Baryon-number violation by two units and the deuteron lifetime

We calculate the lifetime of the deuteron with dimension-nine quark operators that violate baryon number by two units. We construct an effective field theory for $\mathrm{\mid }\mathrm{\Delta }B\mathrm{\mid }=2$ interactions that give rise to neutron-antineutron ($n$-$\bar{n}$) oscillations and dinucleon decay within a consistent power counting. We calculate the ratio of the deuteron lifetime to the square of the $n$-$\bar{n}$ oscillation time up to next-to-leading order. Our result, which is analytical and has a quantified uncertainty, is smaller by a factor $\simeq 2.5$ than earlier estimates based on nuclear models, which impacts the indirect bound on he $n$-$\bar{n}$ oscillation time and future experiments. We discuss how combined measurements of $n$-$\bar{n}$ oscillations and deuteron decay can help to identify the sources of baryon-number violation.