), and the gauge group of the electroweak interaction is SU(2)×U(1). Therefore, the Standard Model is often referred to as SU(3)×SU(2)×U(1). The Higgs boson is the only boson in the theory which is not a gauge boson; it has a special status in the theory, and has been the subject of some controversy. Gravitons, the bosons believed to mediate the gravitational interaction, are not accounted for in the Standard Model.

Fermions There are twelve different types, or "flavours", of fermions in the Standard Model. Amongst the proton, neutron, and electron, those fermions which constitute the vast majority of matter, the Standard Model considers only the electron a fundamental particle. The proton and neutron are aggregates of smaller particles known as quarks, which are held together by the strong interaction.

The fermions can be arranged in three "generations", the first one consisting of the electron, the up and down quarks, and the electron neutrino. All ordinary matter is made from first generation particles; the higher generation particles decay quickly into the first generation ones and can only be generated for a short time in high-energy experiments. The reason for arranging them in generations is that the four fermions in each generation behave almost exactly like their counterparts in the other generations; the only difference is in their masses. The electron and the muon both have half-integer spin and unit electric charge, but the muon is about 200 times more massive.

The electron and the electron-neutrino, and their counterparts in the other generations, are called "leptons". Unlike the other fermions, they do not possess a quality called "color", and therefore their interactions (weak and electromagnetic) fall off rapidly with distance. On the other hand, the strong force between quarks gets stronger with distance, so that quarks are always found in colorless combinations called hadrons. These are either fermionic baryons composed of three quarks (the proton and neutron being the most familiar example) or bosonic mesons composed of a quark-antiquark pair (such as pions). The mass of such aggregates exceeds that of the components due to their binding energy.

Spontaneous symmetry breaking Spontaneous symmetry breaking in physics takes place when a system that is symmetric with respect to some Lie group goes into a vacuum state that is not symmetric. At this point the system no longer appears to behave in a symmetric manner. A common example to help explain this phenomenon is a ball sitting on top of a hill. This ball is in a completely symmetric state. However, it is not a stable one: the ball can easily roll down the hill. At some point, the ball will spontaneously roll down the hill in one direction or another. The symmetry has been broken because the direction the ball rolled down in has now been singled out from other directions.

In physics, one way of seeing spontaneous symmetry breaking is through the use of Lagrangians. Lagrangians, which essentially dictate how a system will behave, can be split up into kinetic and potential terms It is in this potential term (V(φ)) that the action of symmetry breaking occurs. An example of a potential is

as illustrated in the graph. This potential has many possible minimums (vacuum states) given by for any real θ between 0 and 2π.

The system also has an unstable vacuum state corresponding to φ = 0. In this state the Lagrangian has a U(1) symmetry. However, once it falls into a specific stable vacuum state (corresponding to a choice of θ) this symmetry will be lost or spontaneously broken. In the Standard Model, spontaneous symmetry breaking is accomplished by using the Higgs boson and is responsible for the masses of the W and Z bosons.

Tests and predictions The Standard Model predicted the existence of W and Z bosons, the gluon, the top quark and the charm quark before these particles had been observed. Their predicted properties were experimentally confirmed with good precision. The Large Electron-Positron collider at CERN tested various predictions about the decay of Z bosons, and found them confirmed.

Challenges to the Standard Model Although the Standard Model has had great success in explaining experimental results, it has never been accepted as a complete theory of fundamental physics. This is because it has two important defects: The model contains 19 free parameters, such as particle masses, which must be determined experimentally (plus another 10 for neutrino masses). These parameters cannot be independently calculated. The model does not describe the gravitational interaction.

One attempt to address the first defect is known as grand unification. The so- called grand unified theories (GUTs) hypothesized that the SU(3), SU(2), and U(1) groups are actually subgroups of a single large symmetry group. The first theory of this kind was proposed in 1974 by Georgi and Glashow, using SU(5) as the unifying group. The Higgs boson, which is predicted by the Standard Model, has not been observed as of 2004.

A further extension of the Standard Model can be found in the theory of supersymmetry, which proposes a massive supersymmetric "partner" for every particle in the conventional Standard Model. Supersymmetric particles have been suggested as a candidate for explaining dark matter.