If you wanted to learn all fundamental particle physics,
you would first need to know that the world we live in is governed by four forces. The strong,
weak, electromagnetic and gravitational force. We have a quantum description for 3 of these
forces. The odd one out is gravity, for which there is no quantum theory as yet.
But it is so weak, that it doesn’t have a significant effect at the quantum level,
since the other forces overpower it. So it is generally ignored in quantum calculations.
But after almost a hundred years of scientific progress, we can very accurately describe the
other three forces in terms of quantum field theories. These theories explain how particles
like quarks and electrons interact with each other via these three forces. Each force is mediated
by a force carrier, also called a mediator. The electromagnetic force is mediated by the
photon, the weak force by the W and Z bosons, and the strong force by gluons. In a quantum
field theory, we represent each of these mediator particles with a field. For example, the photon
field mediates the electromagnetic force between electrically charged particles like electrons.
Other fundamental particles of the standard model are also represented by their own
respective fields. And these fields can interact with each other. Thus, the photon field can
interact with the electron field causing a repulsion of two electrons for example
If we generalize this concept of force carrying particles interacting with other particles, we
can get all fundamental particle physics. We can take spacetime, add a quantum field for each type
of fermion, like quarks, add quantum fields for the appropriate bosons, like gluons, that mediate
the force that the quark is subject to, and we can get a great representation of how it all works.
These theories can be complicated, but American physicist Richard Feynman came up with an
ingenious way to represent these interactions in what is now called Feynman diagrams.
And even though these diagrams represent complicated mathematical equations,
they can be visualized intuitively and drawn for any process using some simple rules.
If you want to understand all fundamental particle physics with the help of these
simple intuitive Feynman diagrams, then Merry Christmas, because that’s coming up right now…
Before we review all particle physics I’d like to take a moment to thank
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First, let’s learn to make a simple Feynman diagram. To do this let we’ll start with
the standard model, which is like the periodic table for fundamental particles.
What is important here is to understand what the different classes of particles can do.
So on the left, the 12 fermions are represented with straight lines with arrows in Feynman
diagrams. The arrow is important. Just like how in an electrical circuit,
the current flows through the circuit, the arrows represent the “flow” of fermions.
No two arrows point towards each other. This is to conserve the fermion current, or in other words;
we must have the same number of fermions in the end as we started with. Note there are some other
notations, which use these arrows differently. If we consider time in the x direction, then
we can interpret fermion arrows going forwards in time as matter particles, and fermion arrows
going backwards as antimatter particles. This is the general rule for all fermions.
Now the fermions can be divided up further in terms of charges. When I say charges, I mean
the electric and color charge. If you don’t know what a color charge is,
please check out my previous video on QCD. All 6 quarks have color charges. All particles
with color charges interact with the strong nuclear force, thus all quarks feel this force.
The quarks also have an electric charge, so they also feel the electromagnetic force.
The other class of fermions are the leptons. These can be divided into the electron with
makes up an atom, and its heavier cousins the muon and tau particles. These all have electric
charges but no color charges, so they feel the electromagnetic force but not the strong force.
The last three leptons are the neutrinos. These do not have a color charge or an electric charge;
thus, they are not affected by the strong or electromagnetic forces. And they have very low
mass, so only slightly affected by gravity. This is what makes them very difficult to detect.
You might ask, hey what about the weak force and its charge? The answer is that all fermions carry
something called weak isospin. This can be thought of as a kind of as the “charge,” of the weak force
For fermions it can be plus one half or minus one half.
So all fermions interact with the weak force. But weak iso spin can also be -1, 0, and +1 –
the W- boson has a weak isospin of -1, W+ has +1, Higgs has -1/2, and Z boson and photons
have a weak isospin of 0. Note that this zero is not the same has having no isospin. Both the Z
and photon interact with the weak force. Everything in the standard model has a
weak isospin except gluons. So gluons do not interact with the weak force.
Weak isospin is a quantum number relating to the weak force. It is a property just like electrical
charge is a property of some particles. The number of the charge is just related to how they feel it.
Weak isospin must also be conserved, just like you must conserve electric charge and color charge.
It is a stretch to call the weak force a force. It s more like a power. The weak force has the power
to turn one particle into another particle. So for example, it can turn a down quark into an up quark,
turning a neutron into a proton by emitting a W minus boson. It is the only force that
can do that. Electromagnetism and the strong force can’t do this.
