Connection between $\nu n \rightarrow \bar{\nu} \bar{n}$ reactions and $n$-$\bar{n}$ oscillations via additional Higgs triplets

In this work, we investigate the connection and compatibility between $\nu n \rightarrow \bar{\nu} \bar{n}$ reactions and $n$-$\bar{n}$ oscillations based on the $SU(3)_c \times SU(2)_L \times U(1)$ symmetry model with additional Higgs triplets. We explore the possibility that the scattering process $\nu n\rightarrow \bar{\nu}\bar{n}$ produced by low-energy solar neutrinos gives rise to an unavoidable background in the measurements of $n$-$\bar{n}$ oscillations. We focus on two different scenarios, depending on whether the $(B-L)$ symmetry could be broken. We analyze the interplay of the various constraints on the two processes and their observable consequences. In the scenario where both $(B+L)$ and $(B-L)$ could be broken, we point out that if all the constraints, mainly arising from the type-II seesaw mechanism, are satisfied, the parameter space would be severely constrained. In this case, although the masses of the Higgs triplet bosons could be within the reach of a direct detection at the LHC or future high-energy experiments, the predicted $n$-$\bar{n}$ oscillation times would be completely beyond the detectable regions of the present experiments. In both scenarios, the present experiments cannot distinguish a $\nu n \rightarrow \bar{\nu} \bar{n}$ reaction event from a $n$-$\bar{n}$ oscillation event within the accessible energy range. Nevertheless, if any of the two processes is detected, there could be signal associated with new physics beyond the Standard Model.