Elementary Particles

Space-time is filled with one very complex field that is continually changing. It manifests itself as discrete particles with energy, in a fluctuating background of virtual particles. The latter are particles that are bound in space and time, so exist fleetingly.

When the temperature falls below the maximum mass of elementary particles, about 10³²K or 10²⁷eV (a microgram), the space-time field starts to behave as separate interacting fields (the super-symmetry is "broken"),

The Higgs field is a single scalar complex field (\(\mathbb{C}\)); the gauge boson field could be a 45-dimensional field SO(10); the matter field could be a 24-component field. All these fields are massless at high temperatures.

The bosons are ephemeral, but the matter field is permanent.

The Higgs field

The most basic interaction is that of the Higgs field with matter. Elementary particles are inherently without mass. It is the interaction with the Higgs field that gives mass to the particles, including itself (125GeV). Roughly speaking, a particle interacts with the Higgs at a rate proportional to its energy, \(\color{purple}E=hf\); so it is pushed back and forth (but keeping its spin and charges), which slows it down to speeds less than \(c\), i.e., it has inertia.

Forces

Below 10²⁷K the gauge force field splits into the strong and electro-weak fields; the original symmetry of SO(10) (possibly) breaks down to SU(3)×SU(2)×U(1), called the standard model gauge theory:

Strong force is manifested by 8 gluons and affects particles with color (3²-1 with symmetry SU(3)). Color can be either of three types r, g, b. Different colors can interact through gluons. Gluons themselves have color, but do not interact with the Higgs or weakons, so are massless and chargeless.
(Color is just a name; particles are not colored. Also, they are wave-particles not hard shiny balls.)
Electro-weak force, has symmetry SU(2)\(\times\)U(1) giving particles W₀, W₁, W₂, W₃ with isospin I and hypercharge Y. Below 10¹⁶K, it splits further due to interactions with the Higgs field:
- Electro-magnetic force is effected by one particle, the photon \(\gamma\), massless and chargeless. The force affects only particles with a charge \(Q=I+Y\).
- Weak force is effected by the weakons W⁺, W^-, Z⁰; these interact with the Higgs field and have masses.

	I	Y	Q	Mass
Gluons	0	0	0	0
Photon	0	0	0	0
W⁺	+1	0	+1	80GeV
Z⁰	0	0	0	91GeV
W^-	-1	0	-1	80GeV

At our low temperatures and large scales, the strengths of the four forces are in the ratio

Strong force \(\color{purple}1\), Electromagnetic \(\color{purple}0.015\), Weak force \(\color{purple}10^{-6}-10^{-13}\), Gravity \(\color{purple}10^{-40}\).

This is because

gluons themselves have color so can keep interacting with each other over distance and thus the force is approximately constant independent of the separation of the colored particles;
photons have no charge, so the interaction is weaker with distance;
weakons have mass, so their range is very limited;
gravity is extremely weak compared to the others because space-time is enormous; however it is attractive and builds up.

Color, isospin, and hypercharge are just names for internal configurations; possibly there are three colors because there are three reflective symmetries in 3-D.

Matter

The Matter field cannot be created or destroyed, but is preserved (however, anti-particles must be counted as the negative of a particle). As fermions, matter particles have to keep 'out of each other's way'. At low energies, the matter field is quantized into particles with stable characteristics that interact differently with the different forces.

Matter particles are described by 3 'colors' and 2 inner 'charges': ; the two 'charges' determine the isospin and hypercharge, and hence the charge and spin (chirality).