To recap, quarks interact with all forces, electron-like particles interact with
electromagnetism and the weak force, but do not interact with the strong force. Neutrinos
only interact with the weak force and nothing else. Only quarks and gluons carry the strong
force. Higgs bosons do not interact with photons or gluons. They confer mass to
fundamental particles, so all fundamental particles with mass interact with Higgs.
With that, you have the basics needed to understand Feynman diagrams.
There are potentially a large number of diagrams, but we can build almost
everything by looking at the most important ones where fermions interact with forces.
The simplest force is electromagnetic force described by QED, which as we know interacts
with quarks and leptons. Note that the W bosons which are the mediator particles for the weak
force are charged, so they also feel this force, but we’ll ignore them for the moment.
Let’s interpret one of the simplest diagrams shown here. The X axis represents time. An arrow
pointing to the right represents matter particles.
There are two ways this diagram can be interpreted. We can view it as
an electron moving from left to right, while at the same time a photon moves from bottom to top.
This would depict a photon being absorbed by an electron. This is how the electron in an
atom can move from a lower orbit to a higher orbit by absorbing the energy from the photon.
We can also view this as an electron moving from left to right, emitting a photon,
and then continuing. In this scenario, it would represent the electron losing energy by emitting
a photon. This is how an electron in an atom moves from at higher orbit to a lower orbit.
By the way, this is also how a laser works. How is electromagnetic repulsion depicted in
Feynman diagrams? As we discussed, the force carrying particle for electromagnetism is
the photon. This diagram, also called Møller scattering, depicts repulsion.
Two electrons come near each other, an exchange of virtual photons causes a transfer of momentum,
which pushes the two electrons apart. Note that we cannot measure the virtual photons,
only the incoming and outgoing electrons. So sometimes this diagram is drawn like this.
These both depict the same process What about electromagnetic attraction?
The diagram for this called Bhabha scattering diagrams. There are two potential diagrams. The
first diagram depicts an electron and positron, that have opposite charges, attracting each other.
This also happens through the exchange of virtual photons. This looks very similar to
the diagram for repulsion. The only difference is that the photon exchange in this case results
in the exchange of negative momentum which attracts two particles, instead of positive
momentum which repels two particles. We can see this in our boat analogy
where the boats represent electrons and the object being thrown is like the virtual photon. Positive
momentum exchange is like the two people throwing basketballs at each other which pushes the boats
apart. But a negative momentum exchange is like two people throwing boomerangs, which results
in the boats being attracted to each other. The second diagram shows a different phenomenon
which can also occur when electrons and positrons are near each other.
This show that when the particle
antiparticle pair come near each other, they annihilate, resulting in energy production or
photons being created. The energy of these photons, in turn, can create a new electron positron pair.
This leads us on to the slightly more complicated weak force. This force is felt by all of the
standard model particles, except gluons. The most interesting weak force diagrams
involve W-bosons which can have a plus one or minus one electric charge.
These particles can do something very special. They can change the identity or flavor of the
particle. For example, they can change an up quark into a down quark. This is so important
that we probably would not exist without it. So for example, here’s one of the most important
weak force interactions relevant to life. This involves a neutron decaying into a combination
of a proton, electron and antineutrino. On the left side, we have a neutron which is
composed of one up quark and two down quarks. One of the down quarks can change flavor and become
an up quark. This happens due to the W- weak force mediator particle. When a W- boson it
emitted, the down quark changes its flavor to an up quark. This W- boson then almost immediately
decays into an electron and anti neutrino. Because the new particle now has two up quarks
and one down quark, our original neutron has turned into a proton.
Note that charge is still conserved because the emitted negative charge of the electron is
balanced by the positive charge of the proton. And weak isospin is also conserved because the isospin
change of +1 created when a down quark changed to an up quark, is balanced by the combined -1
spin of the electron and antineutrino. If this decay did not occur,
the early universe may have been awash with neutrons and atoms may never have formed.
Another interesting weak force interaction involves the Z-boson. It has no electric charge
just like the photon. But unlike the photon, it can mediate interactions with electrically
neutral particles like the neutrino and the Higgs. So for example as the Feynman diagram shows,
a Z boson can transfer spin or momentum between an electron and a neutrino. But in the process
of doing so, it does not transfer any charge and leaves the particles otherwise unaffected.
This brings us the strong force, which is the most complicated mathematically, but since it only
relates to quarks and gluons, there are fewer interactions to understand.
