Generation of isospin sum rules in heavy hadron weak decays

Abstract: Isospin symmetry is the most precise flavor symmetry. In this work, we propose an approach to generate isospin sum rules for heavy hadron decays without the Wigner-Eckhart invariants. The effective Hamiltonian of heavy quark weak decay is fully invariant under a series of isospin lowering operators $I_-^n$ and then the isospin sum rules can be generated through several master formulas. It provides a systematic way to study the isospin symmetry of $c$- and $b$-hadron weak decays. The theoretical framework of this approach is presented in detail with the nonleptonic decays of $D$ and $B$ mesons as examples. In addition, the $V$-/$U$-spin sum rules are derived in a similar algorithm by replacing $I_-^n$ with $V_-^n$/$U_-^n$.