Summary

1
Summary
Standard Model of Particles (SM) - particles
and interactions - the electro-weak model
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The situation in the sixties
Chaotic
similar to chemistry of 1800
3
The periodic table
Mendeleev (1869) introduced the periodic table
4
Atomic model explains theMendeleev table
Rutherford (1912) showed that atoms contain a
central nucleus
10-10 m
5
The Standard Model of Particles
Matter
Interactions (quanta)
Electric charge e
n
n
n
e
Weak (W, W-, Z)
m
t
0
-
-
-
Electromagetic (photon)

e
m
t
1
-
u
c
t
2/3
Quarks
d
s
b
-1/3
Strong (gluons)
spin 1/2 spin 1
Gravity is absent hopefully its effects are too
weak...
how to distinguish these two ?
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Elementary particles in interactione. m.
Exchange of photons Affects all the
electrically charged particles quarks e, m, t
Feynman graph
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Elementary particles in interactionWeak
Exchange of W and Z Affects the full set of
particles
Feynman graph
8
Elementary particles in interactionStrong
Exchange of gluons Affects only quarks
Feynman graph
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Quark model
Quarks hold together by "strong interaction" to
form "hadrons" baryons (half-integer
spin) p, n, D, ... mesons (integer
spin) p, r, K, B, ...
A few examples protons and neutrons are made of
3 quarks
Q1
Q0
Charge mirror
Q-1
Q0
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Quark model .2
Easier to indicate the quark content of the
hadrons with a vector. Proton and neutrons and
their antiparticles are
C represents the "charge mirror"
More precisely, the "wave function" of a proton
must contain the information of the movement of
the 3 quarks, of their spin orientation, of the
quark "flavour", and of of an entity called the
"colour" of the quark
new concept
similar to atomic wave functions
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Quark model .3
The mesons are built with one quark and one
antiquark.
Lightest meson system are the 3 "pions"
the 1/sqrt(2) is to "QM average" the 2 possible
configurations uubar and ddbar
the minus sign is to respect a special condition
of symmetry!
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Quark model .4
Theory must calculate the masses, spin, magnetic
moments, decay probabilities, ... , of the
hadrons. Quite a difficult task M(proton) 1
GeV (remember c1)
3 quarks in the proton 1 GeV/3330
MeV/quark M(pion) 140 MeV 2 quarks in the
pion 140 MeV/2 70 MeV This shows that
the strong interaction dynamics defining the
binding energy is very important, very
"strong". The theory of strong interactions is
the colour theory "chromodynamics". If one
"switch of" strong interactions, the mass of the
quarks should be M(u)ltM(d)lt10 MeV, M(s)100
MeV, M(c) 1.2 GeV, M(b)4.5
GeV, M(t)174 GeV
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Hadron decay
p is (seems) stable, lifetime is at least 1029
years n is unstable, lifetime 15min
pions are unstable, for instance
this is an e.m. interaction
W is the vector of the weak interactions
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The leptons
Neutrinos are neutral and have masses 0. The
electron is the lightest (known) charged particle
(511 keV). The muon m (106 MeV) and the tau t
(1780 MeV) are unstable.
time
Seen by the theory of weak interactions the
process look like this
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Measurement of masses
Mass of a particle of momentum p and energy
E M sqrt(E2 - p2)
Example of measurement p0 ? gg
- measure the 2 photons 4-vectors (E1, p1),
(E2, p2) - compute the parent (p0) four-vector
(E, p)(E1 E2, p1 p2) - compute M
E1
g1
E2
p0
g2
detector (e.m. calorimeter)
M135 MeV
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The measurement of masses .2
The production threshold method was used by BES
to measure with very high precision the tau mass
Mt
Production rate
e e- collider with beam energy Ebeam. Minimal E
needed to produce 2 taus is Emin 2 Mt c2
Ebeam
Each beam must have at least Ebeam Mt c2
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The BES method
In order to optimize the search, the energy scan
was done by the method of signal appearance /
disappearance
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Summary on SM elementary particles
The "elementary particles" of the Standard Model
there are the quarks and the leptons (spin 1/2,
they are "Fermions") Quarks have fractional
charge (units of e), and they are the
building blocks of hadrons (p, n,..., pions,
kaons,...). Lepton have charge 0 or -1 (1 the
anti-leptons).
How can we explain this mass spectrum ?
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The interactions
interaction gravitation e.m.
weak strong manifestation
weight light beta
decay nuclear forces
range
weak
Coupling w/o dimension
lifetime
by analogy
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The interactions .2
Coulomb scattering of an electron by the field of
a nucleus
Decay of a muon in electron and 2 neutrini
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The interactions .3
annihilation of e e- into photon/Z decaying into
a pair of particles
when the 2 particles are quarks, they
"hadronize" (i.e. they become hadrons) producing
jets of particles
... we have not seen individual quarks !
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Open a parenthesis jets of particle is an
evidence of the existence of quarks
Jets of hadrons
TASSO event at PETRA
q
1cos2q distribution proving that the quark is a
1/2 spin particle
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The interactions .4
We have also events with 3 or more jets
quarks and gluons hadronize into one jet each
ECAL
HCAL
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Phenomenology of hadronization
How individual quarks (or gluons) transform into
jets of hadrons ? This phenomenon is difficult to
treat analytically because the intensity of the
force is too strong (cannot do a "perturbative"
calculation)
Potential model of qq interaction
Coulomb at very short r (lt 1fm)
E grows fast with r (but not as much as elastic
E kd2/2)
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Phenomenology of hadronization .2
Field lines at very small r
Field lines stay concentrated when you pull the
two quarks apart. They form a string.
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Phenomenology of hadronization .3
