Download Particles, Fields and Computers

Particles, Fields and Computers
The building blocks of nature
and their numerical study
Fernando Pérez
Prof. Tom DeGrand
Prof. Anna Hasenfratz
Francesco Knechtli
Archie Paulson
Colorado College, Colorado Springs
December 2000
Outline
• What is the world made of? An overview
◦ Air, Earth, Fire and Water
◦ Mendeleev’s periodic table (1871)
◦ The 20th century: atoms can be divided after all
(protons, electrons and neutrons)
◦ And then, even protons and neutrons can be divided
→ too many particles!
◦ The fundamental blocks: Quarks and Leptons.
• Theory: understanding our world
◦
◦
◦
◦
The Theory of Relativity
Quantum Mechanics
Relativistic Quantum Mechanics
Quantum Field Theory
• The Standard Model
◦
◦
◦
◦
Electromagnetism: light and chemistry
The weak force: radioactive decay
The strong force: holding the nucleus together
Gravity: planets and the universe (doesn’t fit in)
• What about mass? The Higgs boson
1
• Quantum Chromo Dynamics (QCD): only three
colors, but plenty of work to do!
◦ Quarks and gluons: a strange theory of things we
can’t see
◦ Non-perturbative behavior: a hard theory of things
we can’t compute with standard methods
• Lattice QCD: solving the theory (or a version of it)
on a computer
◦ Theoretical problems
◦ Numerical problems
• Experimental particle physics: the largest experiments on Earth
• The future: physics beyond the Standard Model?
• Resources on the web
2
What is the world made of?
• The ancient Greeks: Air, Earth, Fire and Water
They already (Leucippus of Miletus and Democritus of
Abdera–5th century BC) had the idea of the atom
(ατ oµoν, “that which cannot be divided”)
• Mendeleev’s periodic table (1871)
3
The Rutherford Experiment
1911: atoms can be divided after all.
Sir
Ernest Rutherford performs the first “particle physics”
experiments.
Prevailing model at the time: the atom is a blob of neutral
charge with no distinct components (plum pudding model).
Rutherford probes this by scattering α particles (Helium
nuclei) through a thin gold film.
The resulting atomic model: small, positive nucleus with
electrons orbiting it (a “mini solar system”).
4
Understanding the Nucleus
At this point we can ask: is the nucleus just a point with
positive charge (the “new atom”)?
Answer: No. The Proton and the Neutron (James
Chadwick, 1932) show up in the nucleus.
Two problems arise:
1. Why doesn’t the nucleus explode?
2. Nucleons can be divided → too many particles!
Models of nuclear structure were developed by assuming
the existence of some type of interaction between
the nucleons which could hold them together against
electrostatic repulsion.
5
Quarks: Nature’s Lego
M. Gell-Mann and G. Zweig (1964): protons, neutrons and
most other known particles are made up of something even
smaller: quarks.
1. Only a few (6) are needed to explain the particle zoo:
2. They interact via the strong force, and the residual force
holds the whole nucleus together:
3. Quarks would have to be fractional charge particles.
Why have we never seen such a thing? Later...
Our current view of the atom:
6
The fundamental blocks
We’ve seen the following physical scales:
1
1/10,000
Atoms (electromagnetic forces). Chemistry
Nuclei (residual strong force). Radioactive
phenomena (weak force).
1/100,000 Protons & neutrons (strong force).
1/100,000,000 Quarks & electrons: fundamental (we think).
Matter in the universe (that we know about):
7
Theory: constructing
the Standard Model
Special Relativity: Einstein, 1905. Mass and energy are
ultimately equivalent:
E = mc2
Quantum Mechanics: 1900-1925.
• All matter exhibits wave-like properties (interference,
diffraction, etc.)
• Classically forbidden processes may occur (small prob.).
• Anything that is not forbidden will happen.
• We can only predict the probability of each possible
outcome.
Relativistic Quantum Mechanics: Dirac, 1928
• For every particle there must be an anti-particle.
• Spin was naturally explained: fermions (spin n2 =
1 3
2 , 2 , . . .) and bosons (integer spin).
Quantum Field Theory: 1928-1972. Everything
(particles, energy–force) is a field whose “intensity”
determines how many particles we find.
It provides a natural language to describe particle creation
and annihilation processes, matter, antimatter and energy
in a single, clean framework.
8
The “Standard Model”
The world as (we think) we know it, minus gravity
“Matter”: Quarks and Leptons, three generations with 2
quarks and 2 leptons per generation.
“Energy” (Interactions): Gauge bosons, one type per
fundamental interaction (force).
Name
Acts on
Gauge Boson
Range
Strength
Weak Force
Everything but γ
W ± , Z 0 (3)
< 10−17 m
10−5
Electromagnetism
Charged matter
Photon, γ (1)
Long: F ∼ r −2
1/137
Strong Force
Quarks and gluons
Gluons, g (8)
10−15 m
1
Gravity
Everything
Graviton g (1)
Long: F ∼ r −2
∼ 10−39
The Standard Model describes the first three in a very
coherent manner, but gravity doesn’t fit into the picture.
9
What about mass? The Higgs boson
A (technical) problem with the Standard Model: it doesn’t
like particles to have a mass. Yet the quarks, the leptons,
the W ± and the Z 0 are all massive. What to do?
