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Current Topics in Particle Physics

Paul Newman

Email: p.r.newman@bham.ac.uk

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