Energy accumulates in the string
when enough energy/fm couples quark-antiquark can
be produced
mesons fly apart
jet 2
jet 1
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The interactions .5
Quantum mechanics interactions are mediated by
quanta
Interaction quanta mass typical range Strong 8
gluons 0 1 fm E.m. photon 0
infinite Weak W, Z 100 GeV 10-3
fm Gravity graviton 0 infinite
later we will try to understand why only Weak
forces have quanta which are massive...
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The interactions .5
A photon travelling from a source to your eye
has mass0. If you measure p and E of this
photon, you will find that it has mass0 E2 -
p2 0. This is a "real" photon. In a
"collision", two charged particles exchange some
p and E. QM says that this exchange is mediated
by a photon.
Ex electron and muon are charged particles, they
can exchange the E and p transported by a photon,
the quantum of e.m. interaction
g
m
e
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The interactions .6
with
pa (Ea, pa), etc...
the transferred momentum is q pa - pc - (pd
- pb)
photon
charged particles
If you try to compute the mass of this photon,
you will find a value different from zero this
is a "virtual" photon.
This is possible within some restrictions imposed
by the Heisenberg uncertainty principle...
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The interactions .7
Heisenberg measurements of position and momentum
can only be done with a finite precision because
the microscopic processes are controlled by
A virtual photon violating momentum conservation
by some Dp, can travel a length Dx
1/Dp. Real photons do not violate anything and
they can travel as much as they want.
This photon can travel 1/mass 1/q
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The interactions .8
We are interested to determine the probability
for a particle a to interact with particle b
giving momenta pc and pd. Consider a and b like 2
wires carrying electric currents IaQava and
IbQbvb. The force acting between the 2 is given
by
The QM result is similar
Ia
Ib
1/mass of the photon distance
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The interactions .9
The QM theory of e.m. is called Quantum
ElectroDynamics (QED) From the idea seen before
we can infer a theory to compute the probability
that a given process take place. The typical
behaviour of a QED process, for instance of
e e- ? m m-
expressed as a function of the total energy E is
Probability of the QED process (aem / E)2
Indeed we have the cross section which has the
nice behaviour s ? 0 when E ? infinity, no
"ultraviolet catastrophe".
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The interactions .10
All these calculations are possible at the
"perturbative level", which means that the
"higher order corrections" must become smaller
and smaller (expansion must converge).
Diagrammatically something like
contribution from one quantum 2
quanta 3 quanta
gt ...
gt
gt
Mathematically
Aa lt Ba2 lt Ca3 lt Da4lt .....
where A, B, C, D,... come from (often complex)
calculations.
One sees that the coupling constant has better to
be lt 1 !
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The interactions .11
The technique has been generalized to the other
interactions. "Currents J" of particles with
charges g interact via their specific quanta.
g
g
J1
J2
e.m. charge is e (or a fraction of e for the
quarks) and the quanta are the photons (or use a
aem ? e2) weak interaction charge is gW (or
simply g), quanta are W and Z strong
interactions charge is gs (or as ? gs2) with 8
gluons
While Coulomb needs only 1 kind of charge, and
-, strong interactions have 3 kinds (r,g,b and
-r,-g,-b) !!!
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The interactions .12
While Coulomb needs only 1 kind of charge, and
-, strong interactions have 3 kinds (r,g,b and
-r,-g,-b) !!!
Consider the Coulomb force between 2 particles An
electron has charge minus e, its anti-particle
has charge plus e. Quarks have electric charge
(2/3)e or (-1/3)e , and opposite sign for
antiparticles. Consider the strong force now.
The electron does not have strong interaction
its strong charge is 0. Quarks strongly
interacts with a much more complicated
algebra. They behaves like if they could be of 3
kind (SU(3) group) For instance, in a proton they
must be of the 3 different colours to give a
white particle (rgb white).
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The interactions .13
For a quark u, there are 3 possibilities u, u, u,
etc.
During e.m. interaction, the electric charge
stays on the particle, because the photon is
neutral. During strong interaction, the charge
can be transferred because the gluons carry the
colour charge. Example
time
red and blue quarks blue-antired gluon
exchange blue and red quarks
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The interactions .14
Coloured gluons belongs to the 8 of
g4
(r,g,b is an arbitrary index !)
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Interactions some results
QED is capable to predict the Landé factor g for
electron and muon at the level of 10-9 precision
for the electron
with aem 1/137.0339... from "static"
measurement of e
QED (g-2)/2 ( 1'159'652.2 0.2 )
10-9 measured ( 1'159'652.188
0.004 ) 10-9
dipolar magnetic moment of a particle of spin s,
charge q, masse m
g2 for the Dirac electron
g Landé factor
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Positronium gives aem at low energy
E2
Coulomb potential
E1
gt
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aem at 100 GeV
jet1
jet2
The relevant parameter is aem giving
the interaction strength
at 100 GeV aem1/128
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Some results .3
The relevant parameter is as (alpha
strong) giving the interaction strength.
at 100 GeV as 0.11
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as at low(er) energy
_at_ 3 GeV _at_ 10 GeV
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Running of the alphas
It is found that both the e.m. coupling constant
aem and as vary with the energy of the process
running of as
At 1 GeV (proton mass) asgt1, while at LEP energy
(100 GeV) we have as 0.1. The opposite happens
for aem. At low energy its value is 1/137,
and 1/128 at LEP.
E of the process GeV
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Running of the alphas
Hint of an unification of forces at high E ?
a

