Classification of particles

What you'll learn:

How to divide all particles into two major families: hadrons and leptons.
The difference between baryons and mesons.
The specific roles of the pion, kaon, and muon.
How to predict whether a particle interaction can actually happen by checking the conservation of baryon number, lepton number, and strangeness.

The Great Divide: Hadrons vs. Leptons

When physicists first started smashing particles together, they discovered hundreds of new particles. To make sense of this "particle zoo", they grouped them based on how they interact with the fundamental forces of nature.

The biggest dividing line in particle physics is the strong nuclear force (the force that holds the nucleus together). Every particle in the universe either "feels" this force or is completely blind to it.

Definition

Hadrons and Leptons

Hadrons are particles that can feel the strong nuclear force.
Leptons are fundamental particles that cannot feel the strong nuclear force.

Classification of subatomic particles

Hadrons: Baryons and Mesons

Hadrons are the heavyweights of the particle world. Because there are so many of them, we split them into two further sub-categories based on their mass and internal structure (which you'll learn about when we look at quarks). These two sub-categories are baryons and mesons.

1. Baryons

Baryons are the heaviest hadrons. The two you already know perfectly are the proton and the neutron. Every baryon has a corresponding anti-baryon (like the antiproton and antineutron).

A crucial rule of the universe is that the proton is the only stable baryon. This means that if you leave any other baryon alone for long enough, it will eventually decay into a proton (either directly or through a chain of decays). For example, a free neutron decays into a proton in about 15 minutes!

2. Mesons

Mesons are generally lighter than baryons. The AQA specification requires you to know about two specific types of mesons:

Pions ( $π\pi$ ): These are the lightest mesons. The pion acts as the exchange particle of the strong nuclear force. When protons and neutrons bind together in a nucleus, they do so by tossing pions back and forth between them.
Kaons ( $K$ ): These are heavier mesons. They are unstable and decay into pions.

Key Idea

Baryon Number ( $B$ )

To keep track of baryons during particle interactions, physicists assign them a quantum number called the baryon number, represented by the symbol $B$ .

All baryons have $B = + 1$ .
All anti-baryons have $B = - 1$ .
Everything else (mesons, leptons, photons) has $B = 0$ .

In any interaction, the total baryon number before must equal the total baryon number after. If it doesn't, the interaction is completely impossible.

Example

Checking Baryon Number Conservation

A student suggests that two protons could collide at high speeds to produce two protons, a neutron, and a positive pion, according to the equation:

\begin{aligned} p + p \to p + p + n + \pi^+ \end{aligned}

Determine whether this interaction can occur by checking the conservation of baryon number.

Write down the baryon number ( $B$ ) for every particle involved. Protons and neutrons are baryons ( $B = + 1$ ). Pions are mesons, not baryons ( $B = 0$ ).
Calculate the total baryon number on the left-hand side (LHS). We have two protons:

\begin{aligned} \text{LHS } B &= (+1) + (+1) \\ &= +2 \end{aligned}

Calculate the total baryon number on the right-hand side (RHS). We have two protons, one neutron, and one pion:

\begin{aligned} \text{RHS } B &= (+1) + (+1) + (+1) + 0 \\ &= +3 \end{aligned}

Compare the two sides. Since $\neq +3$ , baryon number is not conserved. This interaction is physically impossible.

Leptons: The Fundamental Lightweights

Unlike hadrons, leptons do not feel the strong nuclear force at all. As far as we know, leptons are truly fundamental—they have no internal structure and cannot be broken down into anything smaller.

You need to know about three specific leptons (and their antiparticles):

The Electron ( $e^-$ ): The familiar, stable particle orbiting the nucleus.
The Muon ( $μ−\mu^-$ ): You can think of the muon as a "heavy electron". Because it is heavier, it is unstable. It eventually decays into an electron.
The Neutrinos ( $νe\nu_e$ and $νμ\nu_\mu$ ): These are incredibly light, uncharged particles that rarely interact with anything. There is a specific electron-neutrino ( $νe\nu_e$ ) associated with the electron, and a specific muon-neutrino ( $νμ\nu_\mu$ ) associated with the muon.

Conservation of Lepton Number

Just like baryon number, lepton number must be conserved. However, there is a catch! The universe treats the "electron family" and the "muon family" as strictly separate. You must conserve the electron lepton number ( $L_e$ ) and the muon lepton number ( $LμL_\mu$ ) independently.

Tip

Assigning Lepton Numbers

Is it an electron or an electron-neutrino? Then $L_e = +1$ .
Is it a positron or an anti-electron-neutrino? Then $L_e = -1$ .
Is it a muon or a muon-neutrino? Then $Lμ=+1L_\mu = +1$ .
Is it an anti-muon or an anti-muon-neutrino? Then $Lμ=−1L_\mu = -1$ .
Is it a hadron? Then both $L_e = 0$ and $Lμ=0L_\mu = 0$ .

Example

Checking Lepton Number in Muon Decay

A muon decays into an electron, an anti-electron neutrino, and a muon neutrino:

\begin{aligned} \mu^- \to e^- + \bar{\nu}_e + \nu_\mu \end{aligned}

Show that both muon lepton number ( $LμL_\mu$ ) and electron lepton number ( $L_e$ ) are conserved.

