The RG-improved Twin Higgs effective potential at NNLL

Abstract

We present the Renormalization Group improvement of the Twin Higgs effective potential at cubic order in logarithmic accuracy. We first introduce a modelindependent 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 ∼ 120 GeV with an ultraviolet cut-off m * ∼ 10-20 TeV. Irrespective of any possible ultraviolet completion of the lowenergy Lagrangian, the infrared degrees of freedom alone are therefore enough to account for the observed value of the Higgs mass through running effects.

Neutral naturalness from the brother-Higgs model

“…Moreover, at NLL one also has to consider the effect of higher-dimensional operators (HDO) associated to the NGB nature of the Higgs, which modify the running of the brother top Yukawa. Notably, the effect of RG evolution, compared to the UV threshold contributions generated at m à , is logarithmically enhanced and, as already noticed in the literature [13,14,20,24], almost saturates the observed value of the Higgs quartic (or equivalently the Higgs mass, once the correct EW vacuum has been achieved). Moreover, while the IR contribution is calculable solely in terms of low-energy degrees of freedom and associated observables; thus, being rather model independent (up to details discussed in Appendix C), the UV contributions depend on the spectrum of composite states.…”

“…Besides, as it was shown in Refs. [20,24] (and as it happens in the SM) the LL potential leads to an overestimate of the physical Higgs mass compared to the LL-resummed one. A better estimate (which, at least in the SM, is an underestimate of the LL-resummed result) is obtained after the RG-improvement of the Higgs effective potential at NLL.…”

“…Details on this calculation are given in Appendix C and extensive discussions can be found in Refs. [20,24]. Here we only quote the result, where we have retained only the terms relevant for the physical Higgs mass at NLO.…”

“…All other HDO that can be written with low-energy degrees of freedom have coefficients that either vanish at the scale m à , or cannot be predicted solely in terms of lowenergy parameters. None of these operators contribute up to NLO [20,24].…”

SUSY meets her twin

“…When all the SUSY states are heavy enough one can use effective potential techniques matching to the non SUSY Twin Higgs potential in (2.1). For this potential the higher loop contributions have been computed at NNLL in [57]. We hope that our study elucidated the basic building blocks of Twin SUSY constructions and their connection to the original Twin Higgs proposal.…”