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

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 $K_S^0$ and $K_L^0$ which hold up to second order U-spin breaking.

arXiv comment24 pages, to be published in Physical Review D

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• On $SU(3{)}_F$ Breaking through Final State Interactions and CP Asymmetries in $D\to PP$ Decays
• Measurement of the difference of time-integrated CP asymmetries in $D^0\to K^{-}{K}^{+}$ and $D^0\to {\pi }^{-}{\pi }^{+}$ decays
• Sum Rules of Charm CP Asymmetries beyond the SU(3)${}_F$ Limit
• Charmed baryon decays in $SU(3{)}_F$ symmetry
• Testing SU(3) Flavor Symmetry in Semileptonic and Two-body Nonleptonic Decays of Hyperons
• Non-leptonic beauty baryon decays and $CP$-asymmetries based on $SU(3)$-Flavor analysis
• A self-consistent framework of topological amplitude and its $SU(N)$ decomposition
• Non-leptonic decays of Charmed mesons into two Pseudoscalars
• Beauty baryon non-leptonic decays into decuplet baryons and $CP$-asymmetries based on $SU(3)$-Flavor analysis
• CHARM-2015 Theory Summary
• A model independent method for quantitative estimation of $SU(3)$ flavor symmetry breaking using Dalitz plot
• Pursuit of new physics within the ${\Lambda }_c\to \Delta K$ decays
• $U$-spin sum rules for two-body decays of bottom baryons