Frontiers of particle physics II

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Frontiers of particle physics II
Jan 31 Precision tests of the Standard Model
Steve Snow Feb 7 '' Feb 14 '' Feb
21 Matter-Antimatter asymmetry Stefan
Soldner-Rembold Feb 28 '' Mar 7 '' Mar 14
Interactions of particles with matter Ian
Duerdoth ----- Easter ------ One Interactions of
particles with matter Three Beyond the Standard
Model Brian Cox One Bank Holiday - no lecture
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Course Outline
Precision tests because the SM has already
passed all of the simpler tests at todays
energies.
Precision tests of the Standard Model

• Summary of the Standard Model. List of particles
  and vertices. Feynman diagrams and how they
  relate to a Lagrangian. Tree level diagrams and
  higher orders - equivalence to perturbative
  expansion. Diagrams Amplitudes. Probability
  A.A . Memorise rules and practice drawing
  diagrams. Everything allowed will happen small
  effects precision.
• Input parameters a1/137.036003 from Quantum
  Hall effect. GF1.16637w10-5 GeV-2 from muon
  lifetime. mZ91.188 GeV from LEP.
• Low energy tests muon and electron g-2.
  Sensitivity to SUSY.
• LEP. Z branching ratios. How they are measured.
  Particle ID by dE/dx. Heavy flavour tagging.
• LEP and SLC. Asymmetries forward-backward,
  left-right, and t polarisation. How they are
  measured.
• Putting it all together in global fit. Overall
  c2 . Prediction of mH versus direct search for
  Higgs. Limits on SUSY and Z'.

These slides and other material are at
http//hep.man.ac.uk/u/steve/fpp2.html
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The Standard Model Particles
leptons
quarks

• , Z, W, W-, Higgs boson, gluon

A Model not a Theory because many empirical
patterns are built in to the model but not
explained by it.

• No special relation between generation 1 leptons
  and generation 1 quarks, etc.
• Strong and electromagnetic interactions preserve
  flavours. Weak interaction mixes quarks but not
  leptons.
• No unification of strong with electroweak.

• The fermions are divided into leptons which feel
  only the electroweak force and quarks which feel
  both the EW and strong forces.
• Three generations with increasing mass.

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The Standard Model Vertices
g
q q
g
Q Q-
W
l , q nl ,q
g
Z
f f
f f
g g
H
g g g
g
Z
W,Z W-,Z
W,Z W-,Z
H
Q means charged, f means fermion , l means
lepton , q means quark.
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Feynman Diagrams

• Can be used at two levels
• Given the list of particles and vertices which
  exist in a certain theory, (e.g. the SM) we can
  use FDs to find out all the processes which are
  allowed by the theory, and make rough estimates
  of their relative probability.
• Every vertex and particle corresponds to a term
  in the Lagrangian (the formulation of the theory
  which is the starting point for QFT
  calculations). FDs are used to organise the terms
  in a perturbative solution of the Lagrangian.
  There are rules for transforming any FDk into a
  probability amplitude, ak. As usual in the
  quantum world, the total amplitude for the
  transition from one state to another is the sum
  of the amplitudes of all the possible routes by
  which the transition can happen, ASak .The real
  probability of the transition is A.A times flux
  and phase space factors.

For us
Anything which is not explicitly allowed is
forbidden.
For theorists
This amplitude interference means that it is not
easy to guess whether a small correction will
increase or decrease or just change the phase of
A.
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More Rules

• By convention time is horizontal, space vertical.
• A right(left) arrow can be used to indicate a
  (anti-)fermion
• An incoming particle can be swapped for an
  outgoing anti-particle.

• Four-momentum, spin and charges (colour,
  electric) are conserved at each vertex, BUT
• Internal lines/particles can be virtual, i.e.
  they need not obey the usual relation of the
  particles rest mass m with its energy and
  momentum E2 p2 m2 .
• External lines represent the particles which are
  actually observed they must have the correct
  rest mass.

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Semi-quantitative
There are two features of the rules for
transforming diagrams into amplitudes which we
can use without going into the details Each
vertex is associated with a term which is related
to the type of force involved.

• a.Q2 if the boson is a photon (1/137 for Q1)
• as if the boson is a gluon (1/8 if the energy
  scale is large)
• if the boson is a W or Z the coupling is small,
  like a, within factors of sinqW
• The W couples equally strongly to all the
  fermion doublets en,mn,tn,ud,cs,tb whereas the
  Z coupling depends on the fermion charge.
• The coupling of the Higgs to any other particle
  is proportional to the particles mass

Each virtual particle produces a propagator
term which decreases the amplitude as the
particle becomes more virtual, i.e. as m2 gets
further from E2 p2.
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Tree level and higher
If a process is allowed then you will always
find that there are an infinite number of more
complicated ways of achieving the same result.
Here are just a few of the diagrams for e e - -gt
m m- .
a
b
c
d
f
e

• The lowest order or tree level diagram for e e
  - -gt m m- .
• An extra photon in the final state makes this a
  different process from the theoretical point of
  view, i.e. does not interfere with a). But may it
  be indistinguishable in practice, if so it has to
  be taken into account.
• A higher order correction which can be
  significant and brings in the strong force.
• and e) are second order pure QED corrections.
• f) an electroweak correction.

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Free parameters
Any physics theory (except the ultimate one ?)
has a number of parameters which can only come
from experiment. The combination of theory with
experimental parameters should then predict the
result of any other experiment. For the standard
model there are 18 parameters (assuming massless
neutrinos). The choice of which experiments are
used to define parameters and which ones test the
theory is somewhat arbitrary. Conventionally, the
most accurate experiments are used to set
parameters. Note most accurate will change with
time as technology advances.

• Four parameters of the CKM matrix
• aelectromagnetic and astrong
• The Fermi constant

• Three charged lepton masses
• Six quark masses
• The Z boson mass
• The Higgs mass

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Mini-test
To occupy you for 15 minutes over coffee.
Which of the Feynman diagrams below is valid in
the standard model. For those which are not,
which rule do they break ?