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CP Violation by A. I. Sanda, I. I. Bigi

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9

The theory of KL → ππ decays

In this chapter, we present theoretical expectations for various CP violating observables in K → ππ decays, where we must face up to the challenge of explaining the ΔI = 1/2 rule discussed in Section 5.3. A theoretical description of decay rates involves two main steps:

  • evaluating the underlying Lagrangian at ordinary hadronic scales;
  • calculating the matrix elements of the emerging operators.

 

Below we mainly state the results on operator renormalization and on the size of the relevant matrix elements giving few explanations. A more detailed treatment is found in [81].

9.1 The ΔS = 1 non-leptonic Lagrangian

The electroweak Lagrangian given in Eq. (8.17) is defined at an energy scale MW. At lower scales the

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