SU(3) Sum Rules for Charm Decay

TL;DR

This paper derives flavor SU(3) sum rules for charm meson decays, including decay amplitudes and rates, accounting for symmetry breaking, and uses these to predict CP asymmetry differences in specific decay channels.

Contribution

It introduces second-order SU(3) sum rules for D meson decay amplitudes and rates, incorporating symmetry breaking effects and applying them to CP asymmetry predictions.

Findings

Derived decay amplitude sum rules valid to second order in SU(3) breaking.

Predicted ratios and differences of direct CP asymmetries in D decays.

Provided tests for SU(3) breaking sources via isospin and U-spin sum rules.

Abstract

We present flavor SU(3) sum rules for $D \to PP$ and $D \to PV$ decay amplitudes, that are valid to second order in symmetry breaking by the strange quark mass spurion. Decay rate sum rules are also computed to this order. Particular attention is given to sum rules arising from the isospin and U-spin subgroups, the former providing sensitive tests for alternative sources of SU(3) breaking. We apply the latter together with the postulated $\Delta U = 0$ rule for the large penguin picture to predict the ratio and difference of the direct CP asymmetries for $D \to KK^*$ and $D \to \pi \rho$.