Softly broken conformal symmetry and the stability of the electroweak scale

Abstract

We point out a novel possible mechanism by which the electroweak hierarchy problem can be avoided in the (effective) quantum field theory. Assuming the existence of a UV complete underlying fundamental theory and treating the cutoff scale Λ of the effective field theory as a real physical scale we argue that the hierarchy problem would be solved if the coefficient in front of quadratic divergences vanished for some choice of Λ, and if the effective theory mass parameters fixed at Λ by the fundamental theory were hierarchically smaller than Λ itself. While this mechanism most probably cannot work in the Standard Model if the scale Λ is to be close to the Planck scale, we show that it can work in a minimal extension (Conformal Standard Model) proposed recently for a different implementation of soft conformal symmetry breaking.PACS numbers: 12.60. Fr,1480.Ec,14.80Va The problem of stability of the electroweak scale with respect to the Planck scale (the so-called hierarchy problem) has for almost 40 years been one of the main driving forces of theoretical research in high energy physics. Over the years various mechanisms for solving it at the effective quantum field theory level have been proposed and investigated in detail, of which the most notable are technicolor and low energy supersymmetry. With the discovery of a spin-zero particle at the LHC, and after establishing its basic characteristics, it has become clear that a solution which departs little from the simplest mechanism of the electroweak symmetry breaking realized in the Standard Model (SM) may be preferred. In particular, extensions of the SM which predict only elementary scalars and no new higher spin particles other than right-chiral neutrinos seem distinguished at present. It is therefore of interest that there exists an alternative way (which does not require new spin s ≥ 1 2 degrees of freedom) by which the problem of stability of the electroweak scale could be avoided in the low energy effective theory. It is based on a novel implementation of 'near conformal symmetry' in the effective low energy theory.As is well known, the classical conformal symmetry of the SM is spoiled only by the scalar field mass term necessary to induce phenomenologically viable electroweak symmetry breaking. Moreover, as in any generic quantum field theory, conformal symmetry of the SM is broken by quantum effects. Yet, the idea that 'softly broken conformal symmetry' (SBCS) might be relevant for the solution of the hierarchy problem was expressed already long ago [1]. As one possible concrete implementation of this idea a minimal extension of the SM, the Conformal Standard Model (CSM), has been proposed in [2]. Besides the known particles this model only involves the right-chiral neutrinos and one extra (complex) scalar field. Originally it was assumed that its conformal symmetry is broken only by the anomaly, inducing electroweak symmetry breaking via the Coleman-Weinberg mechanism [3]. However, although there do exist perturbatively stable minima of the potential o...

Two-loop RGE of a general renormalizable Yang-Mills theory in a renormalization scheme with an explicit UV cutoff

“…In this paper we provide the necessary technical tools for developing the approach sketched in [2] and perform the systematic one-loop renormalization of a general renormalizable YM theory coupled to scalars and fermions in arbitrary (but non-anomalous) representations using the explicit UV cutoff proposed there. The paper is organized as follows.…”

“…[2]. In section 9 we recall the basic idea of this solution (which owing to the results presented in this paper gain more solid foundations) and use the derived two-loop RG equations and the coefficient of Λ 2 divergence of the effective potential to discuss (non)viability of this solution in the SM.…”

“…In this paper we would like to adopt a more fundamental point of view on renormalization (close in spirit to the one taken in applications of field theory to statistical physics problems), proposed in [2] (see also [3]), which we motivate (in section 9) by its possible connection with the hierarchy problem. This view precludes using unphysical regularizations like DimReg and requires treating the momentum space cutoff Λ as a bona fide…”

Conformal standard model, leptogenesis, and dark matter

“…In this paper a modified version of this model is presented which has explicit mass terms but which is still conformal in the sense that it postulates the absence of any intermediate scales between 1 TeV and the Planck scale M PL -hence the name, conformal standard model (CSM). The model nevertheless achieves a stabilization of the electroweak hierarchy thanks to an alternative proposal for the cancellation of quadratic divergences presented in [25], and it is in this sense that we speak of softly broken conformal symmetry (SBCS). This term is meant to comprise three main assumptions, namely: (i) the avoidance of quadratic divergences, (ii) the smallness (with respect to the Planck scale) of all dimensionful quantities, and (iii) the smallness of all dimensionless couplings up to M PL .…”

“…(ii) There is no low-energy supersymmetry; instead the electroweak hierarchy is stabilized by the alternative mechanism for the cancellation of quadratic divergences proposed in [25].…”