Precision gluino mass at the CERN LHC in supersymmetric models with decoupled scalars

One way to ameliorate the SUSY flavor and $CP$ problems is to postulate that scalar masses lie in the TeV or beyond regime. For example, the focus point (FP) region of the minimal supergravity (mSUGRA) model is especially compelling in that heavy scalar masses can coexist with low fine-tuning while yielding the required relic abundance of cold dark matter (via a mixed Higgsino-bino neutralino). We examine many of the characteristics of collider events expected to arise at the CERN LHC in models with multi-TeV scalars, taking the mSUGRA FP region as a case study. The collider events are characterized by a hard component arising from gluino pair production, plus a soft component arising from direct chargino and neutralino production. Gluino decays in the FP region are characterized by lengthy cascades yielding very large jet and lepton multiplicities, and a large $b$-jet multiplicity. Thus, as one steps to higher jet, $b$-jet or lepton multiplicity, signal-over-background rates should steadily improve. The lengthy cascade decays make mass reconstruction via kinematic edges difficult; however, since the hard component is nearly pure gluino pair production, the gluino mass can be extracted to $\ifmmode\pm\else\textpm\fi{}8%$ via total rate for ${E}_{T}^{\mathrm{miss}}+\ensuremath{\ge}7\mathrm{\text{\ensuremath{-}}}\mathrm{\text{jet}}+\ensuremath{\ge}2b\mathrm{\text{\ensuremath{-}}}\mathrm{\text{jet}}$ events, assuming $100\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of integrated luminosity. The distribution of invariant mass of opposite-sign/same-flavor dileptons in the hard component exhibits two dilepton mass edges: ${m}_{{\stackrel{\texttildelow{}}{Z}}_{2}}\ensuremath{-}{m}_{{\stackrel{\texttildelow{}}{Z}}_{1}}$ and ${m}_{{\stackrel{\texttildelow{}}{Z}}_{3}}\ensuremath{-}{m}_{{\stackrel{\texttildelow{}}{Z}}_{1}}$. As a consistency check, the same mass edges should be seen in isolated opposite-sign dileptons occurring in the soft component trilepton signal which originates mainly from chargino-neutralino production.