⚛️ phenomenology

PDF effects in high-mass Drell-Yan SMEFT analyses across flavour space

This paper demonstrates that profiling parton distribution functions (PDFs) in high-mass Drell-Yan SMEFT analyses induces a strongly flavor-dependent degradation of sensitivity, with the most significant impacts occurring for operators involving first-generation quarks due to correlations with high- $x$ valence luminosities, while angular information offers a crucial handle to mitigate these degeneracies.

Original authors: David Marzocca, Manuel Morales-Alvarado

Published 2026-07-10

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: David Marzocca, Manuel Morales-Alvarado

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

Imagine the Large Hadron Collider (LHC) as the world's most powerful particle microscope. Scientists smash protons together to look for tiny, invisible cracks in the Standard Model—the rulebook of physics. One of the best ways to peek at these cracks is to watch what happens when protons collide and spit out pairs of heavy electrons or muons (dileptons) at incredibly high speeds. This is called "High-Mass Drell-Yan" production.

Think of the protons not as solid balls, but as fuzzy bags of smaller particles called quarks and gluons. To predict exactly what happens when they smash, physicists need a map of how these fuzzy particles are distributed inside the bag. This map is called a Parton Distribution Function (PDF).

The Great Mix-Up: New Physics vs. Fuzzy Maps

The paper tackles a tricky problem: How do we know if a weird signal is a brand-new particle (New Physics) or just a mistake in our map (PDF uncertainty)?

Imagine you are trying to find a hidden treasure (New Physics) in a forest. But your map of the forest (the PDF) is a little blurry in the deep, dark corners. If you see a strange shape in the distance, is it the treasure, or just a trick of the light caused by the blurry map?

In the past, scientists often treated the map as perfect and fixed. They would say, "If the data doesn't match the map, it must be New Physics!" But this paper argues that's risky. If the map is actually blurry, that "New Physics" might just be us adjusting the map to fit the data.

The Main Discovery: It Depends on Who You Ask

The authors, David Marzocca and Manuel Morales-Alvarado, ran a massive simulation to see what happens when they let the map wiggle around while looking for New Physics. They tested different "flavors" of New Physics, which are like different types of invisible hands pushing the particles.

Here is the big surprise they found: The confusion between the map and the treasure depends entirely on which type of quark is involved.

The "First-Generation" Trouble: When the New Physics involves the lightest, most common quarks (up and down quarks, the "first generation"), the confusion is huge.
- The Analogy: Imagine trying to find a specific type of bird in a forest where that bird is the most common one. If your map of where the birds usually hang out is slightly off, you might think you found a rare, magical bird when you actually just miscounted the common ones.
- The Result: In their simulations, when they allowed the map to wiggle, the limits on these first-generation effects got much worse. For some operators, the uncertainty range (the "search area") grew by 100% to 131% at the future High-Luminosity LHC (HL-LHC). It's like your search area doubling in size because you can't be sure if the map or the bird is the problem.
The "Heavy" Quarks are Easier: When the New Physics involves heavier, rarer quarks (like charm or bottom quarks), the confusion is much smaller.
- The Analogy: These heavy quarks are like rare, exotic birds that don't hang out in the main forest. Since they aren't the main focus of the map's "blurry" areas, it's easier to tell if you see a real exotic bird or just a map error.
- The Result: The uncertainty only grew by about 30% to 50% in the simulations. The map's wiggles didn't hide the treasure as well.

The Magic Angle: A New Tool

The paper also suggests a clever trick to solve this mix-up: Look at the angles!

When particles fly out, they don't just go straight; they scatter at different angles. The paper shows that New Physics often changes the angle of the particles in a specific way, while the map errors (PDFs) don't care about angles—they just change the total number of particles.

The Analogy: Imagine the New Physics is a wind that pushes the birds to the left, while the blurry map just makes you think there are more birds in general. If you only count the birds, you get confused. But if you look at which way they are facing, you can tell the difference between the wind and the map error.
The Result: By keeping the angle information separate (instead of squashing it all together), the scientists found they could shrink the "search area" significantly. It acts like a super-sharp lens that separates the signal from the noise.

