USMEFT as a tool for discovery of universal new physics at high luminosity LHC

This paper demonstrates that the Universal SMEFT framework, when applied to high-luminosity LHC Drell-Yan processes with minimal theoretical bias, can effectively discover universal new physics and accurately extract its properties while maintaining stability across different orders of EFT truncation.

The Gist

Imagine the Large Hadron Collider (LHC) as a giant, high-speed billiard table where scientists smash particles together to see what happens. Usually, they look for "new balls" (new particles) popping out of the collision. But what if the new physics is too heavy to be seen directly, like a giant bowling ball hidden behind a curtain? You can't see the ball, but you can see how the other balls bounce off the invisible wall.

This paper is about a new way to look at those bounces to find the hidden bowling ball, using a mathematical tool called Universal SMEFT (Standard Model Effective Field Theory).

Here is the breakdown of their work in simple terms:

1. The Problem: The "Invisible" New Physics

Scientists have been smashing particles for years and haven't found any new heavy particles yet. They suspect these particles might be too heavy to create directly, but they might still be influencing the collisions from afar, slightly changing how particles scatter.

To find this "ghostly" influence, scientists look at the tails of the data—the rare, high-energy crashes where the new physics would leave the biggest fingerprint.

2. The Tool: The "Universal" Lens

The authors use a specific type of mathematical lens called USMEFT. Think of this lens as a set of rules that describes how the universe should behave if there are no new particles, and then adds "correction knobs" (called Wilson coefficients) to account for new physics.

• The "Universal" part: They assume the new physics interacts with the known particles in a very standard, predictable way (like a mirror image of the known forces). This simplifies the math, making the lens sharper.
• The "Lens" levels: Usually, scientists only look at the first level of correction (Dimension-6). This paper asks: "What if we also look at the second level of correction (Dimension-8)?" It's like checking not just the shape of the bounce, but also the spin and the air resistance.

3. The Experiment: Simulating the Future

Since the "High-Luminosity" version of the LHC (HL-LHC) hasn't finished collecting all its data yet, the authors created fake data (pseudo-data).

• They simulated two specific scenarios where new heavy particles (a "Mirror U(1)" and a "Mirror SU(2)") exist.
• They ran these simulations forward to the future, assuming the LHC will collect 3000 times more data than it has now.
• They then tried to "fit" this fake data using their Universal Lens to see if they could find the hidden particles.

4. The Results: Finding the Needle in the Haystack

The paper makes three main claims about what happens when you use this Universal Lens:

• It Works: Even without knowing exactly what the new physics is beforehand, the lens can successfully tell you, "Hey, something new is here!" It can detect the existence of these new particles with high confidence (5-sigma, which is the gold standard in physics) if the particles are heavy enough (up to about 7–9 TeV).
• It Describes the Shape: Not only does it find the new physics, but it can also accurately describe what that physics looks like (its mass and how strongly it interacts). It's like looking at a shadow and correctly guessing the size and shape of the object casting it.
• The Lens is Stable: A major worry in this field is that if you add more complex layers to your math (like the Dimension-8 corrections), your results might get messy or change completely. The authors found that their results are very stable. Whether they used the simple lens or the complex, multi-layered lens, they got the same answer. This means the method is robust and reliable.

5. The "Correlation" Hurdle

One interesting finding was that when they added the complex Dimension-8 corrections, two of their "correction knobs" started to get tangled up (correlated). It was like trying to measure two different ingredients in a soup, but the recipe made them taste exactly the same.

• The Fix: The authors found a clever way to rotate their mathematical "knobs" so they could untangle them. Once they did this, they could measure the ingredients separately again, proving that even with the complex math, they could still pinpoint the new physics accurately.

Summary

In short, this paper says: "Don't worry if the new particles are too heavy to see directly. If we use this specific 'Universal' mathematical tool and look at the high-energy tails of the data, we can not only prove new physics exists but also accurately describe its properties, even when we include very complex mathematical corrections."

It's a validation of a strategy: a "blind" search (looking without knowing the answer) using a universal tool can successfully reveal the hidden rules of the universe.

Technical Summary

Technical Summary: USMEFT as a tool for discovery of universal new physics at high luminosity LHC

Problem Statement
Despite the accumulation of significant statistics at the Large Hadron Collider (LHC), no direct evidence of new physics (NP) has been observed. A plausible scenario is that NP states are too heavy to produce resonant signatures within the current kinematic reach but are sufficiently light to induce deviations in the tails of kinematic distributions. In this regime, the Standard Model Effective Field Theory (SMEFT) serves as the optimal model-independent framework for analysis. However, critical questions remain regarding the efficacy of SMEFT fits with minimal theoretical priors (bottom-up approach): Can arbitrary Wilson Coefficients (WCs) provide a clear signature of NP? Do the extracted WCs accurately capture the properties of the underlying Beyond the Standard Model (BSM) theory? Furthermore, how do these answers depend on the order of truncation of the EFT series, particularly when including dimension-eight operators ($O(1/\Lambda^4)$)? Existing literature has addressed correlations in specific UV completions and the impact of dimension-eight operators, but few studies have directly addressed the discovery potential of NP in fits with minimal theoretical bias.

