Download The Structure of Matter The Standard Model of Elementary Particles

The Structure of Matter
The Standard Model of Elementary Particles: the theory of quarks, leptons and gauge
bosons that comprise all matter; the theory of (almost) everything
Particles and Antiparticles
Composite Particles: particles made up of smaller component particles
Examples: protons and neutrons
In the 1950s and 1960s, hundreds of other particles were discovered, many of which are very
unstable and so are not found in ordinary matter.
Elementary Particles: particles not made out of any smaller component particles; 2 elementary
particles of the same kind are completely identical.
3 Classes of Elementary Particles:
a) Quarks
b) Leptons
c) Exchange particles
Antiparticles - to every particle, there corresponds an antiparticle of the same mass as the
particle but of opposite electric charge (and opposite all other quantum numbers)
All antiparticles are denoted with a line above the symbol
Examples:
If a particle has zero electric charge, the antiparticle can still be distinguished because of other
quantum numbers
Example: neutrino vs. antineutrino – have opposite lepton number
Some particles are their own antiparticle and must be electrically neutral
Example: photon vs. graviton
Antimatter – material made up of antiparticles
What happens when antimatter comes into contact with matter? It will annihilate, releasing
energy
Which is predominant in today’s universe, matter or antimatter? antimatter
Quantum numbers: numbers (or properties) used to characterize particles
Examples: electric charge, flavor, colour, strangeness, baryon number, lepton number
Quarks
Quarks: smaller particles that make up protons and neutrons
There is solid experimental evidence for the existence of 6 types or “flavours” of quarks
Quark flavour
Symbol
Electric
Charge (e)
Rest Mass
(MeV c-2)
Spin
(h/2π)
Up
u
+2/3
330
½
Down
d
-1/3
333
½
Strange
s
-1/3
486
½
Charmed
c
+2/3
1,500
½
Bottom
b
-1/3
4,700
½
Top
t
+2/3
175,500
½
Note: A particle’s “spin” is a quantum property that is analogous to, but not actually, angular
momentum (L=mvr). All known particles have spin, which must be either an integral or halfintegral multiple of the quantity h/(2π).
Bosons: have an integral spin
Fermions: have a half-integral spin.
So all quarks are….?
Hadrons – particles made out of quarks
Meson – a hadron formed from 1 quark and 1 antiquark
Baryon – a hadron formed from 3 quarks
The proton is a baryon made out of…. 2 u quarks and 1 d quark (uud);
The neutron is a baryon made out of…. 2 d quarks and 1 u quark (ddu)
1. Show that the charge of a proton is 1.
A proton consists of 2 up quarks and 1 down quark (uud), so
q = 2/3 + 2/3 – 1/3 = +1
2. Show that the charge of a neutron is 0.
A neutron consists of 2 down quarks and 1 up quark (ddu), so
q = -1/3 – 1/3 + 2/3 = 0
___
3. What is the quark content and the charge of an antiproton? (uud)
q = -1
4. What is the quark content and the charge of an antineutron?
q=0
Baryon number (B): Baryons are assigned a quantum number
What is the baryon number for:
protons and neutrons? +1
antiprotons and antineutrons? -1
quarks? +1/3
antiquarks? -1/3
So how does B of an antiparticle compare to B of the particle? Same magnitude, opposite sign
Law of Conservation of Baryon Number: Baryon number is conserved in ALL reactions.
_
Example: n +
p  n + p + p + p
(B=1) + (B=1) = (B=1) + (B=1) + (B=1) + (B=-1)
5. Show that the reaction below cannot occur; if it did, the law of conservation of baryon
number would be violated.
--
p + p  π0 + π0 + n
for this reaction, the baryon # on the left side is 0 and on the right side it is +1.
Leptons
Leptons: the electron and its neutrino, the muon and its neutrino, and the tau and its neutrino,
as well as all of their antiparticles
There is solid experimental evidence for the existence of 6 types of leptons
Lepton
Symbol
e-
Electric
Charge (e)
-1
Rest Mass
(MeV c-2)
0.511
Spin
(h/2π)
½
Electron
Electron
neutrino
Muon
νe
0
very small
½
μ-
-1
106
½
Muon
neutrino
νμ
0
very small
½
Tau
τ-
-1
1,780
½
Tau neutrino
ντ
0
very small
½
Because of their spin, all leptons are…..?
