Naturalness in D-brane inspired models

We examine the naturalness of the D-brane inspired model constructed in flipped $SU(5)$ supplemented with vector-like particles at the TeV scale, dubbed flippons. We find the model can produce a mainly Higgsino-like lightest supersymmetric particle (LSP) and small light stops, as favored by naturalness. In fact, a large trilinear scalar $A_t$ term at the electroweak (EW) scale creates a large mass splitting between the top squarks, driving the light stop to near degeneracy with an LSP that is almost all Higgsino, with $\Delta M(\widetilde{t}_1, \widetilde{\chi}_1^0) < 5$ GeV, evading the LHC constraint on $\widetilde{t}_1 \to c \widetilde{\chi}_1^0$ thus far. Given the smallness of the light stop, generating a 125 GeV light Higgs boson mass is aided by one-loop contributions from the Yukawa couplings between the flippons and Higgs fields. The resulting parameter space satisfying naturalness is rather constrained, thus we assess its viability by means of comparison to the LHC constraint on soft charm jets and direction detection limits on spin-independent cross-sections. Finally, we compute the level of electroweak fine-tuning and uncover a region with $\Delta_{EW} < 30$, $i.e.$, fine-tuning better than 3%, regarded as low electroweak fine-tuning. Given the small light stop, the electroweak fine-tuning from only the top squarks is of $\cal{O}$(1), indicating no fine-tuning from neither the light stop $\widetilde{t}_1$ nor the heavy stop $\widetilde{t}_2$.