Phenomenology with F-theory $SU(5)$

We explore the low-energy phenomenology of an F-theory-based $SU(5)$ model which, in addition to the known quarks and leptons, contains Standard Model (SM) singlets and vectorlike color triplets and $SU(2)$ doublets. Depending on their masses and couplings, some of these new particles may be observed at the LHC and future colliders. We discuss the restrictions by Cabibbo-Kobayashi-Maskawa matrix constraints on their mixing with the ordinary down quarks of the three chiral families. The model is consistent with gauge coupling unification at the usual supersymmetric GUT scale; dimension-five proton decay is adequately suppressed, while dimension-six decay mediated by the superheavy gauge bosons is enhanced by a factor of 5–7. The third generation charged fermion Yukawa couplings yield the corresponding low-energy masses in reasonable agreement with observations. The hierarchical nature of the masses of lighter generations is accounted for via nonrenormalizable interactions, with the perturbative vacuum expectation values (VEVs) of the SM singlet fields playing an essential role.

Figure 1

The trilinear top and bottom Yukawa couplings at the triple intersections of the matter curves with symmetry enhancements ${\mathcal{E}}_6$ and $SO(12)$, respectively. Under a $Z_2$ monodromy we obtain identifications such as $10_{t_1}=10_{t_2}$ so that a “diagonal” top Yukawa coupling can be realized. A $\mu$-term emerges only from nonrenormalizable (suppressed) contributions. $⟨\theta {⟩}^n$ stands for the ratio of singlet VEVs divided by the high (compactification) scale.

Figure 2

Variation of the $M_X$ scale with respect to the dilaton field. For the chosen range of $\varphi \in (0,\infty )$, (strong $g_{IIB}$ coupling regime), there is a lower bound $M_X\sim {10}^{13}\mathrm{GeV}$.

Figure 3

Gauge coupling running in the presence of flux thresholds and the triplet’s decoupling scale $M_X$.

Figure 4

Diagram leading to proton decay. Red and yellow circles represent the nonrenormalizable couplings discussed in the text.