A no-go theorem for scalar fields with couplings from Ginzburg-Landau models

Recently Hod proved a no-go theorem that static scalar fields cannot form spherically symmetric boson stars in the asymptotically flat background. On the other side, scalar fields can be coupled to the gradient according to next-to-leading order Ginzburg-Landau models. In the present work, we extend Hod's discussions by considering couplings between static scalar fields and the field gradient. For a non-negative coupling parameter, we show that there is no asymptotically flat spherically symmetric boson stars made of coupled static scalar fields.