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Elementarteilchenphysik

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Title: Elementarteilchenphysik


1
Elementarteilchenphysik
Antonio Ereditato LHEP University of Bern
Lesson on Electroweak interaction and SM (8)
2
Unification of fundamental interactions
  • Fundamental interactions (fields) each with
    different space-time properties, ranges, coupling
    constants, conservation rules and violations,
  • Can we dream of a Super-Force unifying the four
    interactions at some incredibly high energy
    scale?
  • First successful attempt Maxwell (1865) who
    unified the apparently separate electricity and
    magnetism, by introducing one arbitrary constant
    (c, speed of light) to be determined by
    experiments.
  • Around the end of the 60 Glashow, Salam and
    Weinberg worked-out a theory predicting the
    unification of the weak and the electromagnetic
    interactions into the electro-weak (EW) force,
    with a unique coupling constant, the electric
    charge e and only one parameter (sin2?W), to be
    measured in experiments.
  • Main features of the EW theory exact symmetry
    at high q2 (104 GeV), broken at low energies.
    The breaking of the symmetry makes three of the
    four mediating bosons of the EW theory very
    massive (W, W- and Z0) determining the short
    range of the weak interaction and thus its
    weakness.
  • The EW theory is very well established today
    and its success contributes to the success
    of the so-called Standard Model of particles
    and interactions. It is also a first
    successful step towards a theory of the
    unification of the other forces (Grand
    Unification Theories, GUT)

3
The meaning of force unification the coupling
constants of the various forces are not really
constant, but run with the energy. Therefore,
they could meet (get the same value) at a high
energy scale. This corresponds to a very early
Universe a negligible fraction of second after
the Big Bang
The EW strong force unification
The electroweak unification (?1 and ?2)
The Grand Unification between EM, weak and strong
interactions can be achieved with GUT
Super-Symmetric models
4
The Glashow, Weinberg, Salam Model
The model envisions the unification of weak and
EM interactions (same coupling constant) at some
high energy. The model is based on the
symmetry group SU(2)L x U(1)Y. One has then four
massless mediating bosons, arranged into a
SU(2)L weak isospin triplet (I 1) and a singlet
(I 0) of the weak hypercharge group U(1)Y.
The process of spontaneous symmetry breaking
allows the massless bosons to acquire a mass
without spoiling the renormalizability of the
theory. This is done by introducing the
isospin-doublet, scalar Higgs fields (see
later). The three isospin triplet bosons are
W?? W?(1), W?(2) , W?(3) while B?? is the the
isospin singlet??The physical (massive) states
are the W, W-, Z0 and photon A?. The latter
(neutral bosons) are related to the massless
bosons via mixing (rotation)
?W is called the Weinberg angle
5
The interaction of fermions with the weak bosons
can be expressed in a Lorentz invariant form
through the so-called Lagrangian energy-density,
analogous to the interaction of an electric
current with an electromagnetic field, with g and
g coupling constants
Note that we consider SU(2)L because the weak
isospin current only couples to LH fermions
We define the weak hypercharge, analogously to
the strong hypercharge (apart from a factor 2
difference)
Performing the calculations, recalling the mixing
relation, and setting g/g tan?W , one obtains
i.e. unification of weak and EM interactions
6
In other words, we have expressed the two
experimentally observed neutral currents (the EM
and the weak) in terms of the currents belonging
to the symmetry groups SU(2)L with coupling g,
and U(1)Y with coupling g. These two coupling
constants are replaced by e and by the sin2?W
parameter, the latter to be measured in
experiments
Just as Q generates the group U(1)EM , the Y
operator generates the symmetry group U(1)Y . The
enlarged group SU(2)L x U(1)Y takes into account
the incorporation of neutral weak and EM
interactions. The SU(2)L x U(1)Y group was
introduced by Glasgow (1961) before the discovery
of neutral currents and extended by Weinberg
(1967) and Salam (1968). Another important
result obtained with the EW unification theory is
that one naturally eliminates the divergencies
occurring in calculating graphs in the original
weak interaction theory.
7
Weak boson masses
The Weinberg angle measured in weak interaction
processes (neutrino interactions) and the
masses of the weak bosons measured at the
colliders agree well
Measured masses of the weak bosons MW 80.398
0.025 GeV MZ 91.1876 0.0021 GeV
8
Electroweak couplings
As the EW bosons, also fermions get weak isospin
and hypercharge. In doing so the GWS model has to
take into account that the weak charged-current
interaction violates parity, while the EM
interaction is parity-conserving. Remember that Y
Q - I3
9
Examples of couplings
10
Neutrino scattering
Neutrino electron scattering gave the first
evidence for the correctness of the EW theory and
allowed the first estimates of sin2?W (remember
the Gargamelle experiment). This was followed by
a series of neutrino scattering experiments off
hadrons (for the measurement of structure
functions) and off electrons (to study purely
leptonic, EW processes). For example, the CHARM
II experiment at CERN (1984-1991), that collected
the largest world statistics of and
interactions, for the measurement of sin2?W
11
Neutrino scattering (cont.)
For neutral current reactions
Where s is the cms squared energy y is the
elasticity Ee/E? LL, RR, RL, LR indicate the
helicities of the scattering leptons
For charged current reactions
Lower cross-section for antineutrinos it would
be the same as for neutrinos if the scattering
occurred on RH electrons (forbidden by the V-A
structure of the weak charged current)
Measurement of cross-sections for different
reactions (ambiguities) allows determining the
coupling constants
12
Examples of purely leptonic neutrino interactions
Muon-neutrino off electron scattering can only
proceed via NC reactions
Electron-antineutrino off electron scattering can
proceed via NC and CC reactions

