  We investigate relevant properties of composite operators emerging in
nonsupersymmetric, four-dimensional gauge-Yukawa theories with interacting
conformal fixed points within a precise framework. The theories investigated in
this work are structurally similar to the standard model of particle
interactions, but differ by developing perturbative interacting fixed points.
We investigate the physical properties of the singlet and the adjoint composite
operators quadratic in the Higgs field, and discover that the singlet anomalous
dimension is substantially larger than the adjoint one. The numerical bootstrap
results are then compared to precise four dimensional conformal field
theoretical results. To accomplish this, it was necessary to calculate
explicitly the crossing symmetry relations for the global symmetry group
SU($N$)$\times$SU($N$).