The leptons of each family or generation are assigned a lepton number. Since there are 3
families, there are 3 lepton numbers
Lepton number (L): All leptons have a lepton number of +1 and antileptons have a lepton
number of -1.
Type of Leptons and Lepton numbers: electron, muon, and tau lepton with numbers, Le, Lμ, and
Lτ
The 3 kinds of lepton number are individually conserved in all reactions as is the overall Lepton
number.
Electron, e
Electron neutrino, νe
Muon, μMuon neutrino, νμ
Tau, τTau neutrino, ντ
Le
+1
+1
0
0
0
0
Lμ
0
0
+1
+1
0
0
Lτ
0
0
0
0
+1
+1
6. Show that all lepton numbers are conserved in the following muon decay:
_
μ  e + νe + νμ
-
-
7. Do the following reactions conserve lepton number?
a. p+  e+ + π0
b. π0  e+ + μ-
_
c. τ  π + ντ
+
+
Exchange Particles
Exchange Particles: associated with interactions or forces; includes the photon (γ), the W
and Z bosons (W± and Z0), 8 particles called gluons, and the graviton.
There is solid experimental evidence for the existence of all exchange particles except the
graviton.
Gauge bosons: particles that mediate (or transmit) the force between a pair of particles
The 4 fundamental forces have different ranges and a different boson is responsible for each
force. The mass of the boson establishes the range of the force. The bosons carry the force
between particles.
The Higgs Particle or Higgs boson: a boson-like force mediator, but does not actually mediate
any force;
explains the mass of other particles, including the W and Z bosons;
not known if this particle is elementary;
was tentatively confirmed in 2013 to be positively charged and to have zero spin.
Leptons and quarks of the standard model can be arranged into 3 families or generations.
1st generation
Leptons
e-
Quarks
u
νe
d
μ-
s
νμ
c
τ-
b
ντ
T
nd
2 generation
rd
3 generation
Conservation Laws
In all reactions, the following quantities are always conserved:
1. energy
2. momentum (and angular momentum)
3. electric charge
4. baryon number
5. colour
6. lepton number
Strangeness (S): a property that was initially defined to explain the behavior of massive
particles such as kaons and hyperons.
Strange quark has a strangeness of: -1
Strange antiquark has a strangeness of: +1
When is strangeness conserved? When strange particles are created in a strong interaction, but it
is not conserved when they subsequently decay through the weak interaction.
This is why strange particles are always produced in pairs. If 2 particles interact to produce a
strange particle, then a strange antiparticle must also appear.
In the following reactions, determine if Q, B, L, and S are conserved.
_
_
8. uud + ud  ds + uds
Q: (2/3 + 2/3 – 1/3) + (-2/3 -1/3) = (-1/3 + 1/3) + (2/3 – 1/3 -1/3)
0=0
L: none of the particles are leptons, so the lepton numbers on both sides are 0.
B: (1/3 + 1/3 +1/3) + (1/3 + 1/3) = (1/3 + 1/3) + (1/3 + 1/3 + 1/3)
5/3 = 5/3
S: There are no strange quarks on the left side so the strangeness = 0. On the right side,
there is 1 strange and 1 antistrange quark, so the total strangeness also = 0.
_
_
_
9. ds  ud + ud
_
10. uds  ud + uud
Interactions and exchange particles
Basic interaction vertices:
There are 4 fundamental forces or interactions in nature.
Interaction
Exchange Particle(s)
Photons
Relative Strength
1035
Electromagnetic
Interaction acts on
Particles with electric
charge
W and Z bosons
1024
Weak (nuclear)
Quarks and leptons
only
Gluons (and mesons)
1037
Strong (nuclear)
Quarks and gluons
(and hadrons)
Gravitons
(undiscovered)
1
Gravitational
All particles with
mass
The electromagnetic and weak nuclear interactions have been combined to form the electroweak
interaction.
How does the range of the exchange force relate to the mass of the exchange particle?
The shorter the range of the exchange force, the more massive the exchange particle.
The exchange particles for gravitation and the EM interaction both have infinite range, so must have zero
rest masses. Meanwhile the weak interaction has the heaviest boson because its range is the shortest. The
strong interaction has an exchange particle of intermediate mass.
