A model independent method for quantitative estimation of $SU(3)$ flavor symmetry breaking using Dalitz plot

Abstract

The light hadron states are satisfactorily described in the quark model using $SU(3)$ flavor symmetry. If the $SU(3)$ flavor symmetry relating the light hadrons were exact, one would have an exchange symmetry between these hadrons arising out of the exchange of the up, down and strange quarks. This aspect of $SU(3)$ symmetry is used extensively to relate many decay modes of heavy quarks. However, the nature of the effects of $SU(3)$ breaking in such decays is not well understood and hence, a reliable estimate of $SU(3)$ breaking effects is missing. In this work we propose a new method to quantitatively estimate the extent of flavor symmetry breaking and better understand the nature of such breaking using Dalitz plot. We study the three non-commuting $SU(2)$ symmetries (subsumed in $SU(3)$ flavor symmetry): isospin (or $T$-spin), $U$-spin and $V$-spin, using the Dalitz plots of some three-body meson decays. We look at the Dalitz plot distributions of decays in which pairs of the final three particles are related by two distinct $SU(2)$ symmetries. We show that such decay modes have characteristic distributions that enable the measurement of violation of each of the three $SU(2)$ symmetries via Dalitz plot asymmetries in a single decay mode. Experimental estimates of these easily measurable asymmetries would help in better understanding the weak decays of heavy mesons into both two and three light mesons.

13 pages, 3 figures

References in corpus (11)

• Updating B --> PP, VP decays in the framework of flavor symmetry
• Octet-baryon axial-vector charges and SU(3)-breaking effects in the semileptonic hyperon decays
• Flavor symmetry and decays of charmed mesons to pairs of light pseudoscalars
• Charmless B -> PPP Decays: the Fully-Symmetric Final State
• Flavor symmetry analysis of charmless B --> VP decays
• Update analysis of two-body charmed $B$ meson decays
• Determination of gamma from Charmless B --> M1 M2 Decays Using U-Spin
• SU(3) in D decays: From $30\%$ symmetry breaking to $10^{-4}$ precision
• Systematic Error on Weak Phase $\gamma$ from $B\to {\pi }^{+}{\pi }^{-}$ and $B\to K\pi$
• On testing violations of Bose and $CPT$ symmetries via Dalitz plots and Dalitz `prism'
• Flavor SU(3) analysis of charmless B->PP decays