  We study the crossing equations in $d=3$ for the four point function of two
$U(1)$ currents and two scalars including the presence of a parity violating
term for the $s$-channel stress tensor exchange. We show the existence of a new
tower of double trace operators in the $t$-channel whose presence is necessary
for the crossing equation to be satisfied and determine the corresponding large
spin parity violating OPE coefficients. Contrary to the parity even situation,
we find that the parity odd $s$-channel light cone stress tensor block do not
have logarithmic singularities. This implies that the parity odd term does not
contribute to anomalous dimensions in the crossed channel at this order in
light cone expansion. We then study the constraints imposed by reflection
positivity and crossing symmetry on such a four point function. We reproduce
the previously known parity odd collider bounds through this analysis. The
contribution of the parity violating term in the collider bound results from a
square root branch cut present in the light cone block as opposed to a
logarithmic cut in the parity even case, together with the application of the
Cauchy-Schwarz inequality.
