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

P. Hernandez·M. Laine
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Abstract

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 ΔI=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 ΔI = 3/2 amplitude of the weak decays K to ππas well as the kaon mixing parameter B_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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P. Hernandez, M. Laine. 2004-07-19. Correlators of left charges and weak operators in finite volume chiral perturbation theory. https://doi.org/10.1088/1126-6708%2F2003%2F01%2F063

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