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 2 to 4 times the Higgs mass, $M_H$, only if $M_H \le 710\pm60 ~ GeV$. This bound is the result of a systematic search in the space of dimension six operators and is expected to hold in the {\it continuum}. Given that studying the scalar sector in isolation is already an approximation, we believe that our result is sufficiently accurate and that further refinements would be of progressively diminishing interest to particle physics. Note: The full ps file of this preprint is also available via anonymous ftp to ftp.scri.fsu.edu. To get the ps file, ftp to this address and use for username "anonymous" and for password your name. The file is in the directory pub/vranas (to go to that directory type: cd pub/vranas) and is called num_hig.ps (to get it type: get num_hig.ps)