The RG-improved Twin Higgs effective potential at NNLL

We present the Renormalization Group improvement of the Twin Higgs effective potential at cubic order in logarithmic accuracy. We first introduce a model-independent low-energy effective Lagrangian that captures both the pseudo-Nambu-Goldstone boson nature of the Higgs field and the twin light degrees of freedom charged under a copy of the Standard Model. We then apply the background field method to systematically re-sum all the one loop diagrams contributing to the potential. We show how this technique can be efficient to implicitly renormalize the higher-dimensional operators in the twin sector without classifying all of them. A prediction for the Higgs mass in the Twin Higgs model is derived and found to be of the order of $M_H \sim 120 ~\text{GeV}$ with an ultraviolet cut-off $m_*\sim 10-20 ~\text{TeV}$. Irrespective of any possible ultraviolet completion of the low-energy Lagrangian, the infrared degrees of freedom alone are therefore enough to account for the observed value of the Higgs mass through running effects.