In scalar field theories the Landau pole is an ultraviolet singularity in the
running coupling constant that indicates a mass scale at which the theory
breaks down and new physics must intervene. However, new physics at the pole
will in general affect the running of the low energy coupling constant, which
will in turn affect the location of the pole and the related upper limit
(``triviality'' bound) on the low energy coupling constant. If the new physics
is strongly coupled to the scalar fields these effects can be significant even
though they are power suppressed. We explore the possible range of such effects
by deriving the one loop renormalization group equations for an effective
scalar field theory with a dimension 6 operator representing the low energy
effects of the new physics. As an independent check we also consider a
renormalizable model of the high-scale physics constructed so that its low
energy limit coincides with the effective theory.Comment: 26 pages, 5 figure
