CONSERVATION RULES

We're at the end of this chapter now, and while that's incredibly sad and you're on the verge of bawling your eyes out I don't care - we're discussing conservation now, in terms of what's always conserved, what's sometimes conserved and what's never conserved. 

Quantities that are Conserved for Particular Interactions

Particles and antiparticles decay and interact and have particular properties - and they abide by the rules. The rules are as follows:

1) Conservation of Energy and Charge: This goes for all particles/ antiparticles/ toasters/ wombats etc. Charge and energy cannot be created or destroyed.Without this rule being followed, reactions simply wouldn't occur. 

2) a) Conservation of Lepton Numbers: This goes for particular particle-antiparticle interactions and decays. The total lepton number before a change is equal to the total lepton number after a change, for every lepton branch. Observe the table for the figures concerning the muon lepton number and the electron lepton number.

b) Conservation of Strangeness: This goes for particular particle-antiparticle interactions and decays. Strangeness is only conserved in the strong interaction - all changes involving the strong interaction lead to conservation. 

• Any hadron made up of a strange quark has a strangeness of -1, and a strangeness of +1 if made up of an antistrange quark. 
• Anything that is not a hadron has a strangeness of 0, which is 'strange' due to the numbers being crazy.

3) Conservation of Baryon Numbers: Some reactions have been observed but others haven't, yet all of the above rules are obeyed. In any reaction, the total baryon number is conserved. Remember that anything that isn't a baryon has a baryon number of 0 - so an antibaryon has a baryon number of -1 and a baryon of +1.

An up quark and an up antiquark annihilate each other - sad stuff, I know, but take a look at the quarks and antiquarks rearranging to form mesons. Beautiful. If the above baryon numbers are assigned to each of these guys, leptons have a baryon number of 0, quarks (+1/3) and antiquarks (-1/3). 

SO 0 = (+1 -1) and conservation of their baryon numbers has occured. Amazeballs, right? Like I said before, this heartwarming instance occurs in all reactions. 

It's been great having you guys here, but I'm afraid it's time for me to take my leave. I'll treasure the memories. Hopefully you're solid on this quarks and leptons stuff, and if you're not - that sucks. 

Keep on quarkin'.

QUARKS AND ANTIQUARKS

This is where stuff gets kind of strange. And cute. We're talking about quarks and antiquarks - those pesky little things that form the basis of particles as we know it. We know of their existence due to using the Standford linear accelerator in order to make electrons collide with protons at high speed. Said electrons scattered in particularly different directions, and so quarks with particular characteristics were discovered. 

Did you know that a far more complicated experiment was also attempted, which in turn reconfirmed the existence of quarks and antiquarks? Well, now you know. The annihilation of electrons and positrons was found to produce muon-antimuon pairs or quark-antiquark pairs, which later produce hadrons. The hadrons being made proves it all. Great.

As an AS-Level student, you'll only need to learn about about three quarks: up (u), down (d) and strange (s). Atoms are beyond miniscule, and the quarks and antiquarks that make up the tiny subatomic particles are even smaller, therefore they have fractional charges. I suggest we learn about strangeness first, because it seems pretty weird to me.

Strangeness

Strangeness became a flavor when K mesons were originally called V particles, due to their tracks being v-shaped in cloud chamber photographs. This was deemed 'strange' upon realizing that the v tracks decay into pions only, or pions and protons. Those that decayed into pions only were named K mesons, and the others were found to have higher rest masses than those of a proton and decayed in sequences/ directly into protons and pions.

• Strangeness was introduced in order to specify why certain reactions conserving charge were not observed. 
• Non-strange particles such as protons, neutrons, pions and leptons were given a strangeness of 0, and strange particles such as positive kaons were given +1.

Strangeness is always, always, always conserved in a strong interaction. Decays involving weak interactions don't see this conservation of strangeness. 

To go about understanding hadrons, their constituents (quarks and antiquarks... duh) and their properties need to be understood. This table shows the charges and strangeness of up, down and strange quarks and their antiquarks.