Methodology
The authors assess the potential of the High-Luminosity LHC (HL-LHC) to discover universal NP using the Universal SMEFT (USMEFT) framework. The study focuses on neutral current (NC) and charged current (CC) Drell-Yan (DY) processes ($pp \to \ell^+\ell^-$ and $pp \to \ell^\pm\nu_\ell$).

1. BSM Scenarios: Two specific "universal" models are simulated to generate pseudo-data:

   • Mirror-$U(1)_Y$: A copy of the SM hypercharge field ($X_\mu$) coupling to SM currents with strength scaled by $\beta$.
   • Mirror-$SU(2)_L$: A copy of the SM weak isospin field ($X^a_\mu$) coupling to SM currents with strength scaled by $\beta$.
     In both cases, the new gauge bosons couple dominantly to SM bosons and, if to fermions, via SM currents.

2. EFT Framework: The analysis employs USMEFT up to order $O(1/\Lambda^4)$. This requires evaluating:

   • SM contributions ($|M_{SM}|^2$).
   • Interference between SM and dimension-six amplitudes ($M^*_{SM}M^{(6)}$).
   • Squared dimension-six amplitudes ($|M^{(6)}|^2$).
   • Interference between SM and dimension-eight amplitudes ($M^*_{SM}M^{(8)}$).
     The authors utilize a "rotated basis" where bosonic operators are traded for fermionic operators via equations of motion (EOM) to facilitate Monte Carlo simulations. They identify eight effective Wilson coefficient combinations relevant for DY and Electroweak Precision Observables (EWPO) at this order.

3. Simulation and Fitting:

   • Pseudo-data is generated for DY observables and EWPOs using MadGraph5_aMC@NLO, PYTHIA8, and DELPHES, assuming an integrated luminosity of $3000 \text{ fb}^{-1}$ at $\sqrt{s}=14$ TeV.
   • Fits are performed using $\chi^2$ minimization against the pseudo-data.
   • Four analysis variants are compared to test truncation dependence:
     • $(d=6)$: Linear in dimension-six WCs.
     • $(d=6)^2$: Quadratic in dimension-six WCs.
     • $(d=8)$: Full $O(1/\Lambda^4)$ including linear dimension-eight terms.
     • $(d=8)'$: Full $O(1/\Lambda^4)$ using redefined coefficient combinations to resolve strong correlations.

Key Contributions

• Operator Basis Construction: The paper explicitly constructs the USMEFT basis up to dimension-eight for universal theories, identifying the specific linear combinations of Wilson coefficients that can be independently determined from DY invariant mass distributions.
• Matching Procedure: The authors perform tree-level matching of the Mirror-$U(1)_Y$ and Mirror-$SU(2)_L$ models to the USMEFT up to dimension-eight, deriving the specific relations between the UV parameters ($M, \beta$) and the effective WCs.
• Correlation Resolution: A significant technical contribution is the identification of a strong correlation between the dimension-six coefficient $c_{2JB}$ and the dimension-eight coefficient $c^{(7)}_{\psi4H^2}$ in the Mirror-$U(1)_Y$ scenario. The authors propose a redefinition of the coefficient basis (the "prime" combinations) to diagonalize this correlation, thereby restoring sensitivity to the dominant NP effects.

Results

• Discovery Potential: The HL-LHC is projected to achieve a $5\sigma$ discovery (or $3\sigma$ evidence) of universal NP in the Mirror-$U(1)_Y$ model for masses $M_1$ between 6–8 TeV (up to 9 TeV for evidence) and coupling $\beta \in [1.3, 1.9]$. For the Mirror-$SU(2)_L$ model, a $5\sigma$ discovery is possible for $M_2$ between 5–10 TeV and $\beta \in [0.5, 1.5]$.
• Truncation Stability: The results are found to be stable with respect to the order of EFT truncation. Fits including dimension-eight operators yield results consistent with dimension-six-only fits, though with slightly reduced precision due to the increased parameter space. The inclusion of dimension-eight terms does not obscure the discovery signal.
• Extraction of Properties: The study demonstrates that fits with minimal theoretical bias (arbitrary WCs) can accurately extract the properties of the underlying BSM model. For masses $M \gtrsim 7$ TeV, the true values of the dominant WCs (predicted by matching) fall within the $1\sigma$ allowed regions of the global fit.
• Bias vs. Unbiased Fits: The authors find that imposing the specific relations between WCs generated by the UV model (biased fit) yields results very similar to the minimal-bias fits. This suggests that the data itself is sufficient to constrain the relevant operator combinations without prior knowledge of the specific UV completion.

Significance
The paper claims that the Universal SMEFT framework, even when applied with minimal theoretical priors and extended to include dimension-eight operators, is a robust tool for both the discovery of new physics and the accurate extraction of its properties at the HL-LHC. The results indicate that the EFT approach remains valid and effective for universal scenarios where new physics couples to SM currents, even in the absence of direct resonance production. The ability to resolve strong correlations between dimension-six and dimension-eight operators through basis redefinition is highlighted as a crucial step in ensuring the reliability of EFT interpretations in the high-luminosity era.