Vacuum stability and conditions for Q-ball formation in the Type II Seesaw model

We investigate vacuum stability and the conditions for Q-ball formation in the Type II Seesaw model by analyzing the effective potential for scalar fields, considering renormalization effects. When the quartic coupling for the triplet Higgs becomes zero at a high energy scale, it allows for the possibility of Q-ball formation along the flat direction of the triplet Higgs. Once formed, Q-balls decay into leptons through neutrino Yukawa couplings with the triplet Higgs. While we identify parameter regions where the self-coupling of the triplet Higgs can vanish at high energy scales, we observe that it becomes negative above this scale, leading to an unbounded potential. To stabilize the potential, we introduce higher-dimensional operators. Our analysis reveals the existence of parameter regions where the aforementioned scenario is viable, taking account of various phenomenological constraints.