13
Spontaneous symmetry breaking
This transformation is the result of the
phenomenon of Spontaneous Symmetry Breaking
(SSB). In the case of the electroweak force, it
is known as the Higgs Mechanism.
Spontaneous symmetry breaking (SSB) occurs in a
situation where, given a symmetry of the
equations of motion, solutions exist which are
not invariant under the action of this symmetry
without any explicit asymmetric input (hence the
attribute spontaneous). A situation of this
type can be illustrated by means of a simple
(classical physics) example. Consider the case of
a linear vertical stick with a compression force
applied on the top and directed along its axis.
The physical description is obviously invariant
for all rotations around this axis. As long as
the applied force is mild enough, the stick does
not bend and the equilibrium configuration (the
lowest energy configuration) is invariant under
this symmetry. When the force reaches a critical
value, the symmetric equilibrium configuration
becomes unstable and an infinite number of
equivalent lowest energy stable states appear,
which are no longer rotationally symmetric but
are related to each other by a rotation. The
actual breaking of the symmetry may then easily
occur by effect of a (however small) external
asymmetric cause, and the stick bends until it
reaches one of the infinite possible stable
asymmetric equilibrium configurations. In
substance, what happens is that when some
parameter reaches a critical value, the lowest
energy solution respecting the symmetry of the
theory ceases to be stable under small
perturbations and new asymmetric (but stable)
lowest energy solutions appear. The new lowest
energy solutions are asymmetric but are all
related through the action of the symmetry
transformations. In other words, there is a
degeneracy (infinite or finite depending on
whether the symmetry is continuous or discrete)
of distinct asymmetric solutions of identical
(lowest) energy, that maintain the symmetry of
the theory.
14
Spontaneous symmetry breaking (cont.)
The same picture can be generalized to quantum
field theory (QFT), the ground state becoming the
vacuum state. This means that there may exist
symmetries of the laws of nature which are not
manifest to us because the physical world in
which we live is built on a vacuum state which is
not invariant under them. In other words, the
physical world of our experience can appear to us
very asymmetric, but this does not necessarily
mean that this asymmetry belongs to the
fundamental laws of nature. SSB offers a key for
understanding (and utilizing) this physical
possiblity. The application of SSB to particle
physics in the 1960s and successive years led to
profound physical consequences and played a
fundamental role in the edification of the
current Standard Model of elementary particles.
In the case of a global continuous symmetry,
massless bosons (known as Goldstone bosons)
appear with the spontaneous breakdown of the
symmetry according to a theorem by J. Goldstone
in 1960. The presence of these massless bosons,
first seen as a serious problem since no
particles of the sort had been observed, was in
fact the basis for the solution, by means of the
so-called Higgs mechanism, of another similar
problem. This is the fact that the 1954
Yang-Mills theory of non-Abelian gauge fields
predicted unobservable massless particles, the
gauge bosons. According to the mechanism
established in a general way in 1964
independently by P. Higgs and others, in the
case that the internal symmetry is promoted to a
local one, the Goldstone bosons disappear and
the gauge bosons acquire a mass. The Goldstone
bosons are eaten up to give mass to the gauge
bosons, and this happens without breaking the
gauge invariance of the theory. Note that this
mechanism for the mass generation for the gauge
fields is also what ensures the renormalizability
of theories involving massive gauge fields (such
as the Glashow-Weinberg-Salam electroweak theory.
15
The Higgs mechanism
In the Higgs model particle masses arise in a
beautiful, but complex, progression. It starts
with a particle that has only mass, and no other
characteristics, such as charge, that distinguish
particles from empty space. We can call his
particle H. H interacts with other particles for
example if H is near an electron, there is a
force between the two. H is of a class of
particles called bosons. It is also a scalar
particle (s 0). The parameters in the
equations for the field associated with the
particle H can be chosen in such a way that the
lowest energy state of that field (empty space)
is one with the field not zero. It is surprising
that the field is not zero in empty space, but
the result is all particles that can interact
with H gain mass from the interaction. The
picture is that of the lowest energy state,
"empty" space, having a crown of H particles with
no energy of their own. Other particles get their
masses by interacting with this collection of
zero-energy H particles. The mass (or inertia or
resistance to change in motion) of a particle
comes from its being "grabbed at" by the Higgs
particles. The Higgs particle (field) permeates
the whole Universe at any space-time point
16
Search for the Higgs as a free particle at the LHC
The strength of the Higgs coupling is
proportional to the mass of the particles
involved so its coupling is greatest to the
heaviest decay products which have mass lt mH/2.
For example, if mH gt 2Mz then the couplings for
decay to the following particle pairs Z0Z0
WW- tt- pp µµ- ee- are in the
ratio 1.00 0.88 0.02 0.01 0.001 5.5 x
10-6
Negative searches have been conducted at LEP and
TEVATRON. The present bounds on its mass is 114
GeV, 1000 GeV. The Higgs discovery will be one
of the main goals of the LHC (gt2008) with the LHC
ATLAS and CMS experiments.
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