Each combination gives a particle, e.g.,		is a left-handed 'up quark';
its complementary combination		is its anti-particle, the right-handed up anti-quark;

It is enough to consider combinations with one 'color' , and with none ; those with two 'colors' or with the colorless combination can be considered their anti-particles. The choice of only determines the spin: right- or left-handed. Thus there are four fundamental types of matter particles:

down quark charge: \(-\frac{1}{3}e\) mass: 4.8MeV	up quark charge: \(\frac{2}{3}e\) mass: 2.3MeV
		2 Quarks interact with the strong force; each can have any color r, g, b;
		2 Leptons have no total color; of these the electrons have a charge; the neutrinos do not.
electron charge: \(-e\) mass: 0.5MeV	neutrino charge: \(0e\) mass: 0.1eV?

Below are all the \(2^5=32\) particles in one family (particles with different 'color' are not shown separately):

		I	Y	Q	Mass
up quark	\(u_L\)	+1/2	+1/6	+2/3	2.2MeV
	\(u_R\)	0	+2/3	+2/3
	\(\overline{u}_L\)	0	-2/3	-2/3
	\(\overline{u}_R\)	-1/2	-1/6	-2/3
down quark	\(d_L\)	-1/2	1/6	-1/3	4.7MeV
	\(d_R\)	0	-1/3	-1/3
	\(\overline{d}_L\)	0	+1/3	+1/3
	\(\overline{d}_R\)	+1/2	+1/6	+1/3
electron	\(e_L\)	-1/2	-1/2	-1	0.51MeV
	\(e_R\)	0	-1	-1
positron	\(\overline{e}_L\)	0	+1	+1
	\(\overline{e}_R\)	+1/2	+1/2	+1
neutrino	\(\nu_L\)	+1/2	-1/2	0	0.1eV?
	\(\nu_R\)	0	0	0
	\(\overline{\nu}_L\)	0	0	0
	\(\overline{\nu}_R\)	-1/2	1/2	0

The strong force interacts with colored particles only, i.e., quarks;
The electro-magnetic force interacts with charged particles, i.e., all except neutrinos;
The weak force interacts only with left-handed particles or right-handed anti-particles (in the vertical diagonal plane in gray)

Of all these particles, only \(e, \nu, u, d\) actually exist; their anti-particles exist only fleetingly. Furthermore, the right-handed neutrino does not interact even with the weak force, and has never been observed.

Conservation of Charge: All the gauge forces preserve isospin, hypercharge, and hence charge, during interactions. But when the Higgs particle interacts with particles having mass, it flips their direction left↔right, and hence their isospin and hypercharge change; yet their charge Q remains unchanged.

At our temperature, quarks and leptons are both conserved; (at very high temperatures, 3 quarks can form an anti-lepton).

There are three families of these 32 particles, identical in all aspects except for their masses.

Particle Interactions

Below are the basic interactions between fundamental particles. Any two particles in an interaction can give a virtual third particle, or vice-versa. The larger the charge, the more likely that an interaction happens.

In order, from left to right, they are:

photon and two electrons
photon and two quarks;
three gluons; note photons do not interact with each other;
gluon and two quarks;
W, electron, and neutrino;
W, up, and down quarks;
W⁺, W^-, Z⁰ or photon;
Z⁰ and two left-fermions.

Actual interactions may involve combinations of such basic processes. The following examples involve the same events in different time-orders:

An electron absorbs a photon and becomes virtual ... then re-emits a photon and electron.

Alternatively, the photon gives out an electron and a virtual positron, which then combines with the other electron.

In reality, one cannot know which of these, and other, possibilities has taken place, when the outcome is the same; they all do as a superposition.

Two electrons interact or 'exchange' a virtual photon to repel each other.

An electron and positron annihilate each other.

In reverse, two photons can create a particle/ anti-particle pair.

The Strong Force

Only quarks feel the strong force: quarks of different color interact. Below a certain temperature (\(10^{12}\)K) quarks strongly group together into colorless super-particles called hadrons. If quarks of different colors try to separate, they generate a multitude of gluons that pull them together again, or if pulled further, generate a quark-anti-quark pair. The mass of hadrons is almost entirely due to the gluon energies. There are two types:

Mesons (2 quarks) are made up of the colorless combination of two quarks, e.g., a red up quark and an anti-red down quark.

