Testing Anomalous Higgs Couplings in Triple Photon Production at the Tevatron Collider

We derive bounds on Higgs and gauge--boson anomalous interactions using the CDF data for the process $p \bar{p} \to \gamma\gamma\gamma + X$. We use a linearly realized $SU_L(2) \times U_Y(1)$ invariant effective Lagrangian to describe the bosonic sector of the Standard Model, keeping the fermionic couplings unchanged. All dimension--six operators that lead to anomalous Higgs interactions involving $\gamma$ and $Z$ are considered. We also show the sensitivity that can be achieved for these couplings at Fermilab Tevatron upgrades.