An Exactly Solvable Model for Dimension Six Higgs Operators and $h \to \gamma \gamma$

An exactly solvable large $N$ model is constructed which reduces at low energies to the Standard Model plus the dimension six Higgs-gauge operators $g_1^2 H^\dagger H B_{\mu \nu} B^{\mu \nu}$, $g_2^2 H^\dagger H W^a_{\mu \nu} W^{a\mu \nu}$, $g_1 g_2 H^\dagger \tau^a H W^a_{\mu \nu} B^{\mu \nu}$, and $\epsilon^{abc} W^a_{\mu}{}^\nu W^b_{\nu}{}^\rho W^c_{\rho}{}^\mu$. All other dimension six operators are suppressed by powers of $1/N$. The Higgs-gauge operators lead to deviations from the Standard Model $h \to \gamma\gamma$ and $h \to \gamma Z$ rates. A simple variant of the model can be used to also generate the Higgs-gluon operator $g_3^2 H^\dagger H G^A_{\mu \nu} G^{A\mu \nu}$ which contributes to the Higgs production rate via gluon fusion.