Light color octet scalars in the minimal $SO(10)$ grand unification

We analyze the relation between the present (and foreseen) bounds on matter stability and the presence of TeV-scale color octet scalar states in nonsupersymmetric $SO(10)$ grand unification with one adjoint Higgs representation triggering the symmetry breaking. This scenario, discarded long ago due to tree-level tachyonic instabilities appearing in all phenomenologically viable breaking patterns, has been recently revived at the quantum level. By including the relevant two-loop corrections we find a tight correlation between the octet mass and the unification scale which either requires a light color octet scalar within the reach of the LHC or, alternatively, a proton lifetime accessible to the forthcoming megaton-scale facilities.

Figure 1

The $|{\omega }_{BL}|-\sigma$ plane depicting the allowed part of the parameter space that supports a consistent two-loop gauge unification with a color octet scalar in the TeV domain (color code defined in the section “Gauge-induced ... proton decay.”). For efficiency reasons, we reject all points that, in the one-loop approximation, yield $\sigma$ below ${10}^{10}\mathrm{GeV}$; this leads to a reduction of the plot density in the uninteresting lowest $\sigma$ region at two loops.

Figure 2

The $H_8$ mass range allowed by the two-loop unification constraints and matter stability bounds. The present day bound on matter stability sets an upper bound on the $H_8$ mass of about 2000 TeV. The blurry lower-left boundary of the allowed region is an artefact of the numerical procedure in which, for efficiency reasons, we dump all uninteresting points with $\sigma$ below ${10}^{10}\mathrm{GeV}$ at one-loop. On the other hand, the upper-right boundary (which is the one that sets the stringent limit on the mass of $H_8$) corresponding to the sharp upper cut in Fig. 1 is enforced by the unification constraints and, as such, it is a robust feature of the model.

Figure 3

The same as in Fig. 2 with the inclusion of the $B-L$ scale limits specified in Sec. 2b3 (namely, $\sigma \gtrsim {10}^{12}\mathrm{GeV}$ on the left and $\sigma \gtrsim {10}^{13}\mathrm{GeV}$ on the right). Since these constraints affect the bottom-left parts of the allowed regions, they preserve the upper limits quoted in Sec. 2c2. In all cases $H_8$ turns out to be lighter than about 2000 TeV. The bound shrinks to about 20 TeV for a proton lifetime above ${10}^{35}\mathrm{years}$ (black area).

Figure 4

A sample two-loop gauge unification pattern corresponding to one of the allowed solutions in Figs. 1, 2, 3; see Tables  for further details. The gauge running proceeds through four stages corresponding from top down to the $SO(10)$, $SU(4{)}_C\otimes SU(2{)}_L\otimes U(1{)}_R$, the $\mathrm{SM}+H_8$ and, finally, the pure SM settings. The visible discontinuities in the non-Abelian gauge couplings at the upper two matching points are due to the large threshold corrections generated by the states decoupled at each scale.