What They Ruled Out (and What They Didn't)

They did NOT say: "We found New Physics!" or "The map is useless."
They explicitly showed: That ignoring the map's wiggles (fixing the PDFs) gives you a false sense of security. If you don't let the map wiggle, you think you have a very tight grip on the New Physics, but in reality, the map could be hiding a huge range of possibilities.
They did NOT prove: That New Physics exists. They only simulated how hard it would be to find it. Their results are based on simulations of current data and projections for the future HL-LHC (which will run with 6 ab⁻¹ of data).
They did NOT suggest: That we should stop looking at heavy quarks. In fact, they showed that heavy quarks are actually less affected by these map errors, making them potentially cleaner places to look for certain types of new physics.

The Bottom Line

This paper is a warning label for future experiments. It suggests that as we get more data from the LHC (specifically the High-Luminosity phase), the "fuzziness" of our proton maps will become the biggest obstacle to finding new physics, but only if we are looking at the common, light quarks.

If we want to find the treasure, we can't just stare at the total number of particles. We need to:

Let our maps wiggle and admit they aren't perfect.
Pay extra attention to the angles the particles take.
Understand that some types of new physics are much harder to spot than others because they hide in the "blurry" parts of the map.

The authors conclude that we must treat these uncertainties differently depending on the "flavor" of the physics we are hunting. It's not a one-size-fits-all problem; it's a flavor-dependent mystery.

Technical Summary: PDF Effects in High-Mass Drell-Yan SMEFT Analyses Across Flavour Space

Problem Statement
High-mass Drell-Yan (DY) dilepton production at the LHC serves as a primary probe for semileptonic four-fermion operators within the Standard Model Effective Field Theory (SMEFT). These processes are sensitive to new physics due to the energy growth of interference terms ( $E^2/\Lambda^2$ ). However, these measurements also constrain Parton Distribution Functions (PDFs) in the poorly known large- $x$ region. A critical ambiguity arises because variations in PDFs and SMEFT effects can both produce smooth distortions in the high-mass dilepton spectra. While previous studies have addressed the interplay between PDFs and SMEFT in specific benchmark scenarios or through full simultaneous fits, the dependence of this interplay on the specific quark-flavour structure of the effective operators remains an open question. Specifically, it is unclear how the degradation of SMEFT sensitivity due to PDF profiling varies across different quark generations and chiral structures.

Methodology
The authors perform a joint fit of SMEFT Wilson coefficients and PDF nuisance parameters to quantify the impact of PDF profiling on flavour-dependent constraints.

Experimental Data: The analysis utilizes the CMS search for resonant and non-resonant new phenomena in high-mass dilepton final states at $\sqrt{s} = 13$ TeV (Run-II, 2016–2018). The dataset includes 137 fb $^{-1}$ (dielectron) and 140 fb $^{-1}$ (dimuon). The observable is a two-dimensional binned distribution in dilepton invariant mass ( $m_{\ell\ell}$ ) and the Collins-Soper scattering angle ( $\cos \theta^*$ ), restricted to regions $\cos \theta^* < 0$ and $\cos \theta^* \geq 0$ . High-luminosity (HL-LHC) projections are constructed by rescaling current yields to 14 TeV and 6 ab $^{-1}$ , preserving the binning and correlated systematic structure.
Theoretical Framework: The study focuses on dimension-six semileptonic operators in the Warsaw basis that induce tree-level corrections growing as $E^2/\Lambda^2$ and interfere with the SM amplitude. The analysis considers 18 independent operators for each charged-lepton flavour, excluding top-quark contributions. The cross-section calculation includes linear and quadratic SMEFT terms ( $|A_{SM} + A_{dim6}|^2$ ).
PDF Treatment: To avoid circularity (where the data used for the SMEFT fit is also used to determine the PDF prior), the authors adopt the "DIS+DY (no HM)" PDF set from Ref. [11], which excludes high-mass DY data. This Monte Carlo replica set is converted into a Hessian representation using the MC2Hessian method. The PDF uncertainty is encoded via nuisance parameters $\lambda_\alpha$ representing orthogonal Hessian directions.
Statistical Analysis: A profile likelihood approach is employed. The test statistic $\chi^2$ includes terms for the SMEFT coefficients, PDF nuisance parameters, and experimental systematic uncertainties (modeled via log-normal nuisance parameters). Constraints are derived by profiling over both PDF and experimental nuisance parameters. The "broadening factor" is defined as the relative increase in the 95% CL interval width when PDFs are profiled compared to when they are fixed.

