lecture 3

Report
Topics in Contemporary Physics
Basic concepts
Luis Roberto Flores Castillo
Chinese University of Hong Kong
Hong Kong SAR
January 5, 2015
… last time: Historical Overview
Historical overview (following D. Griffiths, 2nd ed.)
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“Classical Era” (electron, nuclei, neutrons)
Photons (quantum effects become apparent)
Mesons (from Yukawa to the muon)
Antiparticles (Dirac, Anderson, x-ing symm)
Neutrinos (β-decays, Pauli’s solution, 2 types)
Strange Particles (new baryons and mesons)
The Eightfold Way (finding structure)
The Quark Model (an explanation)
The November Revolution (evidence!)
Intermediate Vector Bosons
The Standard Model
L. R. Flores Castillo
CUHK
(1897-1932)
(1900-1924)
(1934-1947)
(1930-1956)
(1930-1962)
(1947-1960)
(1961-1964)
(1964)
(1974-1983, 1995)
(1983)
(1978-?)
January 14, 2015
2
One point to emphasize
• Strong interactions conserve strangeness, weak
interactions don’t
• Please notice the “Notice board” from the website
L. R. Flores Castillo
CUHK
January 14, 2015
3
PART 1
• Brief history
• Basic concepts
• Colliders & detectors
5σ
• From Collisions to
papers
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• The Higgs discovery
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20
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110
• BSM
• MVA Techniques
• The future
L. R. Flores Castillo
CUHK
January 14, 2015
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Outline
– Numbers and Units
– Elementary particle dynamics
(a first quick look at Feynman Diagrams)
• QED
• QCD
• Weak interactions
• Conservation laws
• Unification
L. R. Flores Castillo
CUHK
January 14, 2015
5
On Constants and Units
Two of the most used constants in particle physics:
• c = 299 762 458 m/s
• h = 6.62606957(29) x 10-34 kg m2 / s
Why no uncertainty on c ?
L. R. Flores Castillo
CUHK
January 14, 2015
6
On Constants and Units
Two of the most used constants in particle physics:
• c = 299 762 458 m/s
• h = 6.62606957(29) x 10-34 kg m2 / s
Very impractical values. Why?
• Meter:
– 1790: Length of a pendulum with half-period of one second
– 1791: One ten-millionth of ¼ Earth’s meridian through Paris
– 1799: Platinum meter bar (refined in 1889 and 1927)
– 1960: 1,650,763.73 wavelengths of 2p105d5 of Kr-86
– 1983: Length traveled by light in vacuum in 1/299,762,458 of a sec
– 2002: “… as long as GR effects are negligible.”
L. R. Flores Castillo
CUHK
January 14, 2015
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On Constants and Units
Similarly, the kg is defined by an object
SI: “The kilogram is the unit of
mass; it is equal to the mass of
the international prototype of the
kilogram”
L. R. Flores Castillo
CUHK
January 14, 2015
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On Constants and Units
Similarly, the kg is defined by an object
Comparisons between official copies show some divergence
with time. ~ 5 x 10-8 (50 μg in 100 years)
L. R. Flores Castillo
CUHK
January 14, 2015
9
On Constants and Units
• We can choose units so that c, h, … have value 1.
• The constants chosen to be = 1 determine units of length,
mass, time, temperature and electric charge.
“Natural” units:
• Plank units: c = G = ħ = kB = 1
[ħ] = [ momentum x position ] = L T-1 M L = L2 T-1 M
[c] = [ speed ] = L T-1
[G] = ?
L. R. Flores Castillo
CUHK
January 14, 2015
10
On Constants and Units
• Gravitational constant:
m1m2
F =G 2
r
[F]
M L T-2
M-1 L3 T-2
G
L. R. Flores Castillo
= [ G ] M2 L-2
= [ G ] M2 L-2
=[G]
= 6.67384(80) x 10-11 m3 kg-1 s-2
= 6.67384(80) x 10-11 N m2 kg-2
CUHK
January 14, 2015
11
On Constants and Units
Universal constants can define a length, a mass, a time,
and a temperature.
