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

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