  We study the operator product expansion (OPE) of two identical scalar primary
operators in the lightcone limit in a conformal field theory where a scalar is
the operator with lowest twist. We see that in CFTs where both the stress
tensor and a scalar are the lowest twist operators, the stress tensor
contributes at the leading order in the lightcone OPE and the scalar
contributes at the subleading order. We also see that there does not exist a
scalar analogue of the average null energy condition (ANEC) for a CFT where a
scalar is the lowest twist operator.
