Abstract
In this lecture, we provide a basic introduction into the topic of charmed baryons and their nonleptonic two-body decays. Some features of the baryon weak decays on the quark level are discussed in detail in the framework of effective field theory. The calculation of the matrix elements of the four-quark operators arising in the effective theory proceeds by using the covariant constituent quark model. The model allows one to evaluate not only the factorizing tree-level diagrams but also more complicated diagrams with the internal W–exchange. The technique required for such calculation is discussed in some detail. Finally, the numerical results are presented, and comparison of the contributions coming from the W–exchange diagrams with those from the tree-level are carefully performed.
Highlights
In 1964, Gell–Mann proposed [1] the theory of quarks–fundamental particles that make up most ordinary matter
Its prediction is usually credited to Glashow–Iliopoulos–Maiani [5] for the so-called GIM mechanism, which forbids the flavor-changing neutral currents in the tree diagrams
One can derive from Equation (9) the useful property of the Dirac matrices called the Fierz transformation
Summary
In 1964, Gell–Mann proposed [1] the theory of quarks–fundamental particles that make up most ordinary matter. The starting point is the relativistic three-quark current with quantum numbers of a baryon octet JP. By using the Fierz transformations for both Dirac matrices and SU(3)-matrices, one finds that there exist two independent currents for a baryon octet with quantum numbers. They may be written in the form: Jkm = εkm2m1 δmm Γ1 qma (qma CΓ2qma33 )εa1a2a3 ,. One can derive from Equation (9) the useful property of the Dirac matrices called the Fierz transformation.
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