strong
e.m.
E (GeV)
1 GeV
Energy of (Grand) unification ?
Nice, but why do we whish some sort of
"unification" ?
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Unification of forces
a
Why we whish some sort of "unification" ?
Unification means the reduction the number of
entities in the theory gt more internal
constraints gt less free parameters gt the theory
becomes more "predictive"
First example of (successful) unification of
forces is the Maxwell theory of
electromagnetism. A second example of
unification is the electro-weak theory, which is
part Standard Model.
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The electro-weak theory
Historical background The e.m. theory was
translated into a QM formalism at the beginning
of 1900, giving the Quantum Electro Dynamics. We
have seen that this theory is very
successful. In 1934 E. Fermi wrote a model for
the Weak Interactions (WI) inspired to QED.
Because he didn't know the existence of the W and
Z, he reduced the calculation to a "point-like
theory"
QED Fermi model
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The electro-weak theory .2
The Fermi model works well at very low energy
(beta decay,...), but it cannot work at high
energy
cross section
Probability of a Fermi weak process s(E)
(GF E)2
This grows to infinity quite fast ! Compare to
the nice behaviour of QED
Fermi constant
Probability of a QED process
s(E) (aem / E)2
To avoid the ultraviolet catastrophe the simplest
solution is to introduce a particle playing a
role analogous to the photon in QED. The main
difference with QED is that the W must be
massive...
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The electro-weak theory .3

