Neutral naturalness with bifundamental gluinos

We study constraints on one-loop neutral naturalness at the LHC by considering gluon partners which are required to ameliorate the tuning in the Higgs mass-squared arising at two loops. This is done with a simple orbifold model of folded supersymmetry which not only contains color-neutral stops but also bifundamental gluinos that are charged under the Standard Model color group $SU(3{)}_C$ and a separate $SU(3{)}_C^{\prime }$ group. The bifundamental gluinos reduce the Higgs mass tuning at two loops and maintain naturalness provided the gluinos are lighter than approximately 1.9 TeV for a 5 TeV cutoff scale. Limits from the LHC already forbid bifundamental gluinos below 1.4 TeV, and other noncolored states such as electroweakinos, $Z^{\prime }$ bosons and dark sector bound states may be probed at future colliders. The search for bifundamental gluinos therefore provides a direct probe of one-loop neutral naturalness that can be fully explored at the LHC.

Figure 1

A representative Feynman diagram for bifundamental gluino production and decay at a hadron collider. The stops produced in gluino decay behave as squirks, eventually decaying to dark glueballs, which we take to be invisible on collider scales.

Figure 2

Approximate experimental limits for the bifundamental gluino mass in the case where there is one Dirac gluino (dashed, blue line) or two supersoft Dirac gluinos (solid, orange line), as a function of the corresponding limit on the MSSM stop mass. We have assumed an experimental lower limit on the stop mass, $m_{\tilde{t}}\gtrsim 800\mathrm{GeV}$. The top shaded regions are those in which there is some degree of tuning $(\mathrm{\Delta }{m}_{\tilde{t}}^2\gtrsim m_{\tilde{t}}^2)$ in the $B$-stop mass for one Dirac gluino ($\gtrsim 1.2\mathrm{TeV}$) and two supersoft Dirac gluinos ($\gtrsim 1.9\mathrm{TeV}$).

Figure 3

Contours of the percent tuning in the model, defined from Eq. (20), as a function of the cutoff scale $\mathrm{\Lambda }$, and the (supersoft) bifundamental gluino mass, $m_{\tilde{g}}$. The shaded area depicts the excluded supersoft Dirac masses below 1.4 TeV from LHC MSSM stop mass searches.