Violation in Mixing

1
�È Violation in the �� System
�È symmetry violation is an expected consequence of the Standard Model with three quark generations
(see Sec. 1.4.1): as a matter of fact, the �È violation that shows up in a small fraction of weak decays is
accommodated simply in the three-generation Standard Model Lagrangian. All it requires is that �È is not
imposed as a symmetry.
Some experiments have proved that �È violation occurs in neutral à decays [1], The Ã-decay observations,
together with other measurements, place constraints on the parameters of the Standard Model mixing matrix
(the �ÃÅ matrix [2, 3]) but do not yet provide any test about whether the pattern of �È violation predicted
by the minimal Standard Model is the one found in nature. A multitude of �È -violating effects are expected
in � decays, some of which are very cleanly predicted by the Standard Model.
If enough independent observations of �È violation in � decays can be made then it will be possible to test
the Standard Model predictions for �È violation. Either the relationships between various measurements
will be consistent with the Standard Model predictions and fully determine the �ÃÅ parameters or there
will be no single choice of �ÃÅ parameters that is consistent with all measurements. This latter case would
indicate that there is a contribution of physics beyond the Standard Model: so the main goal for the BABAR
experiment is to measure enough quantities to impose redundant constraints on Standard Model parameters,
including particularly the convention-independent combinations of �È -violating phases of �ÃÅ matrix
elements.
Since the Standard Model accommodates �È -violation, no extension of the Standard Model can be �È -
conserving and thus many extensions have additional sources of �È -violating effects, or effects which
change the relationship of the measurable quantities to the �È -violating parameters of the Standard Model:
� Factories like BABAR can play an important role in measuring most of these parameters.
1.1 È , � and Ì symmetries
The fundamental point is that �È symmetry is broken in any theory that has complex coupling constants
in the Lagrangian which cannot be removed by any choice of phase redefinition of the fields in the theory.
Three discrete operations are potential symmetries of a field theory Lagrangian [9]: two of them, parity
and time reversal are space-time symmetries. Parity, denoted by È , sends Ø� Ü � Ø� Ü , reversing the
handedness of space. Time reversal, denoted by Ì , sends Ø� Ü � Ø� Ü , interchanging the forward
and backward light-cones. A third (non-space-time) discrete operation is charge conjugation, denoted by
�. This operation interchanges particles and anti-particles. The combination �È replaces a particle by its
anti-particle and reverses momentum and helicity.