Asymptotic safety and gauged baryon number

We consider a model with gauged baryon number that may be rendered asymptotically safe when gravitational effects above the Planck scale are taken into account. We study the ultraviolet fixed points in this theory and determine the restrictions on the parameter space of the model at the TeV scale following from the requirement that the asymptotic fixed points are reached. Assuming that the new gauge symmetry is broken at the TeV scale, we comment on the phenomenological implications of these restrictions.

Figure 1

UV critical surfaces in the $g_B\tilde{g}$ plane. The interiors of the ellipse and the line are driven to Gaussian fixed points $(g_B,\tilde{g})=(0,0)$, whereas the ellipse’s boundary and the line’s right endpoint are nontrivial fixed points. Couplings outside the ellipse and outside the line interval are driven to infinite values.

Figure 2

Left: UV critical surfaces (dashed line) mapped back to $\mu =M_{\mathrm{Pl}}$ (dotted line) and to ${\mu }_0=1\mathrm{TeV}$ (solid line). The Gaussian $g_1$ fixed point is described by the ellipses and the interacting $g_1$ fixed point by the line. The requirement that either the boundary of the ellipse or the line is reached leads to a unique relation between $g_B$ and $\tilde{g}$, thereby reducing the degrees of freedom in parameter space of the model. Right: infrared values in detail.

Figure 3

Renormalization group flow of the Abelian gauge couplings and the quartic couplings. Top: Gaussian $g_1$ fixed point. Bottom: interacting $g_1$ fixed point. In the right plots, the shaded areas highlight the value of $\sqrt{\mathfrak{s}}\equiv \sqrt{\lambda {\lambda }_{\varphi }-{\lambda }_m^2}$, where $\mathfrak{s}$, $\lambda$, and ${\lambda }_{\varphi }$ remain positive throughout the entire energy range considered here. The quartic couplings attain their numerically expected fixed point values within our numerical resolution, strongly suggesting stability of the Higgs sector up to arbitrarily high energies. The small deviations of the couplings away from their fixed point values visible at the right sides of the plots is an artifact caused by the finite resolution of our numerical approximation and the fact that the fixed points are unstable. By increasing the resolution of the initial conditions at 1 TeV, these deviations can be pushed out to arbitrarily high energies. At infinite initial resolution, the couplings would hit their fixed point values exactly.

Figure 4

Comparison to the standard model. See the text for discussion.

Figure 5

The effects of varying input parameter values. The first row corresponds to the Gaussian $g_1$ fixed point, while the second corresponds to the interacting one. The solid circles indicate viable solutions with perturbative fixed points that satisfy Eq. (3.30) everywhere, while the crosses represent excluded points. The open circles indicate models with vacuum metastability.