Suggestion: a new particle, the Higgs boson:
(a) Quarks & leptons (b) Gauge bosons (c) Higgs + ?
Have we seen it? Maybe, maybe not...
10
Quantum Chromo Dynamics (QCD)
6 quarks: the components of all hadronic –sensitive to
the strong force– matter.
¯
Proton (uud), Neutron (udd), Pions (uū + dd)
Problem: Quarks are fermionic particles, so they can’t
pile on top of one another. But there’s a particle (the
∆++) with 3 identical quarks, uuu. How can it exist?
Solution: each quark comes in three “colors” (red, green,
blue).
The force between quarks is mediated by gluon exchange.
Gluons are like the photon of QCD, but they also carry
color (and anti-color).
11
Confinement: the world is white
A fundamental property of QCD: the world is white,
we never see isolated quarks.
All hadrons are either made of:
• Three quarks (RGB). The baryons (heavy particles) like
the proton, neutron, ∆++, ...
• A quark/anti-quark pair (RR, GG, BB). The mesons
(medium weight particles): the pions π 0, π ± , ...
The gluon energy increases with distance: think of
confinement as the stretching of a rubber band which snaps
creating new quarks when stretched hard enough.
12
QCD: a Non-Perturbative theory
Consider the exponential function written as a series
ex =
∞
X
xn
n=0
n!
Now look at what happens when we sum a finite number
of terms (n = 0 . . . N ) for different values of x :
N
1
2
3
4
ex
x = 0.5
1.5
1.625
1.6458
1.6484
1.6487
x=5
6
18.5
39.333
65.375
148.41
The electromagnetic and weak forces have characteristic
parameters of order 1/137 and 10−5 while QCD’s coupling
is of order 1.
This makes perturbative calculations (in the form of a finite
series like above) very difficult for QCD.
13
Now consider finding a series expansion for the function
1
−
f (x) = e x
A Taylor series at x = 0 for f (x) is in principle given by
˛
˛
2
1 d f ˛˛
df ˛˛
+
f (x) = f (0) +
˛
dx ˛x=0
2 dx2 ˛
+ ...
x=0
But for our function f (x) we immediately see a problem:
˛
˛
df ˛˛
1 − 1 ˛˛
= 2e x˛
=0
˛
dx x=0
x
x=0
And the same thing will happen to all orders, so we can’t
make a series expansion at all!
1
The function f (x) = e− x is non-analytic at the origin, it
has no power series representation at all. All its derivatives
vanish, even though it looks perfectly well behaved:
0.7
exp(-1/x)
0.6
0.5
0.4
0.3
0.2
0.1
0
0
0.5
1
1.5
2
QCD suffers from both of these problems:
1. Perturbative (series) calculations are slow and difficult
because the relevant parameter isn’t small.
2. Worse, many questions produce non-analytic functions,
where series expansions are simply impossible.
14
Lattice QCD: computational QFT
Discretize space-time as a grid: compute the properties of
QCD “exactly” on it.
With the best supercomputers, the space-time grid can
have a size ∼ 483 × 96.
CU-Boulder: develop “smart” algorithms: put as much
physics as possible into the code, then work on smaller
computers (desktop workstations, clusters of inexpensive
PCs). We can do simulations with lattices ∼ 123 × 24.
Things that can be computed on the lattice:
• Spectrum of QCD (particle masses).
• Decay constants for certain processes.
• Basic properties of the vacuum – confinement.
15
The largest experiments on Earth:
CERN (Switzerland/France)
The 20th century: from bubble chambers to huge
underground tunnels. CERN is a circular accelerator:
Hydrogen bubble chamber image
CERN main ring (27km circ.)
The LHC detector
An event at LEP
16
And SLAC (Stanford)
SLAC: a linear accelerator (less radiation problems):
SLAC accelerator (3km)
BaBar detector
SLAC structure
BaBar detector diagram
17
Beyond The Standard Model
There are still many unanswered questions left by the
Standard Model:
✔ Why do we observe matter and almost no antimatter
if we believe there is a symmetry between the two in
the universe?
✔ What is this ”dark matter” that we can’t see that has
visible gravitational effects in the cosmos?
✔ Why can’t the Standard Model predict a particle’s
mass?
✔ Are quarks and leptons actually fundamental, or made
up of even more fundamental particles?
✔ Why are there exactly three generations of quarks and
leptons?
✔ How does gravity fit into all of this?
Answers: Super Symmetry , String Theory ? A topic for
another day...
18
Web Resources
•
http://ParticleAdventure.org: Welcome to the Particle Adventure.
Main source of images for this talk, excellent site.
•
www2.slac.stanford.edu/vvc/home.html: SLAC Virtual Visitor Center.
Nice descriptions of BaBar.
•
public.web.cern.ch/Public/SCIENCE/TutorialWelcome.html:
plore the Atom - Introduction.
•
CERN official education site.
hepwww.ph.qmw.ac.uk/epp/higgs.html: The Waldegrave Higgs Challenge.
•
Ex-
One page essays explaining the Higgs.
www.superstringtheory.com:
The Official String Theory Web Site.
Very nice animations of particle physics topics.
•
casa.colorado.edu/~ajsh/sr/sr.shtml:
Special Relativity.
Prof.
Andrew Hamilton’s relativity site (CU Boulder).
•
pdg.lbl.gov/particleadventure/other/othersites.html:
Physics Education Sites.
Particle
List with many more links.
19