Topics in Contemporary Physics
Basic concepts 2
Luis Roberto Flores Castillo
Chinese University of Hong Kong
Hong Kong SAR
January 16, 2015
PART 1
• Brief history
• Basic concepts
• Colliders & detectors
• From Collisions to
papers
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• The Higgs discovery
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• BSM
• MVA Techniques
• The future
L. R. Flores Castillo
CUHK
January 16, 2015
2
… last time: Basic concepts 1
• Numbers and units
– Definition of some units
– “Natural units”
– HEP units
• Elementary particle dynamics
– QED
– QCD
– Weak interactions
(following D. Griffiths, 2nd ed., Chapter 2)
L. R. Flores Castillo
CUHK
January 16, 2015
3
Reminder: units
• “Natural units”:
– Plank units (based on c, ħ, kB, G)
– Particle Physics units (based on c, ħ, kB, E=1eV; )
Using these units, c = ħ = kB = 1
L. R. Flores Castillo
CUHK
January 16, 2015
4
Reminder: interactions
QED:
QCD:
Weak:
W/Z:
L. R. Flores Castillo
W/Z/γ:
CUHK
January 16, 2015
5
Reminder: building processes
• All processes in nature can be built from these vertices
(as far as we can tell so far).
• Physical processes are defined by the “external lines”
– observable particles define initial and final states
– their masses are the “correct” ones
• Transition amplitudes (from initial to final state):
weighted sum of all possible histories between them.
L. R. Flores Castillo
CUHK
January 16, 2015
6
Reminder: adding possible histories
+…
L. R. Flores Castillo
CUHK
January 16, 2015
7
Quick exercises
( n: udd, p: uud,
n ® p + e +ne
+
-
p - : ud )
p ® e +ne
-
-
p ® m + nm
-
-
×
μ
×v
μ
(n)
L. R. Flores Castillo
CUHK
January 16, 2015
8
Quick exercises
( Λ: udd, p: uud, Ω-: sss,
L ® p +p
+
-
p - : ud, K - : su )
W- ® L + K -
(Λ)
(Λ)
L. R. Flores Castillo
CUHK
January 16, 2015
9
A few key concepts
W bosons carry away the “missing” charge
[only one type of charge, so just the difference is needed]
quarks carry away the color change.
[with three colors, change of color needs bi-color gluons]
hence, they also interact strongly
L. R. Flores Castillo
CUHK
January 16, 2015
10
A few key concepts
Asymptotic freedom
Source: Phys .Rev. D86 (2012) 010001
Color confinement
(which “saved” QCD [or, rather, the infinite
sum of ever more complex diagrams] )
L. R. Flores Castillo
CUHK
January 16, 2015
11
A few key concepts
• Formally, the W boson can only link
‘up-type’ quarks (u,c,t) into the
corresponding ‘down-type’ (d,s,b).
• However, experimentally, some times it
mixes generations
• Solution: the weak force “sees” slightly
rotated versions of the down quarks:
Cabibbo-Kobayashi-Maskawa matrix
L. R. Flores Castillo
CUHK
January 16, 2015
12
Today’s outline
• Conservation laws
• Unification
• Relativistic Kinematics
L. R. Flores Castillo
CUHK
January 16, 2015
13
Decays and conservation laws
14
Stable particles 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 their antiparticles)
All other particles decay spontaneously
L. R. Flores Castillo
CUHK
January 16, 2015
15
Decays
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, each with its
own probability (“branching ratio”).
For example, K+ decays:
• 64% into μ+ + vμ
• 21% into π++π0
• 6% into π++π++π• 5% into e++ve+π0
•…
Predicting these numbers (lifetimes and branching
ratios) is one of the goals of elementary particle theory.
L. R. Flores Castillo
CUHK
January 16, 2015
16
Nature of decays
• Each decay is usually dominated by one of the
fundamental forces
D++ ® p+ + p +
p ®g +g
0
S- ® n + e- + n e
Σ-: dds, n: udd, p:uud, Δ++: uuu, π: uū
L. R. Flores Castillo
CUHK
January 16, 2015
17
Decay lifetimes
• How to tell which force dominates a decay?
– 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
+
-
mp+me ≅ mn,  τ(n) ~ 15 minutes!
L. R. Flores Castillo
CUHK
January 16, 2015
18
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 16, 2015
19
Decays and conservation laws
• Charge:
– strictly conserved
– if there is a charge difference, it is carried out by a W boson
L. R. Flores Castillo
CUHK
January 16, 2015
20
Decays and conservation laws
• Charge
• Color: the color difference is carried out by the gluon
… but, due to confinement: zero in, zero out.
L. R. Flores Castillo
CUHK
January 16, 2015
21
Decays and conservation laws
• Charge, Color
• Baryon number: the number of quarks present is constant
– In packages of 3 or 0; we might simply use B = #q / 3
– Mesons: zero net quark content, so any number may be
produced (as long as energy is conserved)
L. R. Flores Castillo
CUHK
January 16, 2015
22
Decays and conservation laws
• Charge, Color, Baryon number
• Lepton number: again, unchanged:
– Lepton in  lepton out (even if a different one)
– No cross-generation until recently (neutrino oscillations)
• If generations were unmixed, e, μ, τ conserved separately
L. R. Flores Castillo
CUHK
January 16, 2015
23
Decays and conservation laws
• Charge, Color, Baryon number, Lepton number
• Flavor
– Conserved in strong & EM vertices, but not in Weak ones
– A weak vertex may turn u into d, or even into s
– Weak interactions are very weak, so flavor is
approximately conserved.
• This was Gell-Mann’s reason to postulate “strangeness”
• Strong interactions dominate production, not decay
L. R. Flores Castillo
CUHK
January 16, 2015
24
Decays and conservation laws
To explain that strange particles are always produced in pairs, GellMann postulated conservation of strangeness
p - (du)+ p+ (uud) ® K + (us )+ S- (dds)
p - (du)+ p+ (uud) ® p + (ud )+ S- (dds)
This is only approximate; this 2nd decay can occur weakly, but
(strangeness-conserving) strong processes are much more likely.
In contrast, particles may only have the option of decaying weakly:
• Λ is the lightest strange baryon
• Should decay to (p or n)+meson
• The lightest strange meson is the K, but mp + mK > mΛ
• Only decays to non-strange particles can proceed:
L ® p+ + p -, 64%; L ® n + p 0, 36%;
L. R. Flores Castillo
CUHK
January 16, 2015
25
About unification
•
•
•
•
Electricity+magnetism, space+time, acceleration+gravity
Glashow, Weinberg and Salam: EM+Weak = EW
Chromodynamics + EW ?
The “running” of the coupling constants hints at it
L. R. Flores Castillo
CUHK
January 16, 2015
26
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 16, 2015
27