⚛️ phenomenology

Shortcomings of the squark simplified model

The paper argues that the commonly used squark simplified model significantly underestimates production rates at hadron colliders, implying that realistic LHC squark mass limits are actually in the 2.6–3.0 TeV range rather than the typically quoted 1.7–1.8 TeV.

Original author: Kaustubh Agashe, Roberto Franceschini, Gian F. Giudice, Andre Lessa, Xing Wang

Published 2026-11-04

📖 7 min read🧠 Deep dive

CC BY 4.0

Original author: Kaustubh Agashe, Roberto Franceschini, Gian F. Giudice, Andre Lessa, Xing Wang

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 author. For technical accuracy, refer to the original paper. Read full disclaimer

In the vast, invisible landscape of particle physics, scientists are searching for a hidden layer of reality that sits just beyond the edge of what we can currently see. This quest is driven by a theory called supersymmetry, which proposes that every known particle has a heavier, invisible partner. Among these hypothetical partners are squarks, the partners of quarks (the building blocks of protons and neutrons), and gluinos, the partners of gluons (the particles that glue quarks together). For decades, researchers at the Large Hadron Collider have been smashing protons together at incredible speeds, hoping to shatter the energy barrier and reveal these new particles. To make sense of the massive amounts of data produced by these collisions, physicists often rely on "simplified models." These are like sketches of a complex machine: they strip away the messy details and focus on just one or two parts to make the math manageable. For squark searches, the standard sketch assumed that squarks exist in isolation, with their heavy partners, the gluinos, being so massive that they effectively do not exist at all.

A new analysis challenges the accuracy of this long-standing sketch. A team of physicists argues that this simplified picture is not just a rough approximation, but a fundamental misunderstanding of how these particles would actually behave if they existed. Their work suggests that the standard model used to interpret collider data has been underestimating the rate at which squarks would be produced by a factor of dozens, or even hundreds. This oversight means that the current limits on how heavy these particles can be are far too low. By correcting the model to include the unavoidable influence of the gluino, the researchers find that the Large Hadron Collider has already ruled out squark masses up to 3.0 TeV, a significant jump from the previously accepted limit of 1.8 TeV. This shift reshapes the search for new physics, suggesting that the collider has been looking in the wrong place for the wrong reasons, and that future machines will have a much greater potential to discover these elusive particles than previously thought.

The core of the problem lies in a theoretical principle regarding the stability of particle masses. In the simplified model, physicists assumed they could treat the squark and the gluino as completely independent entities, with the gluino being infinitely heavy and therefore irrelevant. However, the authors of this study demonstrate that in any realistic version of the theory, the two particles are inextricably linked. If a gluino were to be much heavier than a squark, the laws of quantum mechanics would create a severe instability. The heavy gluino would exert a powerful quantum pressure that would rapidly drive the squark's mass up to match its own. In other words, nature does not allow for a scenario where the gluino is vastly heavier than the squark; the two masses must remain relatively close to each other. The standard simplified model, which assumes the gluino is infinitely heavy, describes a situation that is theoretically impossible in a realistic universe.

This theoretical constraint has a massive impact on what happens inside the collider. When protons collide, they produce squarks through several different pathways. The simplified model only counts the pathways where the squarks are created directly from the collision of other particles, ignoring a crucial third pathway: the exchange of a virtual gluino. Because the gluino is not infinitely heavy, it acts as a bridge, allowing squarks to be produced much more easily than the simplified model predicts. The researchers calculated that for realistic mass ratios, where the gluino is only two or three times heavier than the squark, the total production rate of squarks is more than sixty times higher than the rate predicted by the standard simplified model. It is as if scientists had been counting the number of cars on a highway by only looking at the main road, while completely ignoring a massive, high-speed bypass that carries the majority of the traffic.

The consequences of this miscalculation are immediate and profound for the current limits on squark masses. The Large Hadron Collider has been searching for signs of squarks by looking for specific patterns of energy and missing particles in the debris of collisions. The experiments set a "limit" based on how many events they expected to see if squarks existed at a certain mass. Because the simplified model predicted a very low production rate, the experiments concluded that if they didn't see many events, the squarks must be lighter than 1.8 TeV. However, the new analysis shows that if the squarks were actually being produced at the much higher, realistic rate, the experiments would have seen far more events than they did. Therefore, the fact that they did not see those events means the squarks must be much heavier than previously thought. The authors recast the existing data and found that the current limit on the squark mass is realistically between 2.6 and 3.0 TeV, effectively pushing the boundary of the known universe much further out.

