Isospin sum rules for the nonleptonic $B$ decays

TL;DR

This paper develops isospin sum rules for non-leptonic B meson decays, enabling tests of isospin symmetry and exploration of exotic hadrons, revealing significant isospin breaking in vector meson modes.

Contribution

It derives new master formulas for isospin sum rules in B decays, especially involving multiple decay channels, and suggests potential observation of charm tetraquark resonances.

Findings

Ten percent isospin breaking in vector meson modes.

New isospin sum rules involving three or more decay channels.

Potential detection of charm tetraquark resonances in specific B decay modes.

Abstract

Isospin symmetry, as the most precise flavor symmetry, can be used to extract information about hadronic dynamics. The effective Hamiltonian for bottom quark weak decay is zero under the isospin lowering operators $I_-^n$, which allows us to generate isospin sum rules through several master formulas. In this work, we derive the master formulas of isospin sum rules for the two- and three-body non-leptonic decays of $B$ mesons. Numerous new isospin sum rules, especially those involving three or more decay channels, are proposed. The isospin sum rules can be used to test isospin symmetry and provide hints the isospin partners of exotic hadrons in $B$ decays. It is found ten percent isospin breaking only in decay modes involving two vector mesons, indicating the complex dynamics of vector mesons. Besides, the isospin analysis suggests the charm tetraquark resonances might be observed in the $ B^- \to J/\Psi \pi^-\overline K^0$, $\overline B^0 \to J/\Psi \overline K^0\phi$, and $\overline B^0\to D^0\overline D^0\overline K^0$ modes.