The Quark Model and their Combinations

Pions and kaons are placed into something called the 8-fold-way to show the possible quark combinations – but in actuality there are only six points in this diagram and one new particle, so that’s kind of silly. But whatever, we have something new to learn about now: pi-zero.

(SOURCE: AQA Physics A, Nelson Thornes 2008)

Quarks are combined in particular ways to form baryons and mesons - is some of the previous material beginning to make sense? No? Well, you know what to do - go here. For those of you who've been paying attention, carry on.

Mesons are made up on an antiquark and a quark. The diagram above shows the nine possible combinations and the resulting meson that forms. Things to make a note of would be that:

• Each pair of charged mesons are of a quark-antiquark combination
• A π° can be made up of any particle-antiparticle combination
• Two uncharged kaons can form: the neutral K meson, and the neutral anti K meson
• The antiparticle of a meson is a meson - this is because of a meson being an antiquark-quark pair

Examples of baryons are neutrons and protons - protons having the antiproton as its antibaryon. Baryons are made up of three quarks and antibaryons are made up of three antiquarks. The possible combinations are:

• [uud] QUARKS for a proton
• [udd] QUARKS for a neutron
• [uud] ANTIQUARKS for an antiproton 

Note that the proton is the only stable baryon, as neutrons emit fast-moving electrons in beta decay which showcases their excessive energy and instability. 

The Responsibility of Quarks in Beta Decay

In β⁺ decay, a proton in a proton-rich nucleus changes into neutron - the diagram above shows the release of a positron and an electron neutrino. In terms of quarks, an up quark changes into a down quark.

In β⁻ decay, a neutron in a neutron-rich nucleus changes into a proton - the diagram above shows the release of an electron and an electron antineutrino. In terms of quarks, a down quark changes into an up quark.

Fun fact: Geese are capable of breaking a grown human being's arm when feeling threatened. So be wary of geese. Ducks are cooler. 

LEPTONS AT WORK

So we went over hadrons vaguely last time, concluding that they're composed of particles called quarks/ antiquarks - mesons having a quark and an antiquark, and baryons having three quarks/ three antiquarks. Some carry charge, i.e. (p, Kˉ, K+) and some have no charge, i.e. (n). And if electromagnetic interaction is not involved, they're not charged.

So now we'll get to know leptons. Loopy leptons. Leptons don't interact through the strong interaction and they're lightweights - electrons, muons and neutrinos are fundamental particles with no internal constituents (like quarks). This makes them seem lame and all, but just you wait.

Just like any other particle, there are antiparticles (of an identical mass, with opposite properties) - and when antileptons interact with leptons, we end up with something great: hadrons. If you recall the previous topic, the diagram shows an electron-positron collision, resulting in a showering of hadrons - amazing stuff, right? Leptons can be accelerated to collide and they have an associated neutrino and antineutrino... So we'll move on to a subtopic.

Differentiating Between Neutrino Types

Note: A third family, the 'tau' family, exists, but AQA doesn't care about tau and has therefore excluded them from our lives. Maybe it's for the best. 

I hope you can forever remember that neutrinos are basically a similar variant of the typical electron - but neutrinos carry no charge, hence their being called 'neutrinos'. Shocker. Due to being electrically neutral, neutrinos are not affected by the electromagnetic interaction and only if they have mass do they interact via the gravitational interaction with other massive particles. They tend to pass through ordinary matter easily and are pretty much undetectable, like the Batman. What a life they lead.

• We have the beloved electron neutrino and the muon neutrino to think about now. As mentioned above, we don't care for the tau neutrino.
• Electron neutrinos are far more common in our world, but muon neutrinos are detectable as well. 
• The muon neutrino is associated with the muon (remember, this is the heavier electron), and the electon neutrino with the electron.
• In muon and antimuon decay, neutrinos and antineutrinos create muons when interacting with protons and neutrons - this differs from that of beta decay. 
• One type of antineutrino and neutrino existing would facilitate for the production of electons and and muons of the same number. But we have at least three neutrino-antineutrinos, so whatever. 

