current topics in particle physics paul...
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Current Topics in Particle Physics
Paul Newman
Email: [email protected]
Office: Physics West 210
Lecture timetable slots: Monday 15.00: Poynting Small Lecture Theatre
Wednesday 12.00: Aston Webb G33
All slides (but not material written on the board) at … http://epweb2.ph.bham.ac.uk/user/newman/ctpp2016/ctpp.html Other material - eg problems and solutions - also on that page.
Accessible via CANVAS (just points to the same place)
Everything referred to on slides examinable unless otherwise stated
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Where this course fits Assumes knowledge from earlier courses:
- Y3 Elementary Particles – pre-requisite
- Y2 Particle Physics (Y2 Neutrinos – but will now be assumed)
- Y2/3 Quantum Mechanics
- Y1/2 Classical Mechanics and Relativity
Not required, but fits very well with:
- Y4 Quantum Mechanics
- Y4 Experimental Particle Physics Techniques
In a nutshell:
- The Standard Model of particle physics in as quantitative a way as possible
- Theory underlying current experiments in particle physics
- Open questions and future perspectives
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Course Content 1 Introduction and revision of relativistic kinematics
2 The Yukawa potential and transition amplitudes
3 Scattering cross sections and phase space
4 Feynman diagrams and QED
5 The weak interaction and the CKM matrix
6 CP violation
7 Neutrino masses and oscillations
8 Quantum chromodynamics (QCD)
9 Deep inelastic scattering and proton structure
10 Electroweak unification: the Standard Model and the W and Z boson
11 Electroweak symmetry breaking: the Higgs boson
12 More about LHC experiments
- Order and content may vary as we go on … - Designed to be as up-to-date as possible and to map onto the main current world experimental facilities.
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Recommended Textbooks There are lots of good particle physics textbooks on the market (and some bad)!
Some well suited to this course include:
- Particle Physics, BR Martin & G Shaw, Wiley (3rd edition 2008)
- Introduction to High Energy Physics, DH Perkins, CUP (4th edition 2000)
- Introduction to Elementary Physics, D Griffiths, Wiley (2nd edition 2008)
At a slightly higher level:
- Quarks and Leptons, F Halzen & AD Martin, Wiley 1984
- Modern Particle Physics, M Thomson, CUP 2013
The course will also include some recent material not covered in textbooks. Luckily there is loads of good particle physics material on the internet.
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Modern Particle Physics & Colliders - Particle Physics was born ~50 years ago, with the first accelerators with enough energy to probe inside the nucleon
The most recent particle physics colliders and their key parameters …
Accelerator Year Experiments Beams Ecm Luminosity
(GeV) (x1032 cm-2s-1)
LEP 89-00 ALEPH,DELPHI,L3,OPAL e+e- 88-210 4
PEP-II 99-07 BaBar e+e- 10.5 50
KEK-B 99- Belle e+e- 10.5 200
HERA 92-07 H1, ZEUS e±p 340 0.5 Tevatron 87- CDF, D0 pp 2000 2
LHC 09- ATLAS,CMS,LHCb,ALICE pp 14000 100
Experiments we work(ed) on here in Birmingham include OPAL, BaBar, H1, ATLAS, LHCb and ALICE as well as many SPS experiments from UA1 to NA62
- The central aim of these (and other non-collider experiments) is to build the most fundamental theories possible and test them as precisely as we can. The ‘state of the art’ is the amazingly successful `Standard Model’
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`Natural’ Units in Particle Physics
More appropriate to the energy/time/distance scales of PP than SI units. Distances are typically sub-10-15 m, energies are GeV.
(h/2π =) ħ = c = 1
Energy GeV Time (GeV/ ħ)-1
Momentum GeV/c Length (GeV/ ħc)-1
Mass GeV/c2 Cross-section (GeV/ ħc) -2 Simplify by choosing ħ=c=1 :
Energy GeV Time GeV-1
Momentum GeV Length GeV-1
Mass GeV Cross-section GeV-2
Convert back to SI units by reintroducing “missing” factors of ħ and c : ħc = 0.1973 GeV fm ħ = 6.582 x 10-25 GeV s
e.g. Multiplying time in natural units by ħ=6.582 10-25 gives time in secs e.g. Multiplying distances by 0.1973 gives distances in fermi (10-15 m) e.g. Multiplying areas by 0.389 gives areas in mb (10-31 m2 )
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Reminder of the Standard Model
- Matter described by point-like spin-½ fermions (huge variation in mass) - Forces mediated by exchange of spin-1 `gauge’ bosons (massive/less) - Gravity not incorporated - Higgs bosons (2012) are spin-0 scalars … neither matter nor force …
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- Interaction of gauge bosons with fermions: SM vertices - Fundamental interaction strength given by `charge’ g, which is related to dimensonless coupling `constant’ α
STRONG EM WEAK CC WEAK NC
Never changes flavour Never changes
flavour
Always changes flavour
Never changes flavour
q q
g
d
W
u q q
Z
µ+
γ
µ+
Only quarks All charged fermions
All fermions All fermions
Standard Model Vertices g
gis the fine structure constant e2/4π (= 1/137 )
€
gem = e = !c4πε 0αem → 4παeme.g.
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4 Vectors and Intervals: Some Conventions
In particular: xµ = (t, x, y, z) and xµ =(E, px, py, pz)
… where index µ = 0, 1, 2, 3 … `contravariant’ form here
- `Covariant’ xµ=gµν xν where `Metric Tensor gµν =
- Always sum over repeated indices;
- Also xµ=gµν xν and gµν = gµν
- Space-time is 4-dimensional: intervals generalise Pythagoras: … to square a 4-vector … (4D version of D2=x2+y2+z2) …
xµxµ = Δ2=t2-x2-y2-z2
NB Scalar product of any 4-vector by itself is a Lorentz invariant …
Four-vectors are objects with well-defined transformation properties under Lorentz boosts
1 0 0 0 0 -1 0 0 0 0 -1 0 0 0 0 -1
€
aµaµ = gµν
ν =0,3∑
µ =0,3∑ aµaν = gµν aµaν
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Lorentz Boosts - Object in frame S’ moves along z axis at speed v=β/c as viewed by observer in frame S … Coordinates related by Lorentz transformation:
t’ γ 0 0 -βγ t
x’ 0 1 0 0 x
y’ 0 0 1 0 y
z’ -βγ 0 0 γ z
=
… Lorentz Invariant: s2 = t2 – x2 – y2 – z2
t γ 0 0 βγ t’
x 0 1 0 0 x’
Y 0 0 1 0 y’
Z βγ 0 0 γ z’
=
Reverse transformation … (use of common sense helps get signs right if in doubt …)
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Energy-Momentum Transformation
Lorentz boost β along z-axis: E’ γ 0 0 -βγ E
Px’ 0 1 0 0 Px
Py’ 0 0 1 0 Py
Pz’ -βγ 0 0 γ Pz
=
(Invariant mass)2 = E2 – px2+ py
2 +pz2
The single most powerful equation in relativistic kinematics …
… applies to individual particles (invariant mass = m) … also applies to systems of multiple particles
(invariant mass = √s)
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Summary for today
1 Natural Units
2 The structure of the Standard Model
3 Relativistic Kinematics: Lorentz boost
4 4-vectors and their use
5 Shorthand notation for 4-vectors
6 Invariants, and specifically invariant mass
Next time: describing forces and exchange particles