Transcript Lecture 1 - Particle Physics Group

Frontiers of particle physics II
Jan 31
Precision tests of the Standard Model
Feb 7
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Feb 14
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Feb 21
Matter-Antimatter asymmetry
Feb 28
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Mar 7
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Mar 14
Interactions of particles with matter
Steve Snow
Stefan Soldner-Rembold
Ian Duerdoth
----- Easter -----One
Interactions of particles with matter
Three
Beyond the Standard Model
One
Bank Holiday - no lecture
Brian Cox
Course Outline
Precision tests of the Standard Model
“Precision tests” because the SM has
already passed all of the simpler tests at
today’s energies.
1.
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.
2.
Input parameters: a=1/137.036003 from Quantum Hall effect. GF=1.16637w10-5 GeV-2
from muon lifetime. mZ=91.188 GeV from LEP.
3.
Low energy tests: muon and electron g-2. Sensitivity to SUSY.
4.
LEP. Z branching ratios. How they are measured. Particle ID by dE/dx. Heavy flavour
tagging.
5.
LEP and SLC. Asymmetries; forward-backward, left-right, and t polarisation. How they
are measured.
6.
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
The Standard Model Particles
leptons
quarks
e
m
t
u
c
t
ne
nm
nt
d
s
b
 , 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.
•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.
•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 Standard Model Vertices

Z
Z
Q+
W
l,q
Q-
nl ,q’
f
f
H
f
f
W+,Z
W+,Z
W-,Z
H
g
q
q
g
g
g
g
g
W-,Z
Q means charged, f means fermion , l means lepton , q means quark.
g
g
Feynman Diagrams
Can be used at two levels:
1.
2.
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, A=Sak .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.
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
particle’s 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.
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 Q=1)
• 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 particle’s 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.
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 - -> m+ m- .
a
b
d
e
c
f
a)
The lowest order or “tree level” diagram for e+ e - -> m+ m- .
b)
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.
c)
A higher order correction which can be significant and brings in the strong force.
d)
and e) are second order pure QED corrections.
f)
an electroweak correction.
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.
• Three charged lepton masses
• Four parameters of the CKM matrix
• Six quark masses
• aelectromagnetic and astrong
• The Z boson mass
• The Fermi constant
• The Higgs mass
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 ?