Using these as units, all these constants become 1.
L. R. Flores Castillo
CUHK
January 14, 2015
12
On Constants and Units
Planck units are not adequate for particle physics. Why?
Instead, we can start from an adequate unit of energy:
L. R. Flores Castillo
CUHK
January 14, 2015
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On Constants and Units
• In this system, c = ħ = kB = 1
• And, by construction, the unit of energy is good for
particle physics.
E = mc
2
2 4
2 2
E =m c +p c
2
E =m +p
2
2
2
E =n
L. R. Flores Castillo
CUHK
January 14, 2015
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Elementary Particle Dynamics
15
Brief reminder
• Matter:
quarks & leptons
• Interactions:
Vector bosons
(plus the Higgs)
• Three generations
– One neutrino for
each charged lepton
– Up-type, down-type
quarks
L. R. Flores Castillo
CUHK
January 14, 2015
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QED
17
Quantum Electrodynamics (QED)
All EM phenomena are ultimately reducible to:
• Time flows horizontally
• An electron enters, emits (or absorbs) a photon, and exits
• Any charged particle (lepton, quark, W)
L. R. Flores Castillo
CUHK
January 14, 2015
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Quantum Electrodynamics (QED)
• Combinations describe more complicated processes:
Time
• e’s enter, a photon is exchanged (direction?), both exit
• Coulomb repulsion, or “Møller scattering”
L. R. Flores Castillo
CUHK
January 14, 2015
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Quantum Electrodynamics (QED)
Time
•
•
•
•
Same diagram (“Feynman diagram”), rotated
Line ‘backward in time’ = antiparticle moving forward in time
Above: e+, e- annihilate into a γ, which makes an e+e- pair
Coulomb attraction of opposite charges, “Bhabha scattering”
L. R. Flores Castillo
CUHK
January 14, 2015
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Quantum Electrodynamics (QED)
Time
• Very different diagram, also describes Bhabha scattering
• Both must be included in the calculation
L. R. Flores Castillo
CUHK
January 14, 2015
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Quantum Electrodynamics (QED)
Other diagrams (same two vertices):
Pair annihilation
Pair production
e+ + e- ® γ + γ
γ + γ ® e+ + e-
Compton
scattering
e+ + γ ® e- + γ
Crossing symmetry: twisting or rotating the figure
L. R. Flores Castillo
CUHK
January 14, 2015
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Quantum Electrodynamics (QED)
… why stop there? With 4 vertices:
• In all these:
e+ + e- ® e+ + e(Møller scattering)
• Internal lines:
– irrelevant for the
observed process
– “Virtual particles”
– “Mechanism”
• External lines
– Observable particles
– Physical process
L. R. Flores Castillo
CUHK
January 14, 2015
23
Quantum Electrodynamics (QED)
• Careful! Only one primitive vertex!!
L. R. Flores Castillo
CUHK
January 14, 2015
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Quantum Electrodynamics (QED)
•
•
•
•
Feynman diagrams do NOT represent trajectories
Only interactions
Each diagram represents a NUMBER
“Feynman rules” define how calculate it.
• For a given process (a set of external lines), the sum of
all FD’s with those external lines represents the process
• There are infinitely many, but each vertex brings a factor
α = e2/ħc = 1/137 (the fine structure constant)
– The sum does converge
L. R. Flores Castillo
CUHK
January 14, 2015
25
Quantum Electrodynamics (QED)
…
• Recently: 12,672 Feynman diagrams for electron’s g-2
• Phys Rev Lett 109, 111807 (2012)
L. R. Flores Castillo
CUHK
January 14, 2015
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Quantum Electrodynamics (QED)
• Energy & momentum should be conserved in each vertex
• Consequence:
– Conserved in the diagram as a whole
– The primitive ‘building block’ does not represent a possible
process:
In CM frame: Energy from
mc2 to more than that.
L. R. Flores Castillo
CUHK
In CM frame: from zero total
momentum to a photon.
