Transcript The Standard Model - Stony Brook University

The Standard Model
Particles, Forces, and Other Fun Stuff
By: Alex Ellis
Quantum States
To be considered in the same
quantum state, the following must
be identical:
• Some specification of momentum and position, where
ΔxΔp > h/4π, where Δx and Δp are the uncertainties in
position and momentum, respectively.
• Spin
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!”
- Finnegan’s Wake
Murray Gell-Mann. Freak with a name fetish,
and also one of two independent discoverers of
the quark, along with George Zweig.
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
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.
Unfortunately for our analogy with jelly belly, jelly beans can
not change colors, unless they’re too old.
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
Baryons
• Made of three quarks
or anti-quarks
• All three colors or
anti-color
Mesons
• 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 eElectrons, 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
Lambda-Zero Decay, via Weak
Λ0
>
n
+
π0
B
1
1
0
I3
0
-1/2
0
(I3 is not conserved via weak)
Origin of Electrical Charge
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)
Q = e (B/2 + S/2 + I3)
Examples - Charges of p and
Proton
0
π
Pion-Zero
Family: nucleons, I = 1/2
Members: n, p
Family: pions, I = 1
Members: π -, π0, π+
Family I3 range: (-1/2, 1/2)
p corresponds to I3 = 1/2
p is a baryon, therefore B = 1
Family I3 range: (-1, 1)
π0 corresponds to I3 = 0
π0 is a meson, therefore B = 0
Q = e((1/2) + (1)/2 + (0)/2)
= +e
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 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!!!