Asymptotically safe Pati-Salam theory

Abstract

We provide an asymptotically safe Pati-Salam embedding of the standard model. Safety is achieved by adding to the theory gauged vectorlike fermions and by employing recently developed large number-offlavor techniques and results. We show that the gauge, scalar quartic and Yukawa couplings achieve an interacting ultraviolet fixed point below the Planck scale. The minimal model is a relevant example of a standard model extension in which unification of all type of couplings occurs because of a dynamical principle, i.e., the presence of an ultraviolet fixed point. This extension differs from the usual grand unified theories scenario in which only gauge couplings unify and become free with the remaining couplings left unsafe. We find renormalization group flow solutions that match the standard model couplings values at low energies allowing for realistic safe extensions of the standard model.

Critical Look at β -Function Singularities at Large N

“…Appearance of such singularities on the real-coupling axis seems to be true for all the d = 4 theories analyzed so far, thereby having a dramatic effect on RG flows. In particular, the appearance of singularities in the coefficients of the 1/N expansion for gauge and Yukawa β-functions have inspired speculations of a possible UV fixed point [23][24][25][26][27][28][29].More generally, the UV fate of gauge theories for which asymptotic freedom is lost has broad theoretical interest, and this is in fact the case of matter-dominated theories. There, a non-trivial zero of the β-function can be envisaged if the large-N resummation produces a contribution to β functions such that lim g→r β 1/N (g) = −∞, where r is the radius of convergence of the 1/N series.…”

Asymptotically safe clockwork mechanism

“…We first briefly review the PS embedding of the SM suggested [9] and then argue that the extra vectorlike fermions can naturally play the role of clockwork gears and in the process we kill two birds with one stone.…”

“…The first non-Abelian safe PS and Trinification embeddings were put forward in [9,10]. However, in the minimal models, only one generation of SM fermions can be modeled, since all the Yukawa couplings are determined by the same UV fixed point value with no resulting hierarchy at low energy.…”

“…This is because concrete realizations of the mechanism require the presence of a large number of new vectorlike fermions that is a natural prediction of safe quantum field theories. As proof of concept, we consider a safe PS structure [9] as natural realization of the clockwork idea. Another benefit of this marriage is the use of the clockwork mechanism to generate Yukawa hierarchies [17].…”

Complete asymptotically safe embedding of the standard model

“…By suitable adjustment of the numbers of colours and flavours, a UV fixed point can be achieved that is arbitrarily weakly coupled. Coupled with the "large flavour" fixed points of [24][25][26][27][28][29] operating for the electroweak gauge couplings, one finds an asymptotically safe extension of the Pati-Salam (PS) theory, that has a UV fixed point with gauge group SU (N C ) × SU (2) L × SU (2) R , and a natural breaking down to the SM gauge group in the IR driven partially by radiative symmetry breaking. The main observation of [2] was that the two kinds of fixed points (Veneziano and large N f ) do not interfere with each other.…”