Renormalization Group Evolution Of Couplings Research Articles

The excitation of the global symmetry-breaking vacuum in composite Higgs models

We consider scenarios of Higgs compositeness where the Higgs doublet arises as a pseudo-Nambu Goldstone boson. Our focus is the physical scalar ("radial") excitation associated with the global symmetry breaking vacuum, which we call the "global Higgs". For the minimal case of a $SO(5)/SO(4)$ coset, the couplings of the global Higgs to Standard Model (SM) particles are fully determined by group theoretical factors and two decay constants. The global Higgs also couples to the composite resonances of the theory, inducing an interaction with the SM gauge bosons at one-loop. We thoroughly analyze representative fermionic sectors, considering a global Higgs both in the $\bf 5$ and $\bf 14$ representations of $SO(5)$ and taking into account the renormalization group evolution of couplings in the composite sector. We derive the one-loop effective couplings and all decays of the global Higgs, showing that its decay width over mass can range from $ O (10^{-3})$ to $ O(1)$. Because of the multiplicity of the resonances, the coupling of the global Higgs to gluons is sizeable, potentially opening a new window into composite models at the LHC.

Renormalization group running of Newton’s constantG: The static isotropic case

Corrections are computed to the classical static isotropic solution of general relativity, arising from nonperturbative quantum gravity effects. A slow rise of the effective gravitational coupling with distance is shown to involve a genuinely nonperturbative scale, closely connected with the gravitational vacuum condensate, and thereby related to the observed effective cosmological constant. We argue that in contrast to phenomenological approaches, the underlying functional integral formulation of the theory severely constrains possible scenarios for the renormalization group evolution of couplings. The general analysis is extended here to a set of covariant nonlocal effective field equations, intended to incorporate the full scale dependence of $G$, and examined in the case of the static isotropic metric. We find that the existence of vacuum solutions to the effective field equations in general severely restricts the possible values of the scaling exponent $\ensuremath{\nu}$.