  We derive the flow equations for the symmetry unbroken phase of a dilute
3-dimensional Bose gas. We point out that the flow equation for the interaction
contains parts which are non-analytic at the origin of the frequency-momentum
space. We examine the way this non-analyticity affects the fixed point of the
system of the flow equations and shifts the value of the critical exponent for
the correlation length closer to the experimental result in comparison with
previous work where the non-analyticity was neglected. Finally, we emphasize
the purely thermal nature of this non-analytic behaviour comparing our approach
to a previous work where non-analyticity was studied in the context of
renormalization at zero temperature.
