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

Abstract

An exactly solvable large $N$ model is constructed which reduces at low energies to the Standard Model plus the dimension six Higgs-gauge operators $g_1^2{H}^{†}H{B}_{\mu \nu }{B}^{\mu \nu }$, $g_2^2{H}^{†}H{W}_{\mu \nu }^a{W}^{a\mu \nu }$, $g_1{g}_2{H}^{†}{\tau }^{a}H{W}_{\mu \nu }^a{B}^{\mu \nu }$, and ${ϵ}^{abc}{W}_{\mu }^a{}^{\nu }{W}_{\nu }^b{}^{\rho }{W}_{\rho }^c{}^{\mu }$. 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 $g_3^2{H}^{†}H{G}_{\mu \nu }^A{G}^{A\mu \nu }$ which contributes to the Higgs production rate via gluon fusion.