Fun fact: The terms 'electron neutrino', 'tau neutrino' (why are these guys here again?) and 'muon neutrino' are referred to as flavors. Yeah, flavors. Now, if you'll excuse me, I think some muon neutrino green tea would be nice. Referring to them as 'types' or 'flavors' is fine by the AQA.

Lepton Numbers and the Rules they Obey

Neutrinos are created through radioactive decay or nuclear reactions (like those happening in the Sun, when cosmic rays hit atoms or in nuclear reactors).

When neutrons change into protons or protons change into neutrons, neutrinos are generated. You should recognize those two occurrences are two forms of beta decay. If you didn’t realize that, then go here. Did you go there? Okay, back to this stuff. Leptons interact through the weak interaction (remember, that's responsible for beta decay) and these guys are elementary particles due to them not breaking down further. 

Lepton decay can be sussed out by observing the changes in lepton number - conservation of charge is involved here, of course. Now check out these standardized rules:

1. "In an interaction between a lepton and a hadron, a neutrino or an antineutrino can change into or from a corresponding charged lepton." (AQA Physics A, Nelson Thornes, 2008)

So if we take a look at an electron neutrino interacting with a neutron, a proton and electron are produced. Check out the conservation of charge:

Initially the lepton number is +1 and then +1 after the change too. This is permitted. This is because the lepton was assigned a +1 charge, the antilepton a -1 charge and any nonlepton a charge of 0. 

But if the products were to be an antiproton and a positron, the lepton numbers change.

This is an abomination. The charges go from +1 to -1 and this defies the conservation of charge. This is not permitted.

2. "In muon decay, the muon changes into a muon neutrino. In addition, an electron and an electron antineutrino are created to conserve charge." (AQA Physics A, Nelson Thornes, 2008)

We started off with a muon changing into an electron, an electron antineutrino and a muon neutrino. Inititally the lepton number is +1 and +1 afterwards too (+1 = +1 -1 +1) so this is permitted. 

But oh no, someone wanted a muon antineutrino in the decay products instead of a regular muon neutrino. That's just crazy. Why? Because the lepton numbers just don't add up. See, initially we have a charge of +1, but then through (= +1 -1 -1) we end up with -1. Not cool. This is not permitted. 

So don't do that. 

The above rules are applied to particular branches of leptons, so take the following into account.

1. The electron branch consisting of electron neutrinos, electrons and their counterparts
2. The lepton number for each branch is conserved for all changes
3. Leptons are in two branches: the muon branch and the electron branch
4. The muon branch consists of muons, muon neutrinos and their counterparts
5. Leptons have a lepton number of +1, antileptons have -1 and nonleptons are 0.

To recapitulate:

• Types of leptons include the electron, positron, muon, antimuon, electron neutrino, electron antineutrino, muon neutrino and muon antineutrino. 
• Charged leptons interact through the electromagnetic interaction. Leptons in general interact through the weak interaction - never the strong interaction.
• Leptons can decay into other leptons through the weak interaction and can be produced or annihilated through particle collision. 
• Nonleptons can never be products of this type of decay.
• The lepton number must be conserved at all times. Yes, even on a Sunday. 

PARTICLE SORTING

Classification of Particles and Patterns

So we've come across a bunch of particles and antiparticles that have varying properties, but they still seem to interact similarly. The table below shows the particles we've discussed previously - can you make any links?

Defining Hardons and Leptons

The trick is to lump the above into two categories, depending on whether or not said particle/ antiparticle interacts via the strong interaction. The two categories are hadrons and leptons.

• Hadrons interact through the strong interaction, e.g. protons, neutrons and mesons, and if charged via through the electromagnetic interaction. 
• Leptons do not interact through the strong force, e.g. electrons, muons and neutrinos, and if charged via through the electromagnetic interaction.