At a fundamental level, particle physics views an interaction between 2 elementary particles in
terms of interaction vertices.
All interaction vertices should be read from left to right. The left hand side represents BEFORE
and the right hand side represents AFTER.
Usually the time axis goes to the right and the space or position axis goes upwards, but they can
be reversed.
Because arrows on antiparticles are drawn in the opposite direction to those on particles, we
sometimes say that these antiparticles travel backwards in time. This is just an expression! All
particles/antiparticles move forwards in time.
The electromagnetic interaction is the exchange of a virtual photon between charged particles.
The exchanged photon is not observable. This interaction vertex is show on the left below.
By rotating the arms of the vertices, the following interaction possibilities are generated.
Electric charge, baryon number, and lepton number are conserved at an interaction vertex.
The total Q, B, and L, going into a vertex must equal the total Q, B, and L leaving the vertex.
Feynman Diagrams
Feynman diagrams: pictorial representations or “spacetime diagrams” of particle interactions
that uses interaction vertices in order to build up possible physical processes.
Examples: below left is electron-electron scattering (the exchange of a virtual photon in the
interaction between electrons), below right is Higgs decay to two photons via top loop;
In this Feynman diagram below, an electron and positron destroy each other, producing a virtual
photon which becomes a quark-antiquark pair. Then one radiates a gluon.
Other examples of Feynman diagrams for basic interaction vertices.
To build a Feynman diagram, the following are needed:
1) The basic interaction vertex – points at which lines come together
2) Lines with arrows to represent particles (often electrons and positrons)
3) Wavy or broken lines that have no arrow to represent photons or exchange particles
Examples: Draw the Feynman diagram for the following processes:
11. e- + e+  e- + e+
12. e- + e+  γ + γ
13. beta minus decay in which a neutron decays into a proton, an electron, and a neutrino
14. positive beta (positron) decay: p  n + e- + νe
Quark Confinement (or confinement of colour): It is not possible to observe isolated quarks
(and gluons). They only exist in groups within hadrons. Quarks inside a hadron always appear in
colour combinations that result in zero net colour number.
Why is this so?
Suppose you wanted to remove a quark from inside a meson. The force between the quark and the
antiquark is constant no matter what their separation is. Therefore, the total energy needed to separate the
quark from the antiquark gets larger and larger as the separation increases. To free the quark completely
would require an infinite amount of energy, and so it is impossible. If you insisted on providing more and
more energy in the hope of isolating the quark, all that would happen would be the production of a
meson-antimeson pair and not free quarks.
Table of some baryons
Particle Symbol Quark Mass
Content MeV/c2
Proton p
uud
938.3
Neutron n
ddu
939.6
++
Delta
Δ
uuu
1232
Delta
Δ+
uud
1232
0
Delta
Δ
udd
1232
Delta
Δ
ddd
1232
0
Lambda Λ
uds
1115.7
+
Sigma Σ
uus
1189.4
Sigma Σ0
uds
1192.5
Sigma Σ
dds
1197.4
0
Xi
Ξ
uss
1315
Xi
Ξ
dss
1321
Omega Ω
sss
1672
Mean
lifetime (s)
Stable
885.7±0.8
6×10-24
6×10-24
6×10-24
6×10-24
2.60×10-10
0.8×10-10
6×10-20
1.5×10-10
2.9×10-10
1.6×10-10
0.82×10-10
Decays to
Unobserved
p + e- + νe
π+ + p
π+ + n or π0 + p
π0 + n or π- + p
π- + n
π- + p or πo + n
π0 + p or π+ + n
Λ0 + γ
π- + n
Λ0 + π0
Λ0 + πΛ0 + K- or Ξ0 + π-
Table of some mesons
Particle
Symbol AntiQuark
Mass
Mean
Principal
particle Content MeV/c2 lifetime (s)
decays
+
−
-8
+
Charged Pion π
π
ud
139.6 2.60×10
μ + νμ
Neutral Pion π0
Self
uu - dd
135.0 0.84×10-16 2γ
Charged Kaon K+
K−
493.7 1.24×10-8 μ+ + νμ or π+ + π0
Neutral Kaon K0
K0
ds
497.7
Eta
η
Self
uu + dd - 2ss 547.8 5×10-19
Eta Prime
η'
Self
uu + dd + ss 957.6 3×10-21