First, let's check the muon lepton number ( $LμL_\mu$ ).
On the LHS, the muon ( $μ−\mu^-$ ) has $Lμ=+1L_\mu = +1$ .
On the RHS, the $e^-$ and $νˉe\bar{\nu}_e$ are in the electron family, so they have $Lμ=0L_\mu = 0$ . The $νμ\nu_\mu$ is a standard muon neutrino, so $Lμ=+1L_\mu = +1$ .
LHS $Lμ=+1L_\mu = +1$ , RHS $Lμ=+1L_\mu = +1$ . Muon lepton number is conserved.
Now, let's check the electron lepton number ( $L_e$ ).
On the LHS, the muon is not in the electron family, so $L_e = 0$ .
On the RHS, the electron ( $e^-$ ) has $L_e = +1$ . The anti-electron neutrino ( $νˉe\bar{\nu}_e$ ) is an antiparticle, so $L_e = -1$ . The muon neutrino has $L_e = 0$ .
Calculate the RHS total: $L_e = (+1) + (-1) + 0 = 0$ .
LHS $L_e = 0$ , RHS $L_e = 0$ . Electron lepton number is conserved. The decay is permitted!

Strange Particles

In the mid-20th century, scientists studying cosmic ray showers in cloud chambers noticed a new particle. It was produced very quickly in high-energy collisions, but it decayed much more slowly than expected. Because of this unexpectedly long lifespan, physicists named them strange particles. The kaon ( $K$ ) is the classic example of a strange particle.

We now understand why they act this way, and it involves two different fundamental forces:

Strange particles are produced through the strong interaction.
Strange particles decay through the weak interaction.

The Strangeness Quantum Number ( $s$ )

To explain this behaviour, physicists invented a new quantum number called strangeness ( $s$ ).

The rule is that the strong interaction conserves strangeness, but the weak interaction does not.

Because normal matter (like protons and neutrons) has a strangeness of 0, creating strange particles via the strong interaction means the total strangeness must remain 0. The only way to do this is to create strange particles in pairs—one particle with a positive strangeness, and one with a negative strangeness.

When a strange particle eventually decays, it has to do so via the weak interaction. In a weak interaction, strangeness can change by 0, +1 or -1.

Life cycle of a strange particle

Example

Strangeness Conservation in Particle Production

A negative pion ( $π−\pi^-$ ) collides with a proton ( $p$ ) via the strong interaction to produce a neutral kaon ( $K^0$ ) and a Lambda particle ( $Λ0\Lambda^0$ ).

\begin{aligned} \pi^- + p \to K^0 + \Lambda^0 \end{aligned}

Pions and protons are not strange particles. The $K^0$ has a strangeness $s = + 1$ . Determine the strangeness of the $Λ0\Lambda^0$ particle.

Identify the interaction type. The question states this is a production via the strong interaction, meaning strangeness must be perfectly conserved.
Calculate the total strangeness on the LHS. Neither the pion nor the proton is strange, so:

\begin{aligned} \text{LHS } s = 0 + 0 = 0 \end{aligned}

Set up the RHS equation. The $K^0$ has $s = + 1$ . Let the strangeness of the $Λ0\Lambda^0$ be $sΛs_\Lambda$ .

\begin{aligned} \text{RHS } s = +1 + s_\Lambda \end{aligned}

Equate LHS and RHS to find $sΛs_\Lambda$ :

\begin{aligned} 0 &= +1 + s_\Lambda \\ s_\Lambda &= -1 \end{aligned}

The Lambda particle has a strangeness of -1. (This illustrates that strange particles are created in pairs to conserve overall strangeness!)

Common Mistake

Confusing the forces in Strangeness

A very common exam error is forgetting which force does what. Remember:

Strong = Fast = Production = Conserves strangeness.
Weak = Slow = Decay = Does not conserve strangeness.

Big Science and Collaboration

Particle physics today isn't done by a single scientist looking through a microscope. Studying these interactions requires accelerating particles to enormous speeds and colliding them, simulating the high-energy environments of cosmic rays.

Facilities like CERN require the collaborative efforts of large teams of scientists and engineers. Building a 27 km particle accelerator (the Large Hadron Collider) and processing the petabytes of data it generates is impossible for one person. Teams from all over the world must peer-review data, validate computer simulations, and confirm findings before new knowledge is accepted by the scientific community.

Exam technique

In the exam

When asked to check if a reaction is possible, always check Charge ( $Q$ ), Baryon number ( $B$ ), and Lepton number ( $L$ ) (checking $L_e$ and $LμL_\mu$ separately). If any of these are not conserved, the reaction is impossible.
If asked what the exchange particle for the strong nuclear force is, answer pion. If asked what a kaon decays into, answer pions. If asked what a muon decays into, answer an electron (plus neutrinos).
If an exam question mentions a particle with an unusually long lifetime, or mentions particles created in pairs, you should immediately think of strange particles and the strangeness quantum number.

Self review

Check yourself

What is the fundamental difference between a hadron and a lepton?
What is the only stable baryon?
Why must you check electron lepton number and muon lepton number separately?
Which fundamental force is responsible for the production of strange particles, and which is responsible for their decay?

What you'll learn:

How to divide all particles into two major families: hadrons and leptons.
The difference between baryons and mesons.
The specific roles of the pion, kaon, and muon.
How to predict whether a particle interaction can actually happen by checking the conservation of baryon number, lepton number, and strangeness.

The Great Divide: Hadrons vs. Leptons

Definition

Hadrons and Leptons

Hadrons are particles that can feel the strong nuclear force.
Leptons are fundamental particles that cannot feel the strong nuclear force.

Classification of subatomic particles