This correction also changes the outlook for the future of particle physics. The High-Luminosity Large Hadron Collider, an upgrade scheduled to run in the coming years, is expected to collect far more data. Previous projections, based on the flawed simplified model, suggested this machine would be able to probe squark masses up to about 2.4 TeV. With the new, more accurate model, the researchers project that the same machine could actually reach masses between 3.2 and 3.6 TeV. The potential for discovery is even more dramatic for future, even larger colliders, such as the proposed Future Circular Collider. While the simplified model suggested a reach of about 13 TeV, the corrected analysis indicates that such a machine could potentially discover squarks with masses up to 20 TeV. The gap between the simplified prediction and the realistic potential is not a small margin of error; it represents a fundamental shift in our understanding of what these machines can achieve.

The authors also examined whether the reverse situation—assuming the squarks are infinitely heavy and ignoring them in gluino searches—would suffer from the same problem. They found that the gluino simplified model is actually quite sound. Unlike the squark case, the theoretical arguments do not forbid the squarks from being much heavier than the gluinos, and the contribution of heavy squarks to gluino production is small and quickly fades away. This means that while the standard approach to searching for gluinos is reliable, the standard approach to searching for squarks has been misleading. The paper concludes that the field must move away from the old simplified model. Instead of assuming the gluino is infinitely heavy, future analyses should use a model that includes the gluino mass as a variable, constrained by the realistic limit that it cannot be more than about three times heavier than the squark.

By correcting this long-standing oversight, the study does more than just adjust a number; it redefines the landscape of the search for supersymmetry. It suggests that the Large Hadron Collider has already explored a much deeper territory than we realized, and that the next generation of machines holds a much brighter promise for discovery. The lesson is a reminder that in the complex world of high-energy physics, simplifying a theory too much can sometimes hide the very phenomena we are trying to find. The reality of these particles is more interconnected than the sketches suggested, and acknowledging that connection is the key to unlocking the secrets of the universe.

Technical Summary: Shortcomings of the Squark Simplified Model

Problem Statement
The paper addresses a critical discrepancy between the "squark simplified model" currently employed in collider analyses (specifically by ATLAS and CMS) and realistic low-energy supersymmetric (SUSY) theories. The standard simplified model assumes eight degenerate squarks decaying 100% into a quark and the lightest neutralino ( $\tilde{q} \to q \tilde{\chi}^0_1$ ), with the gluino ( $\tilde{g}$ ) effectively decoupled (mass $m_{\tilde{g}} \to \infty$ ). This model is defined by only two parameters: the squark mass ( $m_{\tilde{q}}$ ) and the neutralino mass ( $m_{\tilde{\chi}^0_1}$ ).

The authors argue that this model fails to represent realistic SUSY scenarios because it ignores the theoretical constraints on the gluino-to-squark mass ratio, $r_{\tilde{g}\tilde{q}} = m_{\tilde{g}}/m_{\tilde{q}}$ . In realistic models, a large hierarchy ( $r_{\tilde{g}\tilde{q}} \gg 1$ ) is quantum mechanically unstable due to the naturalness problem: heavy gluinos induce large, quadratically divergent quantum corrections to squark masses, rapidly destabilizing any large mass hierarchy. Consequently, the simplified model's assumption of $r_{\tilde{g}\tilde{q}} \to \infty$ is physically unrealistic. Furthermore, ignoring the gluino leads to a severe underestimation of the squark production cross-section at hadron colliders, as the gluino mediates significant $t$ -channel contributions.

Methodology
The authors employ a multi-faceted approach combining theoretical renormalization group (RG) analysis with phenomenological cross-section calculations:

