Coloured Scalar Mediated Nucleon Decays to Invisible Fermion

Abstract

We investigate nucleon decays to light invisible fermion mediated by the coloured scalar ${\bar{S}}_1=(\bar{3},1,-2/3)$ and compare them with the results coming from the mediation of $S_1=(\bar{3},1,1/3)$. In the case of ${\bar{S}}_1=(\bar{3},1,-2/3)$ up-like quarks couple to the invisible fermion, while in the case of $S_1=(\bar{3},1,1/3)$ the down-like quarks couple to the invisible fermion. For the mass of invisible fermion smaller than the mass $m_p-m_K$, proton (neutron) can decay to $K$ and invisible fermion and the masses of ${\bar{S}}_1$ and $S_1$ are in the region $\sim 10^{15}$ GeV. The decays of nucleons to pions and invisible fermion can occur at the tree-level, but in the case of ${\bar{S}}_1$ they come from dimension-9 operator and are therefore suppressed by several orders of magnitude compared to the decays into kaons. For the invisible fermion mass in the range $(937.8\mathrm{MeV},938.8\mathrm{MeV})$, decay of neutron $n\to \chi \gamma$ induced by ${\bar{S}}_1$ is possible at the loop level, while the proton remains stable. The branching ratio of such decay is $\le 10^{-6}$, which does not explain neutron decay anomaly, but is in agreement with the Borexino experiment bound. We comment on low-energy processes with the nucleon-like mass of $\chi$ in the final state as $\Lambda \to \chi \gamma$ and heavy hadron decays to invisibles.

Comments: 10 pages, 12 figures, to be published in Phys. Rev. D