Abstract
In the literature, the asymptotic freedom property of the (-phi(4)) theory is always concluded from realline calculations while the theory is known to be a non-real-line one. In this article, we test the existence of the asymptotic freedom in the (-phi(4))(3+1) theory using the mean field approach. In this approach and contrary to the original Hamiltonian, the obtained effective Hamiltonian is rather a real-line one. Accordingly, this work resembles the first reasonable analysis for the existence of the asymptotic freedom property in the PT-symmetric (-phi(4)) theory. In this respect, we calculated three different amplitudes of different positive dimensions (in mass units) and find that all of them go to very small values at high energy scales (small coupling) in agreement with the spirit of the asymptotic freedom property of the theory. To test the validity of our calculations, we obtained the asymptotic behavior of the vacuum condensate in terms of the coupling, analytically, and found that the controlling factor Lambda has the value (4 pi)(2)/6 = 26.319 compared to the result Lambda = 26.3209 from the literature, which was obtained via numerical predictions. We assert that the nonblowup of the massive quantities at high energy scales predicted in this work strongly suggests the possibility of the solution of the famous hierarchy puzzle in a standard model with the PT-symmetric Higgs mechanism.