pMSSM versus complete models and the excellent prospects for top-squark discovery at HL-LHC

LHC sparticle search limits are usually performed within the context of simplified models and subsequently interpreted within the 19 parameter phenomenological MSSM (pMSSM) as to how many models avoid search limits for a particular sparticle mass, often including WIMP dark matter constraints. We provide a critical discussion of this procedure and how it can go wrong due to the introduction of new prejudices. By ameliorating these conditions, one is pushed into the more plausible four extra parameter non-universal Higgs model (NUHM4). Implementing a decoupling/quasi-degeneracy solution to the SUSY flavor and CP problems leads to first/second generation sfermions in the tens-of-TeV range. In this case, the natural solutions typically contain top-squarks in the 1-2 TeV range which are accessible to high-lumi LHC (HL-LHC) searches. This search channel, along with higgsino and wino pair production, may allow a nearly complete scan of natural/plausible parameter space by HL-LHC.

💡 Research Summary

The paper critically examines the prevailing methodology of interpreting LHC supersymmetry (SUSY) search limits. Traditionally, experimental collaborations present results in the context of simplified models—specific production processes with a single decay topology—and then map these limits onto the 19‑parameter phenomenological MSSM (pMSSM). While the pMSSM offers a broad, model‑independent parameter space, the authors argue that this approach inadvertently introduces several theoretical prejudices that can mislead conclusions about the viability of weak‑scale SUSY.

Key criticisms include: (i) the allowance of arbitrary, non‑universal gaugino mass ratios, which contradicts the universal gaugino masses expected in gravity‑mediated (SUGRA) constructions where the gauge kinetic function is typically proportional to the dilaton; (ii) the neglect of matter scalar mass unification within each generation, despite the fact that in SO(10) GUTs all 16 matter fields of a generation sit in a single spinor representation, suggesting intra‑generation universality; (iii) the abandonment of renormalization‑group evolution (RGE) of soft terms, thereby discarding the successful gauge‑coupling unification and radiative electroweak symmetry breaking (REWSB) that are hallmarks of the MSSM; (iv) artificial upper bounds and log‑uniform sampling in pMSSM scans that bias the statistical outcome; (v) reliance on conventional naturalness measures that are ill‑defined for the pMSSM, whereas the newer electroweak fine‑tuning measure Δ_EW depends only on the weak‑scale spectrum and is thus model‑agnostic; (vi) the use of a degeneracy solution to the SUSY flavor/CP problem (setting first‑ and second‑generation soft terms equal), which conflicts with expectations from gravity mediation; and (vii) the imposition of WIMP dark‑matter relic density constraints, despite the growing recognition that neutralino dark matter may coexist with axions or other candidates.

To remedy these issues, the authors turn to a more complete framework: a four‑parameter non‑universal Higgs model (NUHM4) that can be viewed as the low‑energy effective field theory of gravity‑mediated SUSY breaking. In this setup, the first two generations of sfermions acquire masses in the 20–50 TeV range (a “decoupling/quasi‑degeneracy” solution), thereby suppressing flavor‑changing neutral currents and CP violation. The third generation remains lighter, with top‑squark masses naturally falling in the 1–2 TeV window, thanks to large trilinear A‑terms (of order the gravitino mass) that also raise the Higgs boson mass to the observed 125 GeV without excessive fine‑tuning.

The paper demonstrates that, within NUHM4, the bulk of the phenomenologically viable parameter space lies near the boundary of charge‑ and color‑breaking (CCB) vacua, explaining why LHC Run 2 has not yet observed SUSY. Crucially, the natural region predicts stop masses ≤ 2 TeV, which are within the projected reach of the High‑Luminosity LHC (HL‑LHC, 14 TeV, 3 ab⁻¹). In addition, light higgsinos (µ ≈ 100–300 GeV) and winos (M₂ ≈ 1 TeV) are expected, providing complementary discovery channels through electroweak‑ino pair production.

Simulation studies presented in the paper show that stop pair production combined with higgsino/wino searches can essentially scan the entire natural NUHM4 parameter space at HL‑LHC. This contrasts sharply with pMSSM‑based interpretations, which often underestimate the discovery potential because they ignore the high‑scale constraints and the decoupling of the first two generations.

In summary, the authors argue that pMSSM‑only analyses are insufficient for robust conclusions about SUSY’s status. By adopting a more theoretically motivated model—NUHM4 with gravity‑mediated SUSY breaking, universal intra‑generation scalar masses, and proper RGE evolution—they recover a natural spectrum where the top squark remains light enough for discovery at the HL‑LHC, while simultaneously solving the flavor/CP problems and accommodating the measured Higgs mass. The paper thus provides a compelling case that the HL‑LHC has excellent prospects for discovering top squarks, and that a comprehensive search strategy including both strong (stop) and electroweak (higgsino/wino) production channels could effectively close the remaining natural SUSY window.