Numerical analysis of the Higgs mass triviality bound

Previous large N calculations are combined with numerical work at N=4 to show that the minimal standard model will describe physics to an accuracy of a few percent up to energies of the order two to four times the Higgs mass, M_H, only if M_H<=710+/-60 GeV. This bound is the result of a systematic search in the space of dimension-six operators and is expected to hold in the continuum. Given that studying the scalar sector in isolation is already an approximation, we believe that our result is sufficiently accurate and before further refinements are attempted their relevance to particle physics should be carefully considered.