We investigate the a theorem for nonsupersymmetric gauge-Yukawa theories beyond the leading order in perturbation theory. The exploration is first performed in a modelindependent manner and then applied to a specific relevant example. Here, a rich fixed point structure appears including the presence of a merging phenomenon between nontrivial fixed points for which the a theorem has not been tested so far.
At high energy the standard model possesses conformal symmetry at the classical level. This is reflected at the quantum level by relations between the different β functions of the model. These relations are known as the Weyl consistency conditions. We show that it is possible to satisfy them order by order in perturbation theory, provided that a suitable coupling constant counting scheme is used. As a direct phenomenological application, we study the stability of the standard model vacuum at high energies and compare with previous computations violating the Weyl consistency conditions.
Near conformal dynamics is employed in different extensions of the standard model of particle interactions as well as in cosmology. Many of its interesting properties are either conjectured or determined using model computations. We introduce a relevant four-dimensional gauge theory template allowing us to investigate such dynamics perturbatively. The gauge theory we consider is quantum chromodynamics with the addition of a mesonlike scalar degree of freedom as well as an adjoint Weyl fermion. At the two-loop level, and in the Veneziano limit, we firmly establish the existence of several fixed points of which one is all directions stable in the infrared. An interesting feature of the model is that this fixed point is lost within the perturbative regime by merging with another fixed point when varying the number of quark flavors. We show the emergence of Miransky scaling and determine its properties. The theory exhibits walking behavior in the region close to the lower bound of the conformal window, and by providing a suitable definition we determine the walking region. Finally, we also determine the anomalous dimension of the fermion mass, which is a highly relevant quantity for near conformal dynamics.
We unveil the dynamics of four dimensional chiral gauge-Yukawa theories featuring several scalar degrees of freedom transforming according to distinct representations of the underlying gauge group. We consider generalized Georgi-Glashow and Bars-Yankielowicz theories. We determine, to the maximum known order in perturbation theory, the phase diagram of these theories and further disentangle their ultraviolet asymptotic nature according to whether they are asymptotically free or safe. We therefore extend the number of theories that are known to be fundamental in the Wilsonian sense to the case of chiral gauge theories with scalars.
We present and discuss the "Tetrad Model", a large colour/flavour embedding of the Standard model which has an interacting ultraviolet fixed point. It is shown that its extended-Pati-Salam symmetry is broken radiatively via the Coleman-Weinberg mechanism, while the remaining electroweak symmetry is broken when mass-squared terms run negative. In the IR the theory yields just the Standard Model, augmented by the fact that the Higgs fields carry the same generation indices as the matter fields. It is also shown that the Higgs mass-squareds develop a hierarchical structure in the IR, from a UV theory that is asymptotically flavour symmetric, opening up an interesting direction for explaining the emergence of the observed flavour structure.
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