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## Basics

Now you should learn some background information needed to take up the challenge of discovering new particles.

### Detection of single particle "tracks" Throughout the project you will be looking at different "events" which happen when there is a proton-proton collision. The first item which you will observe in every event, there are the traces which the particles leave in the different parts of the detector and lines called "tracks" which join the traces belonging to the same particle. The detector surrounds the region where the collisions take: in the following picture, it is represented as the red inner circle. Originating from the centre, there are short tracks and long tracks. The short tacks can belong to any kind of charged particles but the long ones belong to muons which are the only charged particles which can reach the outer parts of the detector. The following shows a example of how different particles interact with different parts of a detector. Note that the neutral particles leave traces only in the calorimeters (so you should see no tracks in the inner black circle) but only in the green and red. On the other hand the neutrinos are "invisible" they do not leave any traces! They only way to "guess" their presence is from the missing energy/momentum which is discussed at the end of this page. ### Detection of particles which decay to other particles

#### Measurement of their mass

When you see two or more particle traces in the detector, "tracks" in one "event", originating from the same point, which we will call "vertex", they may belong to one original particle which decayed to these tracks. In order to check this hypothesis one has to calculate the "invariant mass" of the original particle and investigate if these decay products came from the same particle. In other words to investigate if the products belong to the decay of a particle which has a particular invariant mass.

#### The invariant mass

The invariant mass is also called the "rest mass", it is characteristic of a particle. According to Einstein's theory, the invariant mass is a quantity which does not change with velocity or frame of reference. If the units are chosen in such a way that the velocity of light is c=1, then the invariant mass is defined as where E is energy and p = m ν is momentum of the particle. If we are looking at its decay products, one has to measure the energy and momentum of each particle and then sum all their energies
E = E1 + E2 + E3+ ...
and their momenta The result is the invariant mass and if you are looking at one particle, then the mass calculated in each event should be "almost" the same, so if you make the distribution of the masses for various events, you will see a peak around the particle's mass.

#### Measurement of the width of a particle For reasons, which are connected with the uncertainty principle, if the particle is very short lived, then the measurement of its energy and therefore its invariant mass has an uncertainty. It does not always have the same value but its histogram (distribution of values) is peaked around the nominal mass value but follows a certain distribution as shown in the figure. The width at half-maximum is labeled as Γ and is connected to the particle's lifetime. The width of the particle gives very valuable information and has to be measured. As an example we quote that the measurement of the width of the Z particle in LEP (CERN's previous big accelerator which was replaced by LHC) gave a very good determination of the number of different neutrinos types which exist.

#### Emiss: missing momentum/energy This is the momentum/energy which is not detected in the detector, but is expected because of energy and momentum conservation. The Emiss is generally attributed to particles which escape the detector without being detected such as the neutrinos (although apparent missing energy may be caused by mismeasurement of the momentum/energy of detected particles). In LHC, the initial momentum of the colliding constituents along the beam axis is not known (because the energy of each hadron is split, and constantly exchanged, between its constituents), so the amount of missing energy cannot be determined. However, the initial energy and momentum transverse to the beam axis is zero, so any net momentum indicates missing transverse momentum/energy (Etmiss). It is represented (in the event display) with a dashed line which in addition to the value (which is the magnitude of the transverse missing momentum/energy) shows the direction of the missing transverse momentum.