January 14, 2015
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Quantum Electrodynamics (QED)
• Any charged particle would interact with the photon
Pion decay
L. R. Flores Castillo
CUHK
January 14, 2015
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Quick exercise
• Draw the lowest order Feynman diagram representing
“Delbruck scattering”: γ+γ ® γ+γ
L. R. Flores Castillo
CUHK
January 14, 2015
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QCD
30
Quantum Chromodynamics (QCD)
• Color plays the role of charge
• Similar structure, but some important differences:
– Three kinds of color
– Quark color (but not flavor) may change
– Gluons must carry away the difference
L. R. Flores Castillo
CUHK
January 14, 2015
31
Quantum Chromodynamics (QCD)
• Force between quarks, at lower order:
• Gluons have then two colors (color and anticolor)
• 3 × 3 = 9 possibilities, but there are 8 gluons
L. R. Flores Castillo
CUHK
January 14, 2015
32
Quantum Chromodynamics (QCD)
• Gluons do carry color (in contrast with photons)
• Far richer than QED
• Bound states of gluons possible (“glueballs”)
• In contrast with αEM (=1/137), αS > 1 !!! What to do?
L. R. Flores Castillo
CUHK
January 14, 2015
33
Quantum Chromodynamics (QCD)
• With αS > 1, it would be impossible to sum diagrams
• Fortunately, an effect similar to …
– Dielectric shielding of a charge
– Vacuum polarization
plus the features of QCD, end up decreasing the QCD
coupling at short distances.
i.e., within hadrons (p, n, π, …), quarks interact very
weakly. This is called ASYMPTOTIC FREEDOM, and
recovers the possibility of calculating the sums.
L. R. Flores Castillo
CUHK
January 14, 2015
34
Quantum Chromodynamics (QCD)
• One final difference:
naturally occurring particles
are colorless.
• We only observe indirect
effects of color.
L. R. Flores Castillo
CUHK
January 14, 2015
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Color confinement
L. R. Flores Castillo
CUHK
January 14, 2015
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Weak Interactions
37
Weak interactions
•
•
•
•
Leptons have no color, so no strong nuclear interaction
Neutrinos have no charge, so no EM interaction
But all of them carry the “weak charge”
Two types of weak interaction: neutral (Z), charged (W)
NEUTRAL
L. R. Flores Castillo
CUHK
January 14, 2015
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Neutral Weak Interactions
• Examples:
Neutrino-electron scattering
Neutrino-proton scattering
vμ+e- ® vμ+e-
vμ + p ® vμ + p
L. R. Flores Castillo
CUHK
January 14, 2015
39
Neutral Weak Interactions
• Any process mediated by the photon can also be
mediated by the Z:
• These diagrams (including the Z instead of the photon)
also enter in the sum… but are negligible.
L. R. Flores Castillo
CUHK
January 14, 2015
40
Charged Weak Interactions
LEPTONS:
A simple combination:
Two leptons of the
same generation
L. R. Flores Castillo
CUHK
January 14, 2015
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Charged Weak Interactions
• Slightly modified:
m ® e + nm + ne
-
L. R. Flores Castillo
CUHK
-
January 14, 2015
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Charged Weak Interactions
QUARKS:
Mixing lepton and quark diagrams:
L. R. Flores Castillo
CUHK
January 14, 2015
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Charged Weak Interactions
QUARKS:
Time
μ
×
×
With u and d bound by the strong force,
The pair on the right can be μ, vμ:
L. R. Flores Castillo
CUHK
vμ
p ® e +ne
p ® m + nm
-
January 14, 2015
-
44
Charged Weak Interactions
QUARKS:
Time
(n)
It also accounts for neutron beta
decay:
+
-
n ® p + e +ne
L. R. Flores Castillo
CUHK
January 14, 2015
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On Feynman Diagrams
Replacing the lepton vertex
with a quark vertex:
… which also proceeds by
the strong interaction:
D ® p +p
(this is by far the dominant
contribution in this case)
0
L. R. Flores Castillo
+
CUHK
-
January 14, 2015
46
Some complications
• If these vertices did not mix generations, strangeness
would never change, but it does:
L ® p +p
+
-
W- ® L + K -
(Λ)
L. R. Flores Castillo
CUHK
January 14, 2015
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… and a solution
This mixing of generations posed a problem.
