Supersymmetry discovery potential of the LHC at s^1/2 = 10 and 14 TeV without and with missing E_T

We examine the supersymmetry (SUSY) reach of the CERN LHC operating at s^1/2 = 10 and 14 TeV within the framework of the minimal supergravity model (mSUGRA). We improve upon previous reach projections by incorporating updated background calculations including a variety of 2 → n Standard Model (SM) processes. We show that SUSY discovery is possible even before the detectors are understood well enough to utilize either E_T^miss or electrons in the signal. We evaluate the early SUSY reach of the LHC at s^1/2 = 10 TeV by examining multi-muon plus ⩾ 4 jets, and also lepton-free, acollinear dijet events with no missing E_T cuts, and show that the greatest reach in terms of m_1/2 occurs in the dijet channel, where it may be possible to probe m ∼ m ≲ 1 TeV with just 1 fb⁻¹ of integrated luminosity. The reach in multi-muons is slightly smaller in m_1/2, but extends to higher values of m₀. We find that an observable multi-muon signal will first appear in the opposite-sign dimuon channel, but as the integrated luminosity increases the relatively background-free but rate-limited same-sign dimuon, and ultimately the trimuon channel yield the highest reach. The optimized reach in these channels extends to m ≲ 600 (800) GeV for an integrated luminosity of 100 pb⁻¹ (1 fb⁻¹). We show characteristic distributions in these channels that serve to distinguish the signal from the SM background, and also help to corroborate its SUSY origin. We then evaluate the LHC reach in various no-lepton and multi-lepton plus jets channels including missing E_T cuts for s^1/2 = 10 and 14 TeV, and plot the reach for integrated luminosities ranging up to 3000 fb⁻¹ at the SLHC. For s^1/2 = 10 TeV, the LHC reach extends to m = 1.9, 2.3, 2.8 and 2.9 TeV for m ∼ m and integrated luminosities of 10, 100, 1000 and 3000 fb⁻¹, respectively. For s^1/2 = 14 TeV, the LHC reach for the same integrated luminosities is to m = 2.4, 3.1, 3.7 and 4.0 TeV, respectively. The reach estimates for ab⁻¹ luminosities may be over-optimistic due to low statistics of background with very hard cuts.