The Standard Model

Particles, Forces, and Other Fun Stuff

By: Alex Ellis

Quantum States

• Some specification of momentum and position, where ΔxΔp > h/4π, where Δx and Δp are the uncertainties in position and momentum, respectively.

• Spin

To be considered in the same quantum state, the following must

be identical:

The Pauli Exclusion Principle

Two objects can not occupy the same quantum state, in the same place, at the same time.

Fermions - Particles that obey the Principle (spin = 1/2, 3/2, 5/2…)

ex. electrons, protons, all quarks

Bosons - Particles that do not (spin = 0, 1, 2…)

ex. pion, photon, W+

Electromagnetic Force

The electromagnetic force acts as a force vector, proportional to the product of the charges involved, and inversely to the square of the distance.

And it is EQUAL for both particles involved, regardless of which has higher charge!

Feynman Diagrams

A 2D representation of 1D motion, versus the passage of time

Feynman diagrams are a convenient way of showing interactions. For example:

This shows a virtual photon being exchanged between two electrons, causing them to repel. The photon may exist for Δt = h/(4πΔE), where ΔE is the energy of the photon. This is the ONLY case in which Conservation of Energy can be violated.

Quantum Electrodynamics and Anti-Particles

• Part of underlying symmetry in nature

• Identical mass, etc., except opposite charge

• Or, more precisely: An anti-particle is a particle moving BACKWARDS through TIME!

This is an illustration of the third concept here, which will be explained on the next slide.

Explanation #1 of Pair Production

1. Electron and photon are traveling towards each other.

2. Photon splits into an electron and a positron traveling in opposite directions.

3. The initial electron and the produced positron annihilate, and form a photon.

But this is looking in the restricted mindset that time only travels in one direction, which is not true, since time is a dimension!

Explanation #2 of Pair Production

1. An electron moves to the right.

2. It emits a photon to the left, then moves backwards in time, still moving to the right.

3. It emits a photon going back in time going to the right, and starts going forwards in time again.

The photon going backwards in time can technically be called an anti-photon, but this is meaningless, since a photon is indistinguishable from its own anti-particle (since its charge is 0).

Quarks

“Three Quarks for Muster Mark!”

Murray Gell-Mann. Freak with a name fetish, and also one of two independent discoverers of the quark, along with George Zweig.

- Finnegan’s Wake

Types of Quarks

Quarks have “color” and “flavor,” kind of like jelly belly jelly beans. Colors are red, green, blue, anti-red, anti-blue, anti-green.

Gluons and Quantum Chromodynamics (color force)

• Gluons are the force carriers of color charge• There are 3x2 types of color charge, as

opposed to 1x2 for electromagnetism.• Unlike their electromagnetic analogue,

photons, they carry two charges, as opposed to zero. An interesting consequence of this is that color force, or the strong force, INCREASES WITH DISTANCE!!

Gluon Exchange

Unfortunately for our analogy with jelly belly, jelly beans can not change colors, unless they’re too old.

Analgous with QED, gluon exchange in QCD can be explained in two ways.

1. The gluon exchanged is of color “red + anti-blue,” so that the color change obeys conservation of charge on each end.

2. Or, we have red charge going forward in time, and blue going backwards in time, along the gluon.

Combinations of Quarks: Baryons and Mesons

Jelly Belly:

Quarks:

up + up + down = proton

down + anti-bottom = B-zero

To have a stable composite particle of quarks, color charge must be neutralized. This only occurs with red, green, and blue, or any color and its anti-color.

Baryons vs. Mesons

MesonsBaryons

• Made of three quarks or anti-quarks

• All three colors or anti-color

• Made of one quark and one anti-quark

• The quark is the color of the anti-color of the anti-quark

So in general, the bound states of quarks in effect have a neutral color.

Leptons

Electron - symbol e-

Electrons, protons, and neutrons make up almost all matter in existence today. They orbit atomic nuclei, and your physics and chemistry teachers talk about them a lot.

Muon - symbol μ - same, but heavier and almost never found in nature

Tauon - symbol τ - even heavier than that

Neutrino - symbols νe, νμ, and ντ

Each corresponds one of the other leptons, and is a consequence of conservation laws. They are believed to have zero rest mass, and almost never interact with matter. In fact, we are constantly and unknowingly bombarded with them constantly.

The Weak Force• Carried by W+, W-, and Z0 bosons

• Responsible for particle decay

• Acts more slowly than the strong force

• Acts on quarks and leptons

Gravity

We really don’t understand gravity, but Einstein thought he did. So we tend to agree that his approximations were OK. Oh yeah, and he invented that relativity thing.

Generations of Matter

I II III

Up Quark Charm Quark Top Quark

Down Quark Strange Quark Bottom Quark

Electron Muon Tauon

Electron Neutrino Muon Neutrino Tauon Neutrino

Why is it like this? That’s one of the major mysteries today. Evidence based on neutrino masses indicate that a limit of three generations is probable, but there is no good explanation for this.

Conservation Laws

• Strangeness (S) is conserved in strong force interactions

• Charge (Q) is conserved in all interactions

• Baryon number (B) is conserved in all interactions

• Isospin component (I3) is conserved in all non-weak interactions

Examples of Decays that Follow Conservation Laws

Pion-Zero Decay

π0 > γ + γ

B 0 0 0

I 1 0 0 (not conserved)

I3 0 0 0

More Decays

B 1 1 0

Lambda-Zero Decay, via Weak

Λ0 > n + π0

I3 0 -1/2 0

(I3 is not conserved via weak)

Origin of Electrical Charge

Q = e (B/2 + S/2 + I3)

B is baryon number (or number of baryons present)

S is strangeness (1 for s quark, -1 for anti-s)

e is the elementary charge, 1.6 x 10-19 C

I is isospin, where the number of particles in a family is 2I + 1

I3 is isospin component, which is related to sequence of a particle in a family, on the interval if (-I, I)

Examples - Charges of p and π0

Proton Pion-Zero

Family: nucleons, I = 1/2

Members: n, p

Family I3 range: (-1/2, 1/2)

p corresponds to I3 = 1/2

p is a baryon, therefore B = 1

Q = e((1/2) + (1)/2 + (0)/2)

= +e

Family: pions, I = 1

Members: π -, π0, π+

Family I3 range: (-1, 1)

π0 corresponds to I3 = 0

π0 is a meson, therefore B = 0

Q = e((0) + (0)/2 + (0)/2)

= 0

Unification, etc.Currently, there is a partial unification theory of the electromagnetic and weak forces, or “electroweak theory.”

Could all the forces unify, like this? It’s a nice and elegant idea, but is it truebut is it true?

Acknowledgements

• www.jellybelly.com for stolen images

• www.particleadventure.com for more stolen images

• Alec Chechkin for, um... nevermind

• Dr. Stephen Arnold, for pissing of Alec Chechkin

• Ariel Smukler, for pissing him off even more

• “Soupy J” for the soup

• Anderson Huynh, for letting me win in arm-wrestling

• Howard Wang, for not talking

• Mike Shick, for moving when I need the computer

• Ms. Leifer, for angry looks and infinite patience with us testosterone-fueled losers

• and finally… Mr. Bucher for the water cooler!!!