Phase structure of completely asymptotically free SU( Nc ) models with quarks and scalar quarks

Abstract

We determine the phase diagram of completely asymptotically free SUðN c Þ gauge theories featuring N s complex scalars and N f Dirac quarks transforming according to the fundamental representation of the gauge group. The analysis is performed at the maximum known order in perturbation theory. We unveil a very rich dynamics and associated phase structure. Intriguingly, we discover that the completely asymptotically free conditions guarantee that the infrared dynamics displays long-distance conformality, and in a regime when perturbation theory is applicable. We conclude our analysis by determining the quantum corrected potential of the model and summarizing the possible patterns of radiative symmetry breaking. These models are of potential phenomenological interest as either elementary or composite ultraviolet finite extensions of the standard model.

Charting the phase diagram of QCD3

“…Note that the above result, i.e. maximal Higgsing for f < n and degeneracy of nonvanishing eigenvalues for f > n, depends crucially on assuming a quartic scalar potential with both double and single trace contributions (similar observations were done, in a different context, in [3,57] and also appear in [50]). One should also assume λ to be positive to get the aforementioned pattern.…”

Vacuum stability and perturbativity of SU(3) scalars

“…6 Similar terminology is used in the context of walking technicolor to characterise the evolution of the gauge coupling. 7 Linear stability of (4.4) atλ− implies that b λ (λ+ −λ−) ≡ 2δ > 0. where t 1 and t 2 are constants of integration that were inserted by applying the scaling symmetry (4.2) and shift symmetry. They can be determined from initial conditions, that is, from g(µ 0 ) 2 = g 2 0 and λ(µ 0 ) = λ 0 , where g 0 and λ 0 are the values of the couplings measured at the scale µ 0 .…”

“…Realλ ± are fixed points of the system and we order them asλ + λ − so thatλ + represents an UV repellor andλ − is a UV attractor. 7 Vacuum stability additionally demandsλ − 0 from a physical attractor. Note, however, that the rootsλ ± could also be complex.…”

“…This mechanism could provide a dynamical and therefore natural explanation for the origin of the electroweak scale, akin to the framework of technicolor [4,5]. Coloured scalar multiplets may also be utilised in builiding UVcomplete models where complete asymptotic freedom [6,7], i.e. a Gaussian UV fixed point of all couplings, arises.…”

SU(2) with fundamental fermions and scalars

“…For sake of simplicity we restrict ourselves to the case of N S = 1, a more complete analysis can be found in [18].…”