# Correlators of left charges and weak operators in finite volume chiral perturbation theory

Hernandez P, Laine M (2003)

Journal of High Energy Physics (1).

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We compute the two-point correlator between left-handed flavour charges, and the three-point correlator between two left-handed charges and one strangeness violating DeltaI = 3/2 weak operator, at next-to-leading order in finite volume SU(3)(L) x SU(3)(R) chiral perturbation theory, in the so-called epsilon-regime. Matching these results with the corresponding lattice measurements would in principle allow to extract the pion decay constant F, and the effective chiral theory parameter g(27), which determines the DeltaI = 3/2 amplitude of the weak decays K --> pipi as well as the kaon mixing parameter (B) over cap (K) in the chiral limit. We repeat the calculations in the replica formulation of quenched chiral perturbation theory, finding only mild modifications. In particular, a properly chosen ratio of the three-point and two-point functions is shown to be identical in the full and quenched theories at this order.

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Hernandez P, Laine M. Correlators of left charges and weak operators in finite volume chiral perturbation theory.

*Journal of High Energy Physics*. 2003;(1).Hernandez, P., & Laine, M. (2003). Correlators of left charges and weak operators in finite volume chiral perturbation theory.

*Journal of High Energy Physics*(1)Hernandez, P., and Laine, M. (2003). Correlators of left charges and weak operators in finite volume chiral perturbation theory.

*Journal of High Energy Physics*.Hernandez, P., & Laine, M., 2003. Correlators of left charges and weak operators in finite volume chiral perturbation theory.

*Journal of High Energy Physics*, (1). P. Hernandez and M. Laine, “Correlators of left charges and weak operators in finite volume chiral perturbation theory”,

*Journal of High Energy Physics*, 2003. Hernandez, P., Laine, M.: Correlators of left charges and weak operators in finite volume chiral perturbation theory. Journal of High Energy Physics. (2003).

Hernandez, P, and Laine, Mikko. “Correlators of left charges and weak operators in finite volume chiral perturbation theory”.

*Journal of High Energy Physics*1 (2003).
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arXiv hep-lat/0212014