Download From Quantum Mechanics to String Theory

From Quantum Mechanics
to String Theory
Relativity (why it makes
sense) ✓
Quarks and the Strong
Force
Quantum mechanics:
measurements and
uncertainty ✓
Symmetry and Unification
Smashing things together:
from Rutherford to the
LHC ✓
Particle Interactions ✓
Thursday, May 7, 2009
String Theory: a different
kind of unification
Extra Dimensions
Strings and the Strong
Force
Particle Interaction Summary
quantum mechanics and special relativity together imply the
existence of anti-particles
forces are mediated by the exchange of virtual particles,
which carry energy and momentum inconsistent with their
masses using quantum uncertainty. This leads to a decrease
of force strength with distance, and in the case of massive
mediators, an effective range for the force
particle interactions are limited by conservation laws: energy,
momentum, angular momentum, charge, quark number. These
conservation laws lead to particle stability.
virtual electron/positron pairs in the vacuum shield
electromagnetic charges, making them seem smaller than
they are
Thursday, May 7, 2009
Quarks
and
the Strong Force
Thursday, May 7, 2009
The Particle Zoo
for a while it looked like
we were close to a
complete picture, with just
the electromagnetic and
nuclear forces, and the
particles from last time
In the 1950s and 60s
accelerator and cosmic ray
experiments produced a
proliferation of new
particles
heavier particles related to
protons, neutrons, and
pions
Thursday, May 7, 2009
Patterns
try arranging the particles by spin, quark number, charge, mass
Thursday, May 7, 2009
Patterns
try arranging the particles by spin, quark number, charge, mass
Quark Number 3
Thursday, May 7, 2009
Quark Number 0
Patterns
try arranging the particles by spin, quark number, charge, mass
Quark Number 3
Thursday, May 7, 2009
Quark Number 0
Patterns
try arranging the particles by spin, quark number, charge, mass
Quark Number 3
Thursday, May 7, 2009
Quark Number 0
Patterns
try arranging the particles by spin, quark number, charge, mass
Quark Number 3
Thursday, May 7, 2009
Quark Number 0
Quarks
just like with the periodic table, these patterns of particles
indicate some underlying structure
Murray Gell-Mann realized that they could be explained if the
particles were made up of smaller particles he called quarks
the quarks that explain these patterns come in three types: up,
down, and strange (and their anti-particles)
the particles with non-zero quark number (baryons) have 3
quarks each, the ones with zero quark number (mesons) have
one quark, one anti-quark
two of the quarks are very close to identical in the masses
they generate, the third causes (generically) larger masses
Thursday, May 7, 2009
Baryon Decuplet
the ten baryons in this
++
∆
pattern are the ten possible
3-quark combinations of up, (uuu)
down, and strange quarks
by looking at the charges, we
see that the charges of the
three quarks must be
u: +2/3
d: -1/3
s: -1/3
Thursday, May 7, 2009
∆+
∆0
∆−
(uud)
(udd)
(ddd)
∗+
Σ∗0
Σ∗−
(suu)
(sud)
(sdd)
Σ
∗0
Ξ
Ξ∗−
(ssu)
(ssd)
Ω−
(sss)
Baryon Octet
baryon octet similar to
decuplet, except with the
corners cut off and the middle
doubled
since quarks have anti-particle
partners, for each of the
Σ+
baryon patterns there is an
equivalent pattern made up of (suu)
anti-baryons
particles in the decuplet tend
to be extremely unstable,
generically they decay into
particles in the octet
Thursday, May 7, 2009
+
n0
(uud)
(udd)
p
0
Σ−
(sud) (sud)
(sdd)
Σ
0
Λ
Ξ0
Ξ−
(ssu)
(ssd)
Meson Nonets
the mesons are made up of a
quark and an anti-quark. They
are arranged directly opposite
their anti-particles
the 6 mesons in the centers and
to the sides are made up of
¯ ss̄
combinations of uū, dd,
the mesons in the second nonet
tend to be highly unstable and
decay first to the mesons in the
first nonet generally
K + (s̄u)
¯
π ,η
π + (du)
0
0
π − (ūd)
¯
K̄ 0 (ds)
K − (ūs)
K ∗+ (s̄u)
K ∗0 (s̄d)
¯
ρ (du)
+
¯
K̄ ∗0 (ds)
Thursday, May 7, 2009
K 0 (s̄d)
0
ρ ,ω
0
ρ
−
(ūd)
K ∗− (ūs)
η !0
φ0
More Quarks
Deep Inelastic Scattering
Experiments: evidence of 3
quarks in protons, confirmation
of their charges
further experiments revealed three more quarks: charmed, top,
and bottom (which combine in extremely massive, short-lived
mesons and baryons)
quarks and leptons fall into “generations”: each generation needs
all four elements to be mathematically consistent
e (electron) νe (neutrino)
μ (muon)
