Objectives:

• To gain an understanding of the sub categories of hadrons; baryons and mesons.
• To be able to classify hadrons and leptons and understand what forces are associated with each
• To appreciate the existence of particles and their antiparticles and the relationship between the two involving mass and charge

As we saw on the first page on the standard model, there are further sub categories of fundamental particle, these sub categories help with the appreciation of rules for particle physics to work.

Quarks never exist on their own, the reason for this is that it takes more energy to separate any two quarks than the quarks themselves contain. So there must be combinations of quarks that make up other particles;

Hadrons – these are composite particles which are made up of quarks which are held together via the strong force (in a similar way to how molecules are held together via the electromagnetic force). Most of the matter all around us consists of protons, neutrons and electrons. We know now that electrons are themselves fundamental particles and are in the lepton group. Protons and neutrons however are both made up of quarks, this means that protons and neutrons are examples of hadrons.

There are several sub categories of Hadrons, the two of significance for your A levels are baryons and mesons.

Baryons

A baryon is a particle that is a made up of a combination of 3 quarks. Protons and neutrons are both examples of baryons.

Image 1

This image of a baryon shows two up quarks and two down quarks.

Quarks, as shown in the standard model each have their own charge, either $+\frac{2}{3}e$ or $-\frac{1}{3}$.

Everything around else is typically made up of the fundamental particles that are in the first generation of matter.

Image 2

Based on this knowledge can you guess what particle (or baryon) is shown in the image above?

Additionally, can you determine the type of particle in this image to the right?

Image 1 shows two up quarks and 2 down quarks. So the the charge of the baryon is:

$+\frac{2}{3} + \frac{2}{3} + -\frac{1}{3} = 1e$

With combined charge of +1e, we have a proton.

For the second image:

$+\frac{2}{3} + -\frac{1}{3} + -\frac{1}{3} = 0e = 0$

The combined charge is 0 C, so it is a neutron.

Mesons

A meson is a particle that is a made up of a combination of one quark and an antiquark (antiquarks are a type of antimatter and are discussed below). All mesons are unstable, the longest of which has only stuck around for a few hundredths of a microsecond; $<10^{-7} s$ .

Leptons

As spoken about on the first page regarding the standard model. leptons are a type of fermion, as are quarks but they can exist on their own. Unlike quarks that carry a fraction of the elementary charge, leptons carry an integer charge of $0$ or $\pm 1$ .

Hadrons are held together via the strong interaction (strong force), of which gluons are responsible for. Leptons, since they can exist on their own, are not governed by the stop interaction.

Antimatter

Every particle has an antiparticle with the same mass but the opposite electrical charge. The proton has the negatively charged antiproton; the electron has the positively charged anti-electron, or positron.  Neutral particles, like the neutron also has its own antiparticle the antineutron – this becomes clearer;

As stated above, every particle has an antiparticle, so this means the fundamental particles too. every fermion in the standard model has its own equivalent antiparticle. Additionally, antiparticles are all written with the same symbol as ‘normal’ matter but with a ‘hat’, or ‘horizontal bar’ on top of it, some examples are given here;

up quark, $u \rightarrow$ anti-up quark, $\bar{u}$
down quark , $d \rightarrow$ anti-down quark, $\bar{d}$
strange quark, $s \rightarrow$ anti-strange quark, $\bar{s}$
tau , $\tau \rightarrow$ anti-tau , $\bar{\tau}$
electron-neutrino, $\mu_{e} \rightarrow$ antielectron-neutrino , $latex\bar{\mu_{e}}$

Additionally, since a proton is made up of two up quarks and a down quark, an antiproton is made up of two anti-up quarks and an anti-down quark. To check this is correct in terms of charge;

anti-proton: $\rightarrow$ $\bar{u}$$\bar{u}$$\bar{d}$

charge: $-\frac{2}{3}e$$-\frac{2}{3}e$$+\frac{1}{3}e$
Total charge = $-1e$

Since the mass of each anti-quark is the same as its equivalent quark, the anti-proton will have the same mass as the proton.

It is also worth noting that it is not just the charge that is opposite for antimatter, in fact every property of a particular anti-particle is opposite except the mass.

Properties of different types of fundamentals particles

Now you know of a whole range of new types of particle, we are going to start making some sense of them and you will begin to appreciate why they are names differently.

Baryon number

Baryons, those hadrons that are made up of 3 quarks, have a quantum number assigned to them known as the baryon number, the baryon number of a baryon is $+1$ and (as mentioned above every property of a particular anti-particle is opposite except the mass’) an antibaryon has a baryon number of $-1$. Baryons are made up of 3 quarks, each of these quarks (no matter what flavour (type) they are) have their own baryon number of $+\frac{1}{3}$ .

The baryon number is a quantity that needs to be conserved in nature, just like energy and momentum etc.

Mesons, those hadrons that are made up of a quark-antiquark pair have a baryon number of $0$.

Example: A Pion+, $\pi^{+}$ is a subatomic particle consisting of a quark and an antiquark, it is therefore a meson. It contains an up quark and an antidown quark, $u \bar{d}$. The baryon number is therefore $+\frac{1}{3} + -\frac{1}{3} = 0$ and hence the baryon number can confirm it is not a baryon and that it is a meson. Additionally, this is a $\pi^{+}$ meson, the charge can be determined; $+\frac{2}{3} + \frac{1}{3} = +1$ hence $^{+}$ in its name.

A Pion- also exists, $\pi^{-}$, can you determine what it is made out of?

Answer: Baryon number must be zero, so it must contain a quark and an anti-quark. Since it is a Pion it is made up of similar quarks to the $\pi^{+}$. It is a $\pi^{-}$ however and so must have a negative charge, this could come about by using an antiup and a down quark, $\bar{u}d$; Charge: $-\frac{2}{3} - \frac{1}{3}$.

A Pion-0 \$ also exists, $\pi^{0}$, can you determine what it is made out of?

Answer: Baryon number must be zero, so it must contain a quark and an anti-quark. Since it is a Pion it is made up  similar quarks. It is a $\pi^{0}$ however and so must have no charge, this could come about by using an up and an antiup quark $u\bar{u}$ OR a down and an antidown quark, $d\bar{d}$; Charge: $+\frac{2}{3} + -\frac{2}{3} = 0$, OR $-\frac{1}{3} + \frac{1}{3} = 0$.

Lepton number

Leptons, the fundamental particles that can exist on their own, each have a lepton number of $+1$ and similiarly anti leptons have a lepton number of $-1$. Since these particles cannot be broken down any further, there are no particles that have a fraction of a lepton number.

The lepton number is another quantity that needs to be conserved in nature, just like energy and momentum etc.

A table of all the quantum numbers for each quark is shown here;