Renormalization group equation, the naturalness problem, and the understanding of the Higgs mass term

The naturalness problem may be studied on the complex two-dimensional plane with the technique of dimensional regularization. The renormalization group equation of the Higgs mass on the plane suggests the Higgs mass approaches zero at the ultraviolet scale; the scale can be Planck scale when the top quark pole mass M-t = 168 GeV. The real issue of the naturalness problem in the sense of the Wilsonian renormalization group method is not about quadratic divergences but the rescaling effect. The Higgs mass can be considered to be one composed mass. All terms in the Lagrangian in this scenario are marginal terms and no relevant terms are left; thus, no rescaling effect exists to cause the naturalness problem. The renormalization group equation of the vacuum expectation value in the Landau gauge up to two-loop order is studied. Scale-dependent behavior of the composed Higgs mass shows that we can have one tiny Higgs mass at the high energy scale, even around the Planck scale, when M-t <= 170.7 GeV.