Simplified models with baryon number violation but no proton decay

We enumerate the simplest models that have baryon number violation at the classical level but do not give rise to proton decay. These models have scalar fields in two representations of $SU(3)\times SU(2)\times U(1)$ and violate baryon number by two units. Some of the models give rise to $n\overline{n}$ (neutron-antineutron) oscillations, while some also violate lepton number by two units. We discuss the range of scalar masses for which $n\overline{n}$ oscillations are measurable in the next generation of experiments. We give a brief overview of the phenomenology of these models and then focus on one of them for a more quantitative discussion of $n\overline{n}$ oscillations, the generation of the cosmological baryon number, the electric dipole moment of the neutron, and $K^0\mathrm{\text{−}}{\overline{K}}^0$ mixing.

Figure 1

$\Delta B=1$ and $\Delta L=1$ scalar exchange.

Figure 2

Feynman diagram that contributes to tree level $p\to K^{+}{e}^{+}{e}^{-}\overline{\nu }$ from (3, 1, $-4/3$) scalar exchange.

Figure 3

Scalar interactions which may generate baryon number violation.

Figure 4

Interaction which leads to proton decay, $p\to {\pi }^{+}{\pi }^{+}{e}^{-}\nu \nu$, for $X_1=(\overline{3},2,-1/6)$.

Figure 5

Interaction which leads to neutron-antineutron oscillations.

Figure 6

Diagrams contributing to the electric dipole moment of the down quark.

Figure 7

Diagrams corresponding to the decay of $X_2$. The diagrams on top contribute to the $\Delta B=2$ decays, while the diagrams on bottom contribute to $\Delta B=0$.