Two-loop electroweak corrections for theK→πνν¯decays

Abstract

The rare K → πνν decays play a central role in testing the Standard Model and its extensions. Upcoming experiments plan to measure the decay rates with high accuracy. Yet, unknown higher-order electroweak corrections result in a sizeable theory error. We remove this uncertainty by computing the full two-loop electroweak corrections to the top-quark contribution X t to the rare decays K L → π 0 νν, K + → π + νν, and B → X d,s νν in the Standard Model. The remaining theoretical uncertainty related to electroweak effects is now far below 1%. Finally we update the branching ratios to find Br(K L → π 0 νν) = 2.43(39)(6) × 10 −11 and Br(K + → π + νν) = 7.81(75)(29) × 10 −11 . The first error summarises the parametric, the second the remaining theoretical uncertainties.

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“…The leading contribution is contained in the function X t which comprises the top-quark loops. It is known to NLO in QCD and electroweak interactions [36,38,42,44]. The parameter P c describes the short-distance contribution of the charm quark and has been calculated including NNLO QCD [45][46][47] and NLO electroweak corrections [48].…”

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“…Because this decay mode breaks CP symmetry directly and is highly suppressed in the Standard Model (SM) [1], it is sensitive to small effects from new physics.…”

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“…6. A 400 GeV/c primary proton beam extracted from the SPS impinges on a beryllium target to produce a secondary hadron beam at 75 GeV/c EPJ Web of Conferences 00008-p. 6 with a momentum bite of ∼ 1%. Only 6% of the hadrons are charged kaons (unseparated beam).…”

“…3). The SM prediction [6] for the K + → π + νν channel is BR = (7.81 +0.80 −0.71 ± 0.29) × 10 −11 . The error comes mainly from the uncertainty in the CKM matrix elements, while the irreducible theoretical uncertainty amounts to less than 2%.…”