Supersymmetry at High Luminosity LHC

Weak-scale supersymmetry (SUSY) is well motivated as a technically natural solution to the gauge hierarchy problem. LHC limits on superpartners, however, have sharpened the Little Hierarchy problem, raising the question of why $m_{weak}\ll m_{soft}$. We review current collider and dark matter constraints and their implications for leading SUSY-breaking scenarios. Electroweak naturalness is revisited using a weak-scale measure that avoids ambiguities associated with high-scale fine-tuning. Also, within the string landscape, soft terms are statistically favored to be large, while anthropic selection enforces a weak scale near the observed value. This framework often termed \emph{stringy naturalness} – naturally accommodates $m_h\simeq 125$ GeV while placing sparticles above current LHC limits. Updated HL-LHC projections for non-universal Higgs mass (NUHM) models – the most plausible realization consistent with above picture – show that searches for higgsinos, stops, and heavy Higgs bosons will soon begin to probe the core of the viable parameter space.