Pions are made up of the up and down quarks.

Kaons are mesons made up of quarks from the first and second families.

Baryons (3 quarks) are made up of the colorless combination of three quarks, e.g., a red up quark, a green up quark, and a blue down quark.
Protons and neutrons are the most stable, with a spin of ½ (two of the quarks spin in opposite direction).

Deltas are baryons with a higher spin of 3/2 and a higher mass, e.g., three up quarks or three down quarks.

There are similar versions of baryons using quarks from the first and second families.

Although protons and neutrons are colorless, there is still a residual attractive force between them in the very short range of \(10^{-15}\)m. The details of this attraction is unknown, but may involve processes similar to the ones below involving the transfer of virtual or real pion-like pairs:

Below, a proton and anti-proton hit at high energy, the quarks interact with the end-result of a neutron/anti-neutron pair.

Weak Force

The weak force has a very short range, \(10^{-18}\)m, and interacts improbably, since the W and Z particles are so heavy.

The weak force, via the W particles, is the only one that can change a down quark to an up quark, or an electron to a neutrino, (or vice-versa), or change their family type (e.g. muon to electron, or s quark to up quark).

Below, an up quark reacts with an electron to become a down quark and a neutrino.

\(u+e^-\to u+W^-_v+\nu_e\to d+\nu_e\)
(Click to start. A subscript \(v\) means 'virtual'.)

Hence, below roughly \(10^{12}\)K, most of the heavier elementary particles decay into the lighter ones, by means of weak interactions.

Decay		lifetime
down quark → up quark	\(d\to u+W^-_v\to u+e^-+\bar{\nu}_e\)	10^3s
s quark → up quark	\(s\to u+W^+_v\to d+e^++\nu_e\)	\(10^{-8}\)s
c quark → s quark	\(c\to s+W^+_v\to s+e^++\nu_e\)	\(10^{-12}\)s
b quark → c quark	\(b\to c+W^-_v\to c+e^-+\bar{\nu}_e\)	\(10^{-12}\)s
t quark → b quark	\(t\to b+W^+_v\to b+e^++\nu_e\)	\(10^{-25}\)s
muon → electron	\(\mu^-\to \nu_\mu+W^-_v\to \nu_\mu+e^-+\nu_e\)	\(2.10^{-6}\)s
tauon → pions	\(\tau^-\to \nu_\tau+W^-_v\to \nu_\tau+\pi^-+k\pi^0\)	\(2.10^{-13}\)s

\(d\to u+e^-+\bar{\nu}_e\)

\(\mu^-\to e^-+\bar{\nu}_e+\nu_\mu\)

Similarly, at low temperatures, composite particles with high spin or high energy find ways to transform into ones of lower energy.

Pions are not stable:
\(\pi^0\) decays into photons,	\(\pi^0=q+\bar{q}\to \gamma+q_v+\bar{q} \to 2\gamma\)	\(8\times10^{-17}\)s
\(\pi^+\) and \(\pi^-\) decay into a muon and its neutrino,	\(\pi^+ = u+\bar{d}\to W^+ \to \bar{\mu}^++\nu_\mu\)	\(2.6\times10^{-8}\)s.
Neutrons are not stable:
Free neutrons decay to protons, electrons, and neutrinos	\(n\to p+e^{-}+\bar{\nu}_e\)	14.5mins

The proton is the only fully stable composite particle. However down quarks do not decay when close to up quarks because they switch rapidly via pions (e.g., from neutrons to protons). Thus neutrons in close association to companion protons are also stable. For example two protons and two neutrons are very stable, forming an alpha particle.

The conclusion is that, once the strong and weak forces have had their say, the only remaining stable matter particles are protons, (bound) neutrons, electrons, and neutrinos. The latter are uncharged, so do not feel the remaining dominant force, electro-magnetism.