Theoretical Bounds on $r_{\tilde{g}\tilde{q}}$ :
- They analyze the RG evolution of squark masses in the presence of heavy gluinos. Using leading-order (LO) and next-to-leading-order (NLO) calculations, they demonstrate that large values of $r_{\tilde{g}\tilde{q}}$ are unstable.
- They examine specific mediation scenarios, including Gauge Mediation and Gaugino Mediation, showing that even in extreme cases, $r_{\tilde{g}\tilde{q}}$ rarely exceeds 2–3.
- They rule out "tachyonic" boundary conditions as a way to artificially sustain large ratios, citing issues with vacuum stability and radiative electroweak symmetry breaking.
Cross-Section Anatomy:
- The paper decomposes the squark production cross-section ( $\sigma_{pp \to \tilde{q}\tilde{q}}$ ) into four channels based on chirality and particle type: $\tilde{q}\tilde{q}^*$ (squark-antisquark) and $\tilde{q}\tilde{q}$ (di-squark).
- They derive an expansion of the cross-section in powers of $1/r_{\tilde{g}\tilde{q}}$ . Crucially, they identify that the di-squark channel ( $\tilde{q}\tilde{q}$ ), which is entirely mediated by $t$ -channel gluino exchange, is a dominant production mode in realistic scenarios but is completely absent in the simplified model.
- They calculate the coefficients of these channels using NNPDF2.3 parton distribution functions at $\sqrt{s} = 14$ TeV, comparing the full cross-section against the "simplified" limit ( $r_{\tilde{g}\tilde{q}} \to \infty$ ).
Recasting Experimental Limits:
- The authors recast the ATLAS 0-lepton + monojet search (13 TeV, 139 fb $^{-1}$ ) to include finite $r_{\tilde{g}\tilde{q}}$ .
- They utilize the ATLAS exclusion limits on the simplified cross-section ( $\sigma_{UL}$ ) and apply them to the enhanced theoretical cross-sections ( $\sigma_{tot}$ ) calculated for $r_{\tilde{g}\tilde{q}} = 1, 2, 3$ .
- They perform extrapolations to the High-Luminosity LHC (HL-LHC) and Future Circular Collider (FCC-hh) using scaling relations based on parton luminosities and center-of-mass energy.

Key Contributions and Results

Theoretical Upper Bound: The paper establishes that realistic low-energy SUSY models with Majorana gluinos satisfy $r_{\tilde{g}\tilde{q}} \lesssim 2\text{--}3$ . Values significantly larger than this are theoretically untenable due to quantum instability.
Cross-Section Enhancement: The gluino contribution to squark production is dominant for realistic mass ratios.
- For $m_{\tilde{q}} = 3$ TeV and $r_{\tilde{g}\tilde{q}} = 2$ , the total production rate at the LHC is more than 60 times larger than predicted by the simplified model.
- The di-squark channel ( $\tilde{q}\tilde{q}$ ), initiated by valence quarks, provides the largest contribution, a feature entirely missed by the simplified model.
Revised Mass Limits:
- Current LHC: While the simplified model quotes a limit of $m_{\tilde{q}} > 1.7\text{--}1.8$ TeV, the authors find that for realistic $r_{\tilde{g}\tilde{q}}$ , the current exclusion limit is actually in the range of 2.6–3.0 TeV.
- HL-LHC: The simplified model predicts a reach of $\sim 2.4$ TeV. With realistic parameters, the HL-LHC can probe squark masses up to 3.2–3.6 TeV.
- FCC-hh: The simplified model suggests a reach of $\sim 13$ TeV. The authors project a realistic reach of 18–20 TeV (for $r_{\tilde{g}\tilde{q}} = 1\text{--}2$ ), significantly improving the discovery potential.
Electroweak Gauginos: The paper analyzes the impact of Wino and Bino exchange. While they contribute to the cross-section, their effect is subdominant compared to the gluino (enhancing the rate by at most $\sim 50\%$ for Winos and $\sim 10\%$ for Binos) and does not alter the primary conclusion regarding the gluino's dominance.
Validity of the Gluino Simplified Model: In a "mirror" analysis, the authors show that the gluino simplified model (where squarks are decoupled) is sound. Unlike the squark case, large $m_{\tilde{q}}/m_{\tilde{g}}$ ratios are theoretically allowed, and the squark-mediated corrections to gluino production are destructive and modest, meaning the simplified model for gluinos remains a valid approximation.

Significance and Claims
The paper claims that the continued use of the squark simplified model in collider analyses is not merely a conservative approach but a source of misleading results. By assuming $r_{\tilde{g}\tilde{q}} \to \infty$ , experimentalists are effectively ignoring the most significant production mechanism for squarks in realistic theories.

The authors argue that this misrepresentation leads to:

False Exclusions: Regions of parameter space that appear allowed under the simplified model are actually excluded in realistic models.
Underestimated Potential: The discovery reach of future colliders (HL-LHC, FCC-hh) is grossly underestimated.

Recommendation:
The authors propose discontinuing the use of the two-parameter squark simplified model $(m_{\tilde{q}}, m_{\tilde{\chi}^0_1})$ . Instead, they advocate for a three-parameter model $(m_{\tilde{q}}, m_{\tilde{\chi}^0_1}, r_{\tilde{g}\tilde{q}})$ with the constraint $r_{\tilde{g}\tilde{q}} \lesssim 3$ . This parametrization captures the essential features of realistic SUSY models and provides reliable bounds for collider searches. They emphasize that this is not a minor deformation of the existing model but a fundamental shift, as the class of realistic theories populated by $r_{\tilde{g}\tilde{q}} \lesssim 3$ is disjoint from the class of models described by the simplified limit.

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