Key Contributions and Results

Flavour-Dependent Degradation of Sensitivity:
The primary finding is that the impact of PDF profiling on SMEFT constraints is strongly flavour-dependent.
- First-Generation Quarks: Operators involving first-generation quarks (u, d) exhibit the largest degradation. With current data, the broadening is typically $\sim 10\%$ , rising to $\sim 100\%$ (a factor of 2) in HL-LHC projections. This is attributed to the strong correlation between these operators and the high- $x$ valence quark luminosities ( $u\bar{u}, d\bar{d}$ ), which dominate the high-mass spectrum.
- Heavier Flavors: Operators involving second- and third-generation quarks show significantly smaller broadenings (few percent with current data, $\sim 50\%$ at HL-LHC). Their parton luminosities are not valence-enhanced in the relevant kinematic region, reducing the degeneracy with PDF variations.
- Specific Variations: There is operator-dependent variability. For instance, $C_{lu}^{[\ell\ell11]}$ shows a 46% broadening with current data due to the interplay between interference and quadratic terms, whereas $C_{ed}^{[\ell\ell11]}$ shows negligible broadening due to accidental cancellations.
Impact on PDF Posteriors:
The analysis quantifies the reverse effect: how profiling SMEFT coefficients degrades the constraints on PDFs. In the Lepton Flavour Universal (LFU) scenario, profiling SMEFT coefficients leads to a substantial broadening of the posterior PDF uncertainties, particularly for the $u\bar{u}$ luminosity (up to a factor of 3 in the large invariant-mass region). This broadening is roughly twice as large in the general LFU scenario compared to the flavour-universal $(W, Y)$ parameter scenario, indicating that a broader set of quark-flavour structures opens more directions for SMEFT-PDF degeneracy.
Role of Angular Information:
The inclusion of angular information ( $\cos \theta^*$ ) is shown to be a crucial handle for reducing degeneracies.
- In one-parameter fits with fixed PDFs, merging angular bins has a modest effect.
- However, when PDFs are profiled, angular information significantly improves sensitivity. It helps distinguish SMEFT effects (which have specific chirality-dependent angular dependencies) from PDF deformations (which are chirality-independent).
- For operators where interference dominates (e.g., first-generation), merging angular bins can create flat directions in the likelihood that are lifted by including angular bins.
Universal vs. Flavour-General Scenarios:
- In the universal $(W, Y)$ scenario, the broadening is moderate with current data but becomes severe at the HL-LHC (e.g., 104% for $W$ , 131% for $Y$ ).
- In the fully flavour-general scenario (lifting the LFU assumption), the broadening is generally smaller than in the LFU case. This is because PDF variations are universal in lepton flavour, while non-LFU SMEFT directions are not aligned with these variations, allowing the lepton-flavour ratio to act as a discriminator.

Significance
The paper demonstrates that the relevance of PDF uncertainties in high-energy SMEFT fits is not uniform across flavour space. The degradation of sensitivity is most severe for operators involving first-generation quarks, which are precisely the channels most sensitive to high-mass DY data. Consequently, PDF uncertainties must be assessed in a flavour-dependent manner rather than assuming a uniform impact. The study validates that profiling a Hessian PDF nuisance basis captures the dominant PDF variability relevant for these fits. Furthermore, it highlights that angular information is essential for disentangling SMEFT effects from PDF deformations, particularly in the high-luminosity regime where statistical uncertainties are reduced and systematic/PDF uncertainties become dominant. The authors conclude that future analyses should implement finer binning and include charged-current channels to further test these operator structures.

The Great Mix-Up: New Physics vs. Fuzzy Maps

The Main Discovery: It Depends on Who You Ask

The Magic Angle: A New Tool

What They Ruled Out (and What They Didn't)

The Bottom Line

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