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 $|\mathrm{\Delta }B|=2$ interactions that give rise to neutron-antineutron ($n\text{−}\overline{n}$) oscillations and dinucleon decay within a consistent power counting. We calculate the ratio of the deuteron lifetime to the square of the $n\text{−}\overline{n}$ 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 the $n\text{−}\overline{n}$ oscillation time and future experiments. We discuss how combined measurements of $n\text{−}\overline{n}$ oscillations and deuteron decay can help to identify the sources of baryon-number violation.

Figure 1

The two classes of diagrams for deuteron decay. The crossed circle denotes the deuteron. Single lines with arrows to the right (left) denote (anti)nucleon propagators. In the left diagram, the blob depicts a one- or two-nucleon process that converts two nucleons into a nucleon and an antinucleon, and the circle their annihilation into a mesonic final state (dashed lines). In the right diagram, the blob depicts the propagation of two nucleons, and the square their direct annihilation into the same final states.

Figure 2

Diagrams that contribute to $\mathrm{Im}(i\mathrm{\Sigma })$ up to NLO. Circles denote $g_A$ or $H_0$ vertices, the circled circle denotes $C_2$ or $D_2$, and squares denote $|\mathrm{\Delta }B|=2$ vertices. The dashed line represents a pion. Only one ordering per diagram is shown.

Figure 3

Selected contributions to $\mathrm{Im}(i\mathrm{\Sigma })$ beyond NLO. The square-in-square denotes $\mathrm{Im}{C}_0$. Other notation as in Fig. 2.