First observation of the Charmless Decay B to K pi0pi0 and Study of its Dalitz Plot Structure Page: 37 of 201
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1.2. CP violation 8
1.2 CP violation
This section gives a brief overview of the different types of CP violation observed in
meson decays. For a more detailed description refer to Refs. [20, 21]. In quantum
theory a transformation maps a state to another through a unitary operator U
where the unitarity condition is required to maintain normalisation. This can be
generalised by:
4') -- ') = U {) (l.ii)
The symmetry properties of a physical system arise by the invariance of the measured
quantities when performing a transformation. A symmetry violation occurs when a
symmetry, well-established in a class of physical processes, is broken under certain
circumstances. The discrete transfomations of interest here in particle physics are
listed below.
o Charge conjugation: this is the process associated with the exchange of
particles and antiparticles under the transformation of all charges into their
opposite sign by the unitary operator, C. Charge conjugation symmetry re-
quires that for every particle, an antiparticle exists which behaves in exactly
the same way except with all its internal charges reversed.
o Parity: the effect of parity transformation is defined as the inversion of spatial
coordinates with respect to an origin via the unitary operator, P. The most
common interpretation of this transformation is a process under which a right-
handed reference system becomes a left-handed system.
o Time reversal: this is the transformation corresponding to the inversion of
the time coordinate. Time reversal invariance is simply the statement that two
processes related to one another by a reversal of all momenta and angular mo-
menta have equal rates. Since momenta and angular momenta are derivatives
with respect to time, reversing these quantities is mathematically equivalent
to a reversal of sign of the time variable.8
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Puccio, Eugenia Maria Teresa Irene & /SLAC, /Warwick U. First observation of the Charmless Decay B to K pi0pi0 and Study of its Dalitz Plot Structure, thesis or dissertation, March 21, 2012; United States. (https://digital.library.unt.edu/ark:/67531/metadc830373/m1/37/?q=%22Irene%22: accessed June 8, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.