One of the simplest diagrams is the interaction diagram. Here a pair of quarks simply change
color. This process happens all the time inside protons and neutrons. And this color charge
exchange is the glue that binds the quarks together, and keeps them confined to the inside
of nucleons. A blue and red quark, for example, can change colors via the exchange of a gluon. So
on this diagram, we have a red quark coming from the top left, it emits a gluon with a combination
red and anti-blue color charge (gluons always have a combination of color-anticolor charges).
The outgoing antiblue of the gluon, immediately turns the quark into a blue quark. The blue quark
at the bottom absorbs this gluon. Its blue color gets neutralized by the antiblue contained in the
gluon. And this quark turns red by absorbing the red that was also part of the gluon.
Note that color is conserved in this interaction. Because gluons themselves contain color charges,
they also interact with each other via complicated diagrams. These gluon-gluon interactions is what
the flux tubes inside nucleons are made of. These tubes are formed when you try to pull quarks apart
as discussed in the video about QCD. The diagrams here show possible constructions. Now,
let’s look at what is the most complicated Feynman diagram in this video,
but may very well also be the most important. This diagram represents the strong force interaction
that binds protons and neutrons together in the nucleus. Without this interaction,
there would be no atoms heavier than hydrogen, and life as we know it would not exist.
Essentially, this diagram shows that a proton and neutron interact with each other via gluons
yielding some residual energy which becomes mesons. These mesons are a combination of quark,
anti-quark pairs. These, in turn, mediate the strong force between the proton and neutron.
Let's take a close look at exactly how this attractive force works.
We have a proton up top and a neutron at the bottom. Keep in mind that color must always be
conserved. That is, the three quarks inside a proton or neutron must be a combination
of red, blue, and green which combine to make a neutral white color. Let me clarify that this is the
same way that optical colors combine, but color charge is a metaphor and has nothing to do
with colors that you can see with your eyes. Inside the proton, the blue up quark interacts
with the red down quark via a gluon. This turns the up quark red, and the down quark blue.
As this down quark leaves the proton, an anti-blue anti-quark is created together with a green down
quark via a gluon interaction between the green up quark, which was initially green but turns blue.
The blue down quark and anti-blue, anti down quark leaves the proton forming a color charge and
charge neutral pi meson. The newly created green down quark remains in the Proton.
The pi mason now interacts with the neutron. The anti-down quark of the meson annihilates
the down quark of the neutron. At the same time there is a color exchange between the red down,
blue down, and anti-blue anti quark, such that the quark which is not annihilated becomes red.
The down quark of the meson joins the neutron by taking the place of the annihilated down quark.
At the same time, an exchange of colors occurs with the green up quark of the neutron such
that the up quark turns blue and the new down quark from the pi meson turns green.
You might ask, why are so many color exchanges happening in this interaction? The color exchanges
have to happen in order to maintain a neutral color charge in both the proton and neutron.
That's the way quantum chromodynamics works. It can't work without it.
Note that this interaction works equally well both ways, whether you go up or down. Also note
that these virtual meson interactions are what keep protons and neutrons bound together in atoms.
But the attraction is much weaker than the gluon interactions that keep quarks within the nucleons.
And they work only at very short distances, much smaller than the width of the proton.
The last thing I want to show is how physicists produced the long sought-after Higgs boson.
While there are several ways it can be made, the most prominent process
used at the Large hadron collider is the so-called gluon fusion process.
What happens is that in some high energy proton-proton collisions at the LHC,
two high energy gluons can be produced. These can, in some cases ,due to strong force interactions,
turn into top quarks, and fuse together via a triangle loop. This loop represents top quark,
anti-top quark creation and annihilation. The energy of this annihilation can create a Higgs boson.
Because the top quark has the highest mass of all elementary particles, it has the best chance to
decay into a Higgs boson which has the second highest mass of all the elementary particles.
In general, when particles decay, they tend to decay into the next highest mass particle
Even though there are an endless number of Feynman diagrams, if you understand the ones
I just talked about, then you understand the most important diagrams responsible for the physics
of our everyday lives (ignoring gravity). My message to you is that even the most
complicated physics, which involves complex math, can be understood intuitively, especially with the
help of these Feynman diagrams. I hope it inspires some of you to study these phenomena further,
become the next Einstein, and change the world! I will see you in the next video my friend!