⚛️ phenomenology

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

The paper argues that moving from simplified models to more realistic parameter spaces like the NUHM4 reveals that natural supersymmetry solutions likely feature top-squarks in the 1-2 TeV range, making them highly discoverable at the High-Luminosity LHC.

Original authors: Howard Baer, Vernon Barger, Kairui Zhang

Published 2026-02-11

📖 4 min read🧠 Deep dive

CC BY 4.0

Original authors: Howard Baer, Vernon Barger, Kairui Zhang

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Mystery of the Missing Particles: A Guide to the "SUSY" Detective Story

Imagine you are a detective trying to solve a massive mystery: Why is the universe so stable?

In physics, there is a huge problem called the "Higgs instability." According to our current math, the Higgs boson (the particle that gives everything mass) should be wildly unstable, causing the universe to collapse. To fix this, scientists proposed a theory called Supersymmetry (SUSY).

SUSY suggests that for every particle we know, there is a "shadow partner" (a sparticle) that balances the scales. If these shadow particles exist, the universe stays stable. But here’s the catch: we haven't found them yet.

This paper is a critique of how scientists have been searching for these "shadows" and a new map of where they might actually be hiding.

1. The Problem: Searching with a Broken Compass (The pMSSM)

For years, scientists have been using a method called the pMSSM to search for these particles.

The Analogy: Imagine you are looking for a lost cat in a giant forest. Instead of looking for a cat, you decide to create a "mathematical cat." You say, "I'll assume the cat has 19 different traits—it might be orange, it might be heavy, it might be fast, etc.—and I'll test every possible combination of those 19 traits."

The authors argue that this is a bad way to hunt. By treating all 19 traits as totally random and independent, you end up testing "cats" that couldn't possibly exist in nature. It’s like looking for a "cat" that is simultaneously a bird, a fish, and a toaster. Because you are looking for such weird, impossible combinations, you conclude, "I haven't found the cat, so the cat must not exist!"

The authors say this "broken compass" is leading us to the wrong conclusion. We aren't finding SUSY because we are looking in the wrong way.

2. The Solution: Following the "Golden Rules" (The NUHM4 Model)

Instead of the random pMSSM, the authors suggest we use a more "complete" model called NUHM4.

The Analogy: Instead of assuming the cat's traits are random, we use Biology. We know that if it’s a cat, it must have fur, it must have whiskers, and its DNA follows certain rules.

The authors argue that the universe follows "Golden Rules" (like gravity and the way forces unify). When you apply these rules, the "shadow particles" aren't just random numbers; they follow a pattern. Specifically, they suggest a "Decoupling" solution:

The Heavyweights: The first and second generations of particles (the "common" ones) are incredibly heavy—too heavy for our current machines to see. They are like massive boulders sitting in the forest.
The Lightweights: The third generation (the "top-squark") is much lighter and more "natural." This is the particle we should actually be looking for.

3. The "Living Dangerously" Strategy

The paper points out something fascinating: the most "natural" version of the universe exists right on the edge of disaster.

The Analogy: Imagine a tightrope walker. To be "natural" (efficient and balanced), the walker has to stay right near the edge of the rope. If they move too far toward the center, they are too safe (and the math doesn't work); if they move too far toward the edge, they fall (the universe becomes unstable).

The authors show that the particles we are looking for (the top-squarks) are likely hiding right on that "edge." They are heavy enough to have escaped our notice so far, but light enough that the next generation of the Large Hadron Collider (the HL-LHC) should be able to spot them.

The Bottom Line

The Old Way: "We've checked billions of random, impossible combinations of particles and found nothing. SUSY is dead!"

The Authors' Way: "You've been checking impossible combinations. If you follow the actual laws of physics and look for the specific 'lightweight' particles that balance the universe, you'll find them in the next few years at the upgraded LHC."

In short: Don't throw away the map just because you've been using it upside down.

Technical Summary: pMSSM versus Complete Models and the Excellent Prospects for Top-Squark Discovery at HL-LHC

1. Problem Statement

The paper addresses a fundamental methodological issue in Supersymmetry (SUSY) phenomenology: the reliance on the phenomenological MSSM (pMSSM) to interpret LHC sparticle search limits. The authors argue that while the pMSSM (a 19-parameter model defined at the weak scale) is intended to be "general," it introduces several unmotivated theoretical prejudices that lead to erroneous conclusions about the viability of Weak Scale Supersymmetry (WSS).

