Another calculation of the Higgs mass and the top mass from the principles of H. B. Nielsen: $m_H\cong 163$ GeV for $M_t\cong 190$ GeV

Abstract

We calculate the Higgs mass and the top mass starting from the principle that there are two, essentially degenerate minima in the Higgs effective potential; the second is at about the Planck energy scale M P = 1.2 × 1019 GeV. Thus the parameter of the quartic self-coupling λ h vanishes, as does β λH at M P. The new element is the addition of a quantum interaction term which couples the square of the Higgs field to the square of a pseudoscalar field, in the domain of the energy scale between about 1014 GeV and M P. We modify β λH at one loop. The pseudoscalar field which is introduced may be the field which is responsible for a spontaneous breakdown of discrete symmetry — for CP noninvariance at an energy scale of (1015–1016) GeV. The result is then a closer value for m H ≅ 163 GeV for the top pole-mass M t ≅ 190 GeV; both values are now close to the electroweak scale parameter \(\langle {\phi _H}\rangle /\sqrt 2 = 175{\text{ GeV}}\). In terms of dimensionless running coupling parameters, which determine the masses near to the electroweak scale, we get \(\sqrt {{\lambda _H}} \cong 0.06\) and \(gt/\sqrt 2 \cong 0.72\), values that are close to each other and close to unity.