9 Symmetry Violations and Quark Flavour Physics
523
9.2.2 Discrete Symmetries in Quantum Systems
9.2.2.1 Particle–Antiparticle Conjugation
In relativistic quantum mechanics, the Dirac equation requires that for each solution
describing a particle, there is a second solution with opposite charge, describing the
antiparticle. The antiparticle of the electron, the positron, was found in 1933 [10],
and the antiproton was found in 1955 [11]. The particle–antiparticle conjugation
C transforms the field φ of the particle into a related field φ † which has opposite
quantum numbers: the charge, lepton number, baryon number, strangeness, beauty,
etc., for the antiparticle are opposite in sign to the values for the particle.
Invariance under the C transformation is always valid in the strong and electromagnetic interactions. This means, in particular, that the visible spectral lines from
atoms and their antiatom partners are identical, and we cannot use these lines to
identify antimatter in the Universe.
This would be especially important in the science-fiction scenario in which a
man-made spacecraft sets out to meet a distant civilization, where it would be
advisable to know whether the other planet was made of matter or antimatter. In
this case another means of differentiation would have to be found.
9.2.2.2 Violation of Mirror Symmetry: Parity Violation in Weak
Interactions
Lee and Yang [13] suggested that of the four interactions—strong, electromagnetic,
weak and gravitational—the weak interaction might violate mirror symmetry when
it was described by a combination of vector and axial-vector currents in the
Lagrangian (V–A theory). The interference of these two currents could lead to
pseudoscalar observables which would change sign under the parity operation. One
such observable is the scalar product of an axial vector (such as the spin of a particle)
with a polar vector (such as the momentum of another particle in the final state). If
the expectation value of this pseudoscalar is measured to be nonvanishing, then
parity is violated.
An experiment on the beta decay of cobalt-60 [14] measured exactly such an
observable, the scalar product of the spin 5 ¯
h of the 60 Co nucleus and the direction
of the electron from its beta decay into an excited state of 60 Ni with nuclear spin
4 ¯
h. The 60 Co nuclei were polarized by embedding them in a cerium–magnesium
crystal, where the magnetic moments were aligned by a weak external magnetic
field of about 0.05 T. In the strong magnetic field inside this paramagnet, the 60 Co
nuclei are polarized through hyperfine interactions if the temperature is low enough
(0.01 K) to avoid thermal demagnetization. The polarization was measured through
the asymmetry of γ rays from the cascade decay of the 60 Ni state. The measurement
then required the detection of the electron direction relative to the polarization of the
Co nuclei. The experimenters found that the electron was emitted preferentially in
523
9.2.2 Discrete Symmetries in Quantum Systems
9.2.2.1 Particle–Antiparticle Conjugation
In relativistic quantum mechanics, the Dirac equation requires that for each solution
describing a particle, there is a second solution with opposite charge, describing the
antiparticle. The antiparticle of the electron, the positron, was found in 1933 [10],
and the antiproton was found in 1955 [11]. The particle–antiparticle conjugation
C transforms the field φ of the particle into a related field φ † which has opposite
quantum numbers: the charge, lepton number, baryon number, strangeness, beauty,
etc., for the antiparticle are opposite in sign to the values for the particle.
Invariance under the C transformation is always valid in the strong and electromagnetic interactions. This means, in particular, that the visible spectral lines from
atoms and their antiatom partners are identical, and we cannot use these lines to
identify antimatter in the Universe.
This would be especially important in the science-fiction scenario in which a
man-made spacecraft sets out to meet a distant civilization, where it would be
advisable to know whether the other planet was made of matter or antimatter. In
this case another means of differentiation would have to be found.
9.2.2.2 Violation of Mirror Symmetry: Parity Violation in Weak
Interactions
Lee and Yang [13] suggested that of the four interactions—strong, electromagnetic,
weak and gravitational—the weak interaction might violate mirror symmetry when
it was described by a combination of vector and axial-vector currents in the
Lagrangian (V–A theory). The interference of these two currents could lead to
pseudoscalar observables which would change sign under the parity operation. One
such observable is the scalar product of an axial vector (such as the spin of a particle)
with a polar vector (such as the momentum of another particle in the final state). If
the expectation value of this pseudoscalar is measured to be nonvanishing, then
parity is violated.
An experiment on the beta decay of cobalt-60 [14] measured exactly such an
observable, the scalar product of the spin 5 ¯
h of the 60 Co nucleus and the direction
of the electron from its beta decay into an excited state of 60 Ni with nuclear spin
4 ¯
h. The 60 Co nuclei were polarized by embedding them in a cerium–magnesium
crystal, where the magnetic moments were aligned by a weak external magnetic
field of about 0.05 T. In the strong magnetic field inside this paramagnet, the 60 Co
nuclei are polarized through hyperfine interactions if the temperature is low enough
(0.01 K) to avoid thermal demagnetization. The polarization was measured through
the asymmetry of γ rays from the cascade decay of the 60 Ni state. The measurement
then required the detection of the electron direction relative to the polarization of the
Co nuclei. The experimenters found that the electron was emitted preferentially in