Gauge-symmetry hierarchies

Abstract

It is shown that one cannot artifically establish a gauge hierarchy of any desired magnitude by arbitrarily adjusting the scalar-field parameters in the Lagrangian and using the tree approximation to the potential; radiative corrections will set an upper bound on such a hierarchy. If the gauge coupling constant is approximately equal to the electromagnetic coupling constant, the upper bound on the ratio of vector-meson masses is of the order of a-"', independent of the sclar-field masses and their self-couplings. In particular, the usual assumption that large scalar-field mass ratios in the Lagrangian can induce large vector-meson mass ratios is false. A thus far unsuccessful search for natural gauge hierarchies is briefly discussed. It is shown that if such a hierarchy occurred, it would have an upper bound of the order of a-"'.

Status of Precision Tests of the Standard Model

“…The weak scale m is 10 17 times smaller than M P l .Even if the weak scale is set near 250 GeV at the classical level, quantum uctuations would naturally shift it up to where new physics starts to apply, in particular up to M P l if there was no new physics up to gravity. This so-called hierarchy problem [45] is related to the presence of fundamental scalar elds in the theory with quadratic mass divergences and no protective extra symmetry at m = 0 . F or fermions, rst, the divergences are logaritmic and, second, at m = 0 an additional symmetry, i.e.…”

Light non-degenerate composite partners at the LHC

“…Since the sole interaction ofŨ with the SM quark is through a Higgs boson, single production of the up and charm partner is suppressed by the square of the SM-like up and charm Yukawa coupling, respectively, and thus negligible. 4 This contrasts with the top partner case for which the large top mass makes single production one of the dominant mechanism, especially at large top partner mass [54,55]. However, as first pointed out in ref.…”

“…Notice that in the y L = 0 limit the Lagrangian for the composite states and the elementary right-handed up quarks is exactly invariant under the custodial SO(3) c subgroup of SO (4). In fact, the y L mixing in eq.…”

“…[46,47] for a detailed presentation in CHM.) In CCWZ the strong sector resonances are classified in terms of irreducible representations of the unbroken global SO (4). In particular the lightest composite fermions contained in the 5 of SO(5) decompose as a fourplet, Q, and a singlet,Ũ , under SO(4).…”

“…Although the SM dynamics cannot explain several experimental evidences such as neutrino masses, the baryon asymmetry of the universe and the origin of dark matter, one cannot infer with any certainty an energy scale at which the SM would have to be extended, besides the well-known exceptions of the Planck scale related to gravity and the fantastically high scale of the Landau pole associated with the U(1) hyper-charge interaction. Nevertheless, the fact that the Higgs mass is subject to additive renormalization implies that the EW scale is technically unnatural [3][4][5]. Any solution of this UV sensitivity (or fine-tuning) problem of the Higgs mass requires new dynamics beyond the SM (BSM) characterized by an energy scale close to the EW one.…”