τ (tau)
Thursday, May 7, 2009
d (down)
u (up)
νμ (neutrino) s ( strange) c (charmed)
ντ (neutrino) b (bottom)
t (top)
The Color Puzzle
quarks are spin 1/2 particles (fermions)
fermions satisfy the “pauli exclusion principle”: you cannot
have 2 fermions in exactly the same state
consider the particle Δ++, made up of three “u” quarks
it is a spin 3/2 particle, capable of carrying angular
momentum in the z-direction equivalent to all three quarks
having spin in the same direction (+++)
it looks as if we have three identical quarks, all in the same
spin state (u,+)
there must be some other quantity that the quarks carry
that allows them to be in different states: call it “color”
Thursday, May 7, 2009
Colored Quarks
Mesons
Red
Green
Blue
Anti-Red
Anti-Green
Anti-Blue
Baryons
Anti-Baryons
quarks come in 3 colors (and 3 anti-colors)
baryons are made up of one of each color, antibaryons one of each anti-color
mesons are made up of one color and one anti-color
these are called “colorless” combinations: all natural
combinations are colorless
Thursday, May 7, 2009
The Strong Force & Gluons
what role (besides explaining the exclusion principle paradox)
does color play?
the strong force: color is to the strong force what charge is
to the electromagnetic force
the mediators for the strong force are gluons
8 varieties, each a combination of one color and one anticolor--but *not* colorless combinations
gluons are massless and spin 1, like photons. Unlike photons,
they are not colorless and therefore interact directly with
other gluons
Thursday, May 7, 2009
Confinement
no particles found in nature have any net color. Why?
gluons are massless, like photons. Classically the strong force
should behave the same as the electromagnetic force.
qm shielding is a large effect here, because the gluons
themselves carry color
virtual gluons and quarks serve to re-inforce bare colored
particles. Classically the force decreases with distance like 1/
r^2, but quantum mechanically the force increases with
distance like r.
this is spring-like behavior. Colored objects attach to each
other as if by a spring--it requires an infinite amount of
energy to separate them
Thursday, May 7, 2009
Confinement
Energy
quarks close together feel very little
force from each other (like marbles
in a sack). The force becomes strong
when you start to separate them
what would happen if you tried to
pull a meson apart?
as you begin to separate them, you put more and more energy into
the system
eventually, you have put more energy in than is required to
produce a quark/anti-quark pair. They are created out of this
energy, and what results is two (colorless) mesons coming apart
in accelerators, when energies are high enough to probe the insides
of protons and mesons, the result is messier: “jets” of hadrons
Thursday, May 7, 2009
The Effective Nuclear Force
can we explain the behavior of the “nuclear force” between
protons and neutrons in terms of the strong force and
gluons?
the nuclear force is a residual effect of the color
structure of objects that have no net color
it dies off quickly with distance because as you get further
away the color structure “disappears” (parallel:
electromagnetic Van der Walls force)
what about the pion as a nuclear force mediator? Let’s
draw a picture of how a proton and a neutron can interact
Thursday, May 7, 2009
Pion Exchange
can proton/neutron interaction occur
by exchange of a gluon?
the gluon is a colored object, so this
interaction must be *extremely* short
range (even shorter than the nuclear
force range)
but we can make the proton and
neutron “exchange” a color neutral
object:
this can act over a longer distance (up
to what is limited by the pion’s mass)
and becomes the dominant effect in
the nucleus
Thursday, May 7, 2009
d
u
u
d
u
u
gluon
u
d
d
u
d
d
d
u
u
d
u
u
pion
exchange
u
d
d
u
d
d
Quark Summary
mesons and baryons can be fit into patterns according to
quark number, spin, mass and charge: quark structure
baryons are made up of three quarks, mesons are made up
of a quark and an anti-quark
quarks have a quantity called color, which is the “charge” of
the strong force, mediated by gluons (which also carry color)
quantum shielding causes the strong force to grow with
distance, holding colored objects together as if with a spring
the nuclear force and pion exchange is a residual effect
from the color structure of baryons which have no net color
Thursday, May 7, 2009