Chiral matching of dimension-7 baryon-number-violating operators and application to $ΔI=3/2$ nucleon decays

Abstract: We study chiral matching of dimension-7 (dim-7) baryon-number-violating operators in low-energy effective field theory. We show that all dim-7 operators can be classified into two distinct Lorentz structures and their chirality-flipped counterparts, and we derive their leading-order hadronic realizations in chiral perturbation theory. As an application, we systematically investigate $ΔI=3/2$ nucleon decays, including $n\to \ell<sup>-π<sup>+$, $p\to \ell^- π<sup>+π<sup>+$, and $$n\to \ell^- π⁺ (π^0, η)$$, with $\ell=e,~μ$. Using existing experimental bounds on $n\to \ell<sup>-π<sup>+$, we set stringent constraints on the relevant Wilson coefficients and derive improved lower limits on the partial lifetimes of the six three-body modes from their correlations with the two-body modes. We further present a concrete ultraviolet model that generates the dim-7 operators and the associated $ΔI=3/2$ nucleon decays at leading order. Our results pave the way for exploring dim-7 contributions to nucleon decays and motivate future searches for these exotic modes.