Specifically, the authors identify several flaws in current pMSSM-based interpretations:

Lack of Renormalization Group Evolution (RGE): By defining parameters at the weak scale, pMSSM ignores the successes of gauge coupling unification and Radiative Electroweak Symmetry Breaking (REWSB).
Flawed Flavor/CP Solutions: pMSSM assumes generational degeneracy (equal masses for 1st/2nd generation sfermions) to solve flavor problems, which contradicts gravity-mediation expectations.
Unnatural Parameter Scans: Many pMSSM scans use arbitrary upper bounds and sampling methods that include highly fine-tuned, unnatural regions, leading to the false conclusion that most SUSY space is excluded.
Misplaced Dark Matter Constraints: Relying on WIMP relic density constraints is risky, as string-theoretic effects (axions, moduli) can significantly alter dark matter abundance.

2. Methodology

The authors employ a comparative analytical and numerical approach:

Comparative Scans: They perform three distinct types of pMSSM scans (Scan S, T, and U) to demonstrate how varying parameter ranges and implementing gaugino mass unification drastically change the perceived "survival rate" of SUSY models and their naturalness ( $\Delta_{EW}$ ).
Implementation of Complete Models: They move away from the pMSSM toward a more theoretically robust framework: the Non-Universal Higgs Model with four extra parameters (NUHM4). This model is derived from gravity-mediated SUSY breaking (SUGRA) and incorporates:
- RGE running from the GUT scale ( $M_{GUT} \approx 2 \times 10^{16}$ GeV).
- SO(10) Matter Unification: Sfermions within a generation are unified, but different generations are not.
- Decoupling/Quasi-Degeneracy Solution: First and second-generation sfermions are placed in the 10–50 TeV range to solve the SUSY flavor/CP problems, while third-generation sfermions remain near the TeV scale for naturalness.
Numerical Simulation: They use the Isajet program to map the parameter space, specifically focusing on the $m_0(3)$ (3rd generation scalar mass) vs. $m_{1/2}$ (gaugino mass) plane.

3. Key Contributions

Critique of pMSSM: A systematic deconstruction of why pMSSM scans provide a misleading picture of the "excluded" SUSY parameter space.
The NUHM4 Framework: Proposing NUHM4 as the most plausible Low-Energy Effective Field Theory (LE-EFT) for gravity mediation that remains consistent with the $m_h \approx 125$ GeV Higgs mass and naturalness.
Identification of the "Living Dangerously" Region: They show that the most natural SUSY points exist near the Charge-or-Color-Breaking (CCB) minima. In these regions, heavy 1st/2nd generation scalars drive the top-squark (stop) masses to low values via 2-loop RGE effects, but not so low that the vacuum becomes unstable.

4. Results

Naturalness and Mass Gaps: In complete models, the naturalness measure ( $\Delta_{EW}$ ) is highly correlated with the mass spectrum. Unlike pMSSM scans that suggest unnatural higgsino mass gaps, the NUHM4 model shows that natural points are consistent with larger, more theoretically motivated mass gaps.
Top-Squark (Stop) Mass Distribution: The authors find that in the most plausible gravity-mediated scenarios (where 1st/2nd generation scalars are decoupled), the light top-squark mass ( $m_{\tilde{t}_1}$ ) is typically in the 1–2 TeV range.
HL-LHC Reach: The study demonstrates that the High-Luminosity LHC (HL-LHC) reach for top-squark pair production (extending to $\sim 1.8$ TeV) is sufficient to nearly saturate the entire natural parameter space of the NUHM4 model.

5. Significance

The paper shifts the focus of the SUSY search strategy. It suggests that instead of searching for the highly fine-tuned or "degenerate" scenarios favored by pMSSM scans, experimentalists should prioritize top-squark pair production and higgsino/wino pair production.

The conclusion is highly optimistic for the future of particle physics: if gravity-mediated SUSY is the correct description of nature, the HL-LHC has an excellent prospect of discovery in the coming years, as the most natural and theoretically consistent regions of parameter space are precisely within its reach.