Remember: HEAVY HADRONS ARE STRONG! 

              LIGHT LEPTONS ARE WEAK!

"The picture [below] shows particle tracks from an electron-positron collision in the former Large Electron-Positron Collider (LEP) at CERN in Geneva. Here a Z0 particle is produced in the collision, which then decays into a quark-antiquark pair. The quark pair is seen as a pair of hadron jets in the detector." (Source: http://laganphysics.weebly.com/)

As has been mentioned endlessly, energy/ charge/ mass is conserved. Always. The sum of the rest mass energy of a particle/ antiparticle and their kinetic energy equates to the total energy of the particles/ antiparticles before the collision 

AND

the total energy of the particles/ antiparticles after the collision equates to the sum of their rest mass energy and their kinetic energy. Which is all a mumbo-jumbo way of saying that:

So if a K+ meson decayed into its π+, π+ and π counterparts, the maximum kinetic energy of the pi mesons would be calculated as follows (assuming the K meson is at rest before decay):

1. Rearrange the above equation to state that: the kinetic energy of the products equates to total energy before minus the rest energy of the products
2. Substitutue in the appropriate values (by making use of the particle-antiparticle table at the top of this page): kinetic energy = 494 - (140 + 140 + 140) 
3. End up with kinetic energy of the products equating to: 494 - 420
4. The answer is 74MeV. :-)

Baryons and Mesons

Baryons and mesons are classified under the category of hadrons, as they're created through the strong interaction. But they're pretty weird, as they can decay into protons as well as π mesons - this is weird because protons are never the decay products of a K meson. Freaky stuff. Okay, not really. 

SO ANY WAYS these splendid hadrons are divided into baryons and mesons, which - wait for it - are MADE UP OF YET MORE PARTICLES called quarks and antiquarks. But more of that later.

• Baryons are protons (and other hadrons, like neutrons) that decay into protons
• Mesons are hadrons (such as K mesons and π mesons) that do not include protons in their decay products

Energy Principles in Particle Collisions

If you haven't checked out the GLOSSARY then you should go ahead and do that. Good stuff. So you should have grasped the fact that these particles/ antiparticles are like your stereotypical characters in everyday life or games. They interact in very particular ways, and abstain from living life in any other way... Fun stuff.

THE PARTICLE ZOO

The Discovery of Particles and Particle Accelerators

Prior knowledge regarding the constituent particles of the atom (protons, neutrons and electrons) alongside familiarity with the ideas of conservation of energy, charge and mass should enable you to understand particle physics. We’ll be looking at particles classified as hadrons (baryons and mesons) and leptons, each with its own antiparticle and each with their own interactions that occur between particles.

Subatomic particles such as the proton, neutron and electron were identified as major components of the atom, and further particles have been identified too, such as quarks that make up protons and neutrons and particles such as muons, leptons and neutrinos. 

It all seems pretty confusing, and it only gets far more discombobulating – variable “fields” have been observed in the universe that have incredibly important roles in the functioning of the universe, such as: magnetic fields, electrical fields, gravitational fields and more. 

And scientists are looking for more. 

If you haven’t come across the search for a particle called the Higgs boson – a particle potentially responsible for the “field” giving mass to some particles but not others – then you’re missing out. The world’s largest particle accelerator began operations in Europe in 2008, and the search for new particles and fields is expanding.

Likewise, exchange particles called mesons were hypothesized by Japanese physicist Hidekei Yukawa, who predicted the existence of these exchange particles to be of a range of no more than 10⁻¹⁵m and with a mass between that of a proton and electron. 

A cloud chamber photograph obtained by Carl Anderson was thought to have shown a meson, but instead the heavy electron was discovered – the muon – due to the track length of 40mm lasting longer than that of a strong-interacting particle. Years later British physicist Cecil Powell discovered pions, or pi mesons – "microscopic tracks were found in photographic emulsions exposed to cosmic rays at high altitude" (AQA Physics A, Nelson Thornes, 2008).

