  The asymptotic behaviour of the survival or reunion probability of vicious
walks with short-range interactions is generally well studied. In many
realistic processes, however, walks interact with a long ranged potential that
decays in $d$ dimensions with distance $r$ as $r^{-d-\sigma}$. We employ
methods of renormalized field theory to study the effect of such long range
interactions. We calculate, for the first time, the exponents describing the
decay of the survival probability for all values of parameters $\sigma$ and $d$
to first order in the double expansion in $\epsilon=2-d$ and
$\delta=2-d-\sigma$. We show that there are several regions in the $\sigma-d$
plane corresponding to different scalings for survival and reunion
probabilities. Furthermore, we calculate the leading logarithmic corrections
for the first time.
