Naturalness of scalar fields and the standard model

We discuss how naturalness predicts the scale of new physics. Two conditions on the scale are considered. The first is the more conservative condition due to Veltman [Acta Phys. Pol. B 12, 437 (1981)]. It requires that radiative corrections to the electroweak mass scale be reasonably small. The second is the condition due to Barbieri and Giudice [Nucl. Phys. B306, 63 (1988)], which is more popular lately. It requires that physical mass scale not be oversensitive to the values of the input parameters. We show here that the above two conditions behave differently if higher-order corrections are taken into account. Veltman's condition is robust (insensitive to higher-order corrections), while the Barbieri-Giudice condition changes qualitatively. We conclude that higher-order perturbative corrections take care of the fine-tuning problem, and, in this respect, scalar field is a natural system. We apply the Barbieri-Giudice condition with higher-order corrections taken into account to the standard model and obtain new restrictions on the Higgs boson mass.