• Why do we need a massive W ?
• The Fermi model is OK at low energy. It starts to
  be wrong
• only around 100 GeV.
• So the virtual particle must become "real" at
  this energy

This explains why we do not have free W going
around like the photon. To produce them you need
a lot of energy.
q
It also explain why the weak interaction is
"weak" in reality it is weak only at EltltMW. At
high E, it is comparable to e.m. More of this in
a moment.
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The electro-weak theory .4

• Why do we need a neutral Z?

Because "second order" diagrams diverge, like in
the calculation of corrections to e e- ? m m-
this diagram gives a divergent result
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The electro-weak theory .5
... if we impose the correct relations to link
e.m. and weak sectors.

• The needed relations between Z, W and photon are
  incorporated
• in the Glashow Weinberg Salam electroweak theory

Weinberg angle
Here gg is related to the electric charge gg
e/2v2 e1.60 10-19 C We introduce here two
"weak charges" gW (GF(gW)2) and gZ.
gW, and qW are free parameters of the theory (not
predicted)
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Observation of W and Z
In 1982 CERN commissioning of a p - antip
collider with beams of 270 GeV (E in the centre
of mass 540 GeV). W and Z can be created by the
collisions of quarks from the two protons
X and X' are the "spectators" (a lot of particles
which are there to complicate the life of the
physicist).
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Observation of W and Z .2
Once produced the W and Z decay and we have to
observe they decay products in "ad hoc"
detectors. A (quite) simple case is Z? e e-
e
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Observation of W and Z .3
In reality it is not too bad. The 2 electrons can
be selected quite easily and the invariant mass
of the mother computed
one event energy Lego plot
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Observation of W and Z .4
In the '90 the LEP and SLAC have produced Z by
collision of e and e- beams at the correct
energy to excite the Z resonance
Example
E c.m.

• 88 90 92 94 GeV

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ee- into quarks (jets)
1 10
100 GeV
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The electro-weak theory .6
Fighting against infinities is a constant source
of inspiration. Another example the prediction
of the existence of a c quark by Glashow,
Iliopoulos, Maiani (GIM) in 1970
diverges !
K0
stabilized !
g2 sinqC cosqC
g2 (-sinqC) cosqC
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The electro-weak theory .7
We have more instabilities to explore !
In the SM we have 3 families of lepton and
quarks "doublets".
C and L indices will be explained later
The symmetry of the families lepton-quark is very
aesthetic. But do we have any (mathematical)
reason to believe that should be like that ? Yes
breaking this symmetry generates infinities
in the "triangle anomalies".
Each triangle gives or - infinity. The sum of
the triangles gives zero if and only if the sum
of the charges is also zero. Indeed for each
family
any charged fermion
quarks come with 3 colours
symptom for a deeper reality?!
58
The electro-weak theory .8
One more instability...
(or ee- ?WW)
the scattering WW ?WW diverges and violates
"unitarity" around E1 TeV
possible cure add a spin 0 (scalar)
particle with ad hoc couplings. This is one
reason to believe that there must be some new
particle before 1 TeV.
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Summary
We have explored at a qualitative level the
behaviour of particles communicating by the
different kind of interactions. QM requires a
quantification of the (E,p) exchange. This is
obtained via quanta (photon, gluons,
W,Z), playing the role of mediators of the
force. The strength of an interaction in a
process is parametrized by the charges (e.m.,
weak, strong). To avoid infinities in the
calculations we have to assume that the quark
and lepton families are linked e.m. and weak
charges are also linked there is an hint for
the existence of a new 0-spin
particle with mass lt 1 TeV.