• The Stanford Linear Accelerator in California permits electrons to accelerate over 3km through 50,000mV. When these electrons collide with a "target", particle-antiparticle pairs are created.
• The Large Hadron Collider at CERN has a circumference of 27km and is designed in a ring structure underground, differing from a linear accelerator as hadrons are accelerated at more than 7000GeV. Protons, neutrons and mesons go under the hadron subsection.

The search has extended to looking for particles and fields coinciding with dark energy and dark matter. It is known that dark matter fills the universe, exerting a gravitational pull on the regular matter (like stars and planets) surrounding it. But it’s undetectable – no radio waves, no heat – basically no form of energy - is produced from dark matter – therefore physicists are eager to defy the laws of physics and find evidence for dark energy particles or fields.

Ultimately, scientists would need incredibly powerful particle accelerators and a lot of luck in discovering dark energy particles/ fields. In the meantime a new field has been described, called quintessence. 

"One key difference from the vacuum energy is that quintessence would vary with time, so it might not show up at all in the early universe, but exert a powerful influence today. " (http://hetdex.org/dark_energy/)

Several hypotheses exist and all is debatable. NOW BACK TO THE MAIN STORY, THE PARTICLE ZOO! 

Muons, Pions and Kaons 

• Muons: heavy electrons, a negatively charged particle, a rest mass of over x200 regular electron
• Pions: positively charged or negatively charged or neutral, a rest mass greater than a muon but less than a proton
• Kaons: positively charged or negatively charged or neutral, a rest mass greater than a pion but less than a proton

INTRODUCTION

To start off, I'd like to look back at particles and antiparticles - mainly the way they interact. In Chapter 1 of your textbooks you should have come across annihilation and pair production of particles and antiparticles, as well as photons and their role.

Photons

We already know that light is a part of the electromagnetic spectrum of waves, where [λ=c/ f], and the speed of light is [3.00 x 10⁸ ms⁻¹]. 

Packets of electromagnetic waves - i.e. particles of light - are photons. 

The energy of a photon is equal to [h x f], where [f] is the frequency of the wave in Hz, and [h] is Planck's Constant: [6.63 x 10⁻³⁴ Js]. This equation will give us the energy of a photon in joules [J]. 

Matter and Antimatter

Antimatter is the 'mirror image' of normal, everyday matter. The table above shows how antimatter has the same mass as their correspondents, but an equal and opposite charge. 

When matter and antimatter meet, their mass is converted into pure energy in the form of photons - this is called annihilation. 

An absolute minimum of two photons are produced in annihilation, as a single photon being released would negate the Conservation of  Momentum, where charge and mass remain intact. 

The minimum energy of each photon produced can be calculated: [h x f min = E₀], where [E] is the rest mass of the electron (0.511MeV)

Likewise, pair production is the conversion of energy into mass, in the form of an antiparticle and a particle. The minimum energy of the photon needed can be calculated as such: [h x f min = 2E₀]

Recall [E = h x f], remembering that [Emin] equates to [hfmin], which in turn is equal to [2E₀].

[E₀ = mc²], which is the rest mass energy.

The Weak Nuclear Force

W-bosons are the exchange particle that causes a proton to change into a neutron, and vice versa in β decay. These exchange particles:

1) have a non-zero rest mass,

2) have a very short range of no more than 0.001 fm, and

3) are positively charged (the W+ boson) or negatively charged (W- boson)

Here are two instances of W-bosons acting as the exchange particles, and so showing the conservation of charge:

• A neutron interacting with a neutrino creates a β- particle (an electron)
• A neutron of no charge releases a proton of positive charge and a W- boson of negative charge
• The overall charge expelled is zero, which is the same amount going in - charge is conserved

• A proton interacting with an antineutrino creates a β+ particle (a positron) 
• A proton of positive charge releases a neutron of no charge and a W+ boson of positive charge
• The overall charge expelled is positive, which is the same amount going in - charge is conserved