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 \((937.8 \, {\rm MeV},\, 938.8 \, {\rm MeV})\), 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.