First exploratory calculation of the long-distance contributions to the rare kaon decays K →π ℓ+-

Norman H. Christ, Xu Feng, Andreas Jüttner, Andrew Lawson, Antonin Portelli, Christopher T. Sachrajda, RBC Collaboration, UKQCD Collaboration

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Abstract

The rare decays of a kaon into a pion and a charged lepton/antilepton pair proceed via a flavor changing neutral current and therefore may only be induced beyond tree level in the Standard Model. This natural suppression makes these decays sensitive to the effects of potential new physics. The CP -conserving K →πℓ+-decay channels however are dominated by a single-photon exchange; this involves a sizeable long-distance hadronic contribution which represents the current major source of theoretical uncertainty. Here we outline our methodology for the computation of the long-distance contributions to these rare decay amplitudes using lattice QCD and present the numerical results of the first exploratory studies of these decays in which all but the disconnected diagrams are evaluated. The domain wall fermion ensembles of the RBC and UKQCD Collaborations are used, with a pion mass of Mπ ∼ 430 MeV and a kaon mass of M∼ 625 MeV . In particular we determine the form factor, (z), of the K →πℓ+decay from the lattice at small values of z = q2/MK2, obtaining (z) =1.37(36) ,0.68(39), 0.96(64) for the three values of z = -0.5594(12) , -1.0530(34) , -1.4653(82) respectively.
Original languageEnglish
Article number114516
Number of pages37
JournalPhysical Review D
Volume94
Issue number11
DOIs
Publication statusPublished - 27 Dec 2016

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