Flavor SU(3) Topological Diagram and Irreducible Representation Amplitudes for Heavy Meson Charmless Hadronic Decays: Mismatch and Equivalence

Abstract

Flavor SU(3) analysis of heavy meson ($B$ and $D$) hadronic charmless decays can be formulated in two different ways. One is to construct the SU(3) irreducible representation amplitude (IRA) by decomposing effective Hamiltonian according to the SU(3) transformation properties. The other is to use the topological diagrams (TDA). These two methods should give equivalent physical results in the SU(3) limit. Using $B\to PP$ decays as an example, we point out that previous analyses in the literature using these two methods do not match consistently in several ways, in particular a few SU(3) independent amplitudes have been overlooked in the TDA approach. Taking these new amplitudes into account, we find a consistent description in both schemes. These new amplitudes can affect direct CP asymmetries in some channels significantly. A consequence is that for any charmless hadronic decay of heavy meson, the direct CP symmetry cannot be identically zero.

arXiv comment12 pages, 2 figures

References in corpus (21)

• Weak Decays Beyond Leading Logarithms
• An effective field theory for collinear and soft gluons: heavy to light decays
• Averages of $b$-hadron, $c$-hadron, and $\tau$-lepton properties as of summer 2016
• QCD factorization for B->PP and B->PV decays
• QCD Factorization in B -> pi K, pi pi Decays and Extraction of Wolfenstein Parameters
• Penguin Enhancement and $B\to K\pi$ decays in perturbative QCD
• Fat penguins and imaginary penguins in perturbative QCD
• Branching Ratio and CP Violation of B to pi pi Decays in Perturbative QCD Approach
• The $\Delta S=1$ Effective Hamiltonian Including Next-to-Leading Order QCD and QED Corrections
• Implications of LHCb measurements and future prospects
• A proof of factorization for B -> D pi
• Branching ratios and direct CP asymmetries in $D\to PP$ decays
• Two-body hadronic charmed meson decays
• First observation of CP violation in the decays of Bs mesons
• Hadronic Penguin B Decays In The Standard And The Two-Higgs-Doublet Models
• Updating B --> PP, VP decays in the framework of flavor symmetry
• CP asymmetry Relations Between ${\bar{B}}^0\to \pi \pi$ and ${\bar{B}}^0\to \pi K$ Rates
• Topological amplitudes in $D$ decays to two pseudoscalars: a global analysis with linear $SU(3{)}_F$ breaking
• Analysis of Charmless Two-body B decays in Factorization Assisted Topological Amplitude Approach
• A global $SU(3)/U(3)$ flavor symmetry analysis for $B\to PP$ with $\eta -{\eta }^{\prime }$ Mixing
• CP Violation in $B_s^0\to K^{-}{\pi }^{+}$, $B^0\to K^{+}{\pi }^{-}$ Decays and Tests for SU(3) Flavor Symmetry Predictions

Cited by in corpus (33)

• Weak Decays of Antitriplet Charmed Baryons from the Perspective of Flavor Symmetry
• ${\Lambda }_b\to p$ transition form factors in perturbative QCD
• Equivalent $SU(3{)}_f$ approaches for two-body anti-triplet charmed baryon decays
• Semileptonic weak decays of anti-triplet charmed baryons in the light-front formalism
• Non-leptonic beauty baryon decays and $CP$-asymmetries based on $SU(3)$-Flavor analysis
• Fully Heavy Tetraquark $bb\bar{c}\bar{c}$: Lifetimes and Weak Decays
• Diagrammatic analysis of hidden- and open-charm tetraquark production in $B$ decays
• Semileptonic decays of ${\Lambda }_c^{+}$ in dynamical approaches
• A self-consistent framework of topological amplitude and its $SU(N)$ decomposition
• Anomalies in Hadronic $B$ Decays
• Weak Decays of Stable Open-bottom Tetraquark by SU(3) Symmetry Analysis
• Weak Decays of Triply Heavy Tetraquarks $b\bar{c}b\bar{q}$
• Weak Decays of Doubly-Heavy Tetraquarks $b\bar{c}q\bar{q}$
• Improved method to determine the ${\Xi }_c-{\Xi }_c^{\prime }$ mixing
• Beauty baryon non-leptonic decays into decuplet baryons and $CP$-asymmetries based on $SU(3)$-Flavor analysis
• From topological amplitude to rescattering dynamics
• Analysis of three-body charmless $B$-meson decays under the factorization-assisted topological-amplitude approach
• Topological amplitudes of charmed baryon decays in the $SU(3{)}_F$ limit
• Generation of $SU(3)$ sum rule for charmed baryon decay
• The Production of Singly Charmed Pentaquark $\bar{c}qqqq$ from Bottom Baryon
• SU(3) analysis of fully-light tetraquarks in heavy meson weak decays
• Generation of isospin sum rules in heavy hadron weak decays
• Recent advances in charm mixing and $CP$ violation at LHCb
• Flavor $SU(3)$ in Cabibbo-favored $D$-meson decays
• Topological $SU(3{)}_f$ approach for two-body ${\Omega }_c$ weak decays
• From topological amplitude to rescattering dynamics in doubly charmed baryon decays
• Implications of recent LHCb data on CPV in b-baryon four body decays
• Anomalies in Hadronic $B$ Decays: an Update
• Topological amplitudes of bottom baryon decays in the $SU(3{)}_F$ limit
• Isospin sum rules for the nonleptonic $B$ decays
• The study of doubly charmed pentaquark $cc\bar{q}qq$ with the SU(3) symmetry
• Isospin-based EWP-tree Relations
• Estimating QCD-factorization amplitudes through $SU(3)$ symmetry in $B\to PP$ decays