$B$ decays to two pseudoscalars and a generalized $\Delta I=\frac{1}{2}$ rule

Abstract

We perform an isospin analysis of $B$ decays to two pseudoscalars. The analysis extracts appropriate CKM and short distance loop factors to allow for comparison of non-perturbative QCD effects in the reduced matrix elements of the amplitudes. In decays where penguin diagrams compete with tree-level diagrams we find that the reduced matrix elements of the penguin diagrams, which are singlets or doublets under isospin, are significantly enhanced compared with the triplet and fourplet contributions of the weak Hamiltonian. This similarity to the $\Delta I=\frac{1}{2}$ rule in $K\to \pi \pi$ decays suggests that, more generally, processes mediated by Hamiltonians in lower-dimensional isospin representations see enhancement over higher-dimensional ones in QCD.

10 pages, 5 figures

References in corpus (2)

• Measurement of CP violation in the phase space of $B^{\pm }\to K^{+}{K}^{-}{\pi }^{\pm }$ and $B^{\pm }\to {\pi }^{+}{\pi }^{-}{\pi }^{\pm }$ decays
• Measurement of the difference of CP-violating asymmetries in D0 -> K+K- and D0 ->pi+pi- decays at CDF

Cited by in corpus (6)

• The Emergence of the $\Delta U=0$ Rule in Charm Physics
• 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
• Isospin amplitudes in ${\Lambda }_b^0\to J/\psi \Lambda ({\Sigma }^0)$ and ${\Xi }_b^0\to J/\psi {\Xi }^0(\Lambda )$ decays
• The Mathematical Structure of $U$-Spin Amplitude Sum Rules
• Beauty baryon non-leptonic decays into decuplet baryons and $CP$-asymmetries based on $SU(3)$-Flavor analysis