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Abstract: Certain anomalous fermion-gauge boson couplings, such as the flavor diagonal anomalous color magnetic (CMDM) and color electric (CEDM) dipole moments of quarks are not fully gauge invariant under the SM. Restoring the gauge invariance with an elementary Higgs doublet implies that they also contribute to Higgs boson production at the LHC and we study corresponding constraints that can be placed on them. In a similar manner we study the constraints that can be placed on the $\tau$-lepton anomalous magnetic moment, electric dipole moment, and weak dipole moments at the LHC.