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Four-point functions and kaon decays in a minimal AdS/QCD model

Thomas Hambye·Babiker Hassanain·John March-Russell·Martin Schvellinger
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Abstract

We study the predictions of holographic QCD for various observable four-point quark flavour current-current correlators. The dual 5-dimensional bulk theory we consider is a $SU(3)_L \times SU(3)_R$ Yang Mills theory in a slice of $AdS_5$ spacetime with boundaries. Particular UV and IR boundary conditions encode the spontaneous breaking of the dual 4D global chiral symmetry down to the $SU(3)_V$ subgroup. We explain in detail how to calculate the 4D four-point quark flavour current-current correlators using the 5D holographic theory, including interactions. We use these results to investigate predictions of holographic QCD for the $ΔI = 1/2$ rule for kaon decays and the $B_K$ parameter. The results agree well in comparison with experimental data, with an accuracy of 25% or better. The holographic theory automatically includes the contributions of the meson resonances to the four-point correlators. The correlators agree well in the low-momentum and high-momentum limit, in comparison with chiral perturbation theory and perturbative QCD results, respectively.

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Thomas Hambye, Babiker Hassanain, John March-Russell, Martin Schvellinger. 2007-12-19. Four-point functions and kaon decays in a minimal AdS/QCD model. https://doi.org/10.1103/physrevd.76.125017

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