SU(3) in D decays: From $30\%$ symmetry breaking to $10^{-4}$ precision

TL;DR

This paper demonstrates that high-order perturbation theory and careful isospin breaking treatment allow for extremely precise SU(3) symmetry predictions in D meson decays, achieving accuracy down to 10^{-4}.

Contribution

It introduces a high-order perturbation expansion approach that significantly improves the precision of SU(3) symmetry predictions in D meson decays, reaching 10^{-4} accuracy.

Findings

Predicted amplitude relations hold at 10^{-3} to 10^{-4} precision.

High-order symmetry breaking terms are crucial for accurate predictions.

Experimental data confirms the high-precision theoretical relations.

Abstract

Flavor SU(3) symmetry, including $30\%$ first order SU(3) breaking, has been shown to describe adequately a vast amount of data for charmed meson decays to two pseudoscalar mesons and to a vector and a pseudoscalar meson. We review a recent dramatic progress achieved by applying a high order perturbation expansion in flavor SU(3) breaking and treating carefully isospin breaking. We identify a class of U-spin related $D^0$ decays to pairs involving charged pseudoscalar or vector mesons, for which high-precision nonlinear amplitude relations are predicted. Symmetry breaking terms affecting these relations are fourth order U-spin breaking, and terms which are first order in isospin breaking and second order in U-spin breaking. The predicted relations are shown to hold experimentally at a precision varying between $10^{-3}$ and $10^{-4}$, in agreement with estimates of high order terms. We also discuss amplitude relations for $D^0$ decays to pairs of neutral pseudoscalar mesons, and relations for rate asymmetries between decays involving $K^0_S$ and $K^0_L$ which hold up to second order U-spin breaking.