The Weak Force

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The Weak Force
so named because unlike the PROMPT processes
?
qg
e e-
_
rg
e e-
?
qr
which seem instantaneous
?? ? ? ?
or the electromagnetic decay
which involves a 10-17 sec lifetime
path length (gap) in photographic emulsions mere
nm!
weak decays are SLOW processesthe particles
involved ?, ?, ? are nearly stable.
10-6 sec 700 m pathlengths
887 sec
10-8 sec ????? 7 m pathlengths
and their inverse processes scattering or
neutrino capture are rare small probability of
occurrence (small ratessmall cross sections!).
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Such small cross section seemed to suggest
a SHORT RANGE forceweaker with distance
compared to the infinite range of the Coulomb
force
or powerful confinement of the color force
This seems at odds with the predictions of
ordinary gauge theory in which the VECTOR
PARTICLES introduced to mediate the forces like
photons and gluons are massless.
This means the symmetry cannot be exact. The
symmetry is BROKEN.
This does not mean were giving up. There is a
mathematically prescribe way to HIDE
SYMMETRIES or restrict certain states from
exhibiting the full symmetry of their Lagrangian
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Spontaneous Symmetry Breaking Englert Brout,
1964 Higgs 1964, 1966 Guralnick,
Hagen Kibble 1964 Kibble 1967
The Higgs Mechanism
The Lagrangian derived equations of motion for
a system possess symmetries which simply do NOT
hold for a specific ground state of the
system. (The full symmetry MAY be re-stored at
higher energies.)

• (1) A flexible rod under
• longitudinal compression.
• Lagrangian symmetric with respect
• to rotations about the rods axis
• once force exceeds some critical value
• it must buckle sideways forming an
• arc in SOME arbitrary direction
• Although one direction is chosen, the
• complete set of all possible final shapes
• DOES show the full symmetry.

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• (2) IRON SAMPLE
• in absence of external magnetic field
• no preferred orientation of atomic
• magnetic moments
• macroscopic samples
• show no net magnetization
• rotationally translationally invariant
• yet through random fluctuations it
  settles
• into domains destroying (on a microscopic
  scale)
• its spatial invariance.
• (3) FERROMAGNETIC MATERIALS
• Any macroscopic sample, at high temperature
• ? zero net magnetization
• but below the curie temperature atomic magnetic
• moments all align in an arbitrary direction
  (chosen

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What is the GROUND STATE?
lowest energy state
What does GROUND STATE mean in Quantum Field
Theory?
Shouldnt that just be the vacuum state? 0 ?
which has an
compared to 0.
Fields are fluctuations about the GROUND
STATE. Virtual particles are created from the
VACUUM.
The field configuration of MINIMUM ENERGY is
usually just the obvious ? ? 0
(e.g. out of ? away from a particles location)