Solution: to weak interactions, the quark generations are
‘misaligned’
• If the weak force acted on (u,d), (c,s), (t,b)
there would be no “inter-generational” mixing
• However, it acts on rotated versions of d, s and b:
(u,d’), (c,s’), (t,b’)
Cabibbo-Kobayashi-Maskawa matrix
L. R. Flores Castillo
CUHK
January 14, 2015
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The CKM Matrix
• If the KM matrix was the unit matrix,
– “upness-plus-downness”
– “strangeness plus charm”
– “topness plus botomness”
Would each be conserved (just as e, μ & τ lepton numbers)
• However, experimentally:
With three generations of quarks:
three mixing angles + one CP-violating complex phase.
L. R. Flores Castillo
CUHK
January 14, 2015
49
Weak and EM couplings of W and Z
• Similar to gluon-gluon interactions, W and Z couple to
one another:
• Since W is charged, it also couples to the photon:
L. R. Flores Castillo
CUHK
January 14, 2015
50
Decays and conservation laws
Whenever possible, particles decay into lighter particles
i.e., unless prevented by conservation laws
Stable particles:
• Photon: nothing lighter to decay into.
• Electron: lightest charged particle
• Proton: lightest baryon
• Lightest neutrino: lepton number
(plus antiparticles)
All other particles decay spontaneously
L. R. Flores Castillo
CUHK
January 14, 2015
51
Decays and conservation laws
Each unstable particle has
• A characteristic
lifetime:
– μ: 2.2×10-6 s,
– π+: 2.6×10-8 s,
– π0: 8.3×10-17 s,
• Several decay modes:
• K+ decay:
• 64% into μ+ + vμ
• 21% into π++π0
• 6% into π++π++π• 5% into e++ve+π0
•…
• Predicting these numbers is one of the goals of
elementary particle theory
L. R. Flores Castillo
CUHK
January 14, 2015
52
Decays and conservation laws
• Decays are usually dominated by one of the fundamental
forces
– If there is a photon coming out … EM
– If there is a neutrino coming out … weak
– If neither, harder to tell
• The most striking experimental difference: decay times
– strong decays: ~ 10-23 s (about the time for light to cross a p)
– electromagnetic: ~ 10-16 s
– weak: ~ 10-13 s
normally, faster for larger mass differences between original
and decay products.
n ® p + e +ne
+
L. R. Flores Castillo
CUHK
-
January 14, 2015
53
Decays and conservation laws
• Energy and momentum
– Particles cannot decay into heavier ones
• Angular momentum
• From the fundamental vertices:
L. R. Flores Castillo
CUHK
January 14, 2015
54
Decays and conservation laws
• Charge: all conserve it strictly (difference carried out by W)
• Color: difference carried out by the gluon
… but, due to confinement: zero in, zero out.
• Baryon number: number of quarks present is a constant
– They come in packages of 3, so we might simply use B = #q/3
– Mesons: zero net quark content, so any number may be produced
• Lepton number: again, unchanged.
– No cross-generation until recently (neutrino oscillations)
• Flavor
– Approximately conserved… because Weak interactions are weak
L. R. Flores Castillo
CUHK
January 14, 2015
55
About unification
•
•
•
•
Electricity + Magnetism
Glashow, Weinberg and Salam: EM + Weak = EW
Chromodynamics + EW ?
The “running” of the coupling constants hints at it
L. R. Flores Castillo
CUHK
January 14, 2015
56
About unification
•
•
•
•
Electricity + Magnetism
Glashow, Weinberg and Salam: EM + Weak = EW
Chromodynamics + EW ?
The “running” of the coupling constants hints at it
?
L. R. Flores Castillo
CUHK
January 14, 2015
57
58
A couple comments
• Slides: starting next week, the day before class
• Please look at the notice board section of the website
– Announcements about homework and deadlines
– Information about exercise classes
L. R. Flores Castillo
CUHK
January 14, 2015
59

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