Two-Loop Electroweak Corrections for the K -> pi nu anti-nu Decays

TL;DR

This paper computes the full two-loop electroweak corrections to rare kaon decay processes, significantly reducing theoretical uncertainties and providing updated precise branching ratio predictions within the Standard Model.

Contribution

It presents the first complete calculation of two-loop electroweak corrections to key top-quark contributions in rare kaon decays, refining theoretical predictions.

Findings

Electroweak uncertainty reduced to below 1%

Updated branching ratios for K_L and K+ decays

Enhanced precision for testing Standard Model predictions

Abstract

The rare K -> pi nu anti-nu 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 -> pi0 nu anti-nu, K+ -> pi+ nu anti-nu, and B -> X_{d,s} nu anti-nu 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 -> pi0 nu anti-nu) = 2.43(39)(6) * 10^-11 and Br(K+ -> pi+ nu anti-nu) = 7.81(75)(29) * 10^-11. The first error summarises the parametric, the second the remaining theoretical uncertainties.