Lecture 17 - The Higgs Boson - School of Physics and Astronomy
Lecture 17 - The Higgs Boson
? Spontaneous Symmetry Breaking
? The Higgs Mechanism
? Higgs Couplings to Fermions
? Electroweak Constraints on the Higgs
? Direct Searches for Higgs Bosons
? Higgs signatures at the LHC
1
Spontaneous Symmetry Breaking
The ground state configuration of a system does not always display
the full symmetry that might be expected.
The symmetry is spontaneously broken, and is hidden.
Everyday example:
A circle of people are sitting at a dining table. The first person
who picks up a napkin (with Left Hand or Right Hand), breaks
rotational symmetry.
Physics example:
In a ferromagnet spins align in a random direction until an external
magnetic field is applied which breaks rotational symmetry.
2
The Higgs Potential
In electroweak theory the difference between the physical
, W , Z 0 boson masses is created by spontaneous symmetry
breaking of the Higgs field .
The potential energy of the Higgs field is:
V () = ?2 ? + (? )2
?2 < 0
>0
The Higgs is a scalar field that exists in a vacuum
The potential is symmetric under rotations in space
The free energy of a ferromagnet is related to its magnetization M :
G = M 2 + M 4
0
The magnetization exists in the absence of an external field
The free energy is symmetric under rotations in space
3
Vacuum Expectation Value
The Higgs potential has the shape of a mexican hat
It has a minimum which is not at < >= 0
Known as the vacuum expectation value v
|?|
2MW
= 246GeV
v=
=
g
This parameter defines the electroweak scale
4
The Standard Model Higgs Field
The Higgs field is a weak isospin doublet with four components:
?
?
?
?
+
1 ? 1 + i2 ?
?
?
=
=
0
2
3 + i4
A fluctuation around the minimum v spontaneously breaks the
rotational symmetry of the Higgs field.
Choose direction of fluctuation so that vacuum Higgs field is:
?
?
1 ? 0 ?
0 =
2
v
Breaking the symmetry eats three of the four components!
5
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