Ultraviolet boundary condition and the Higgs mass

Abstract

Within the emergence framework, in which infrared physics is not fixed by ultraviolet Lagrangian parameters, the hypothesis that the Higgs quartic coupling vanishes at the Planck scale is tested within the full two-loop Standard Model. With lambda(M_P) = 0 imposed as the sole boundary condition and all other inputs fixed by experiment, a Higgs mass of m_h = 121.99 GeV is obtained from complete two-loop renormalisation-group evolution and full two-loop threshold matching. This lies 3.21 GeV (2.6%) below the measured value of 125.20 GeV. The dominant theoretical uncertainty, +/- 1.5 GeV, arises from unknown three-loop effects and is estimated by perturbative power counting. The calculation tests the simplest ultraviolet boundary condition consistent with the emergence framework of Ref. [1]. The agreement is meaningful at the available precision, since the hypothesis could easily have been excluded by a wide margin. A sharper test requires a complete three-loop calculation and an improved top-quark mass measurement.