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

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

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