⚛️ phenomenology

Tailored PDFs for New Physics searches

This paper evaluates strategies for selecting or fitting Parton Distribution Functions (PDFs) to ensure robust New Physics searches at the High-Luminosity LHC, comparing conservative approaches that exclude potentially contaminated high-energy data against simultaneous fits of PDFs and Standard Model Effective Field Theory (SMEFT) coefficients, with applications to Drell-Yan and top-quark pair production.

Original authors: Ella Cole, Mark N. Costantini, Elie Hammou, Luca Mantani, Francesco Merlotti, Manuel Morales-Alvarado, Maria Ubiali

Published 2026-02-25

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Ella Cole, Mark N. Costantini, Elie Hammou, Luca Mantani, Francesco Merlotti, Manuel Morales-Alvarado, Maria Ubiali

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 you are trying to listen to a very faint, new song playing on the radio. You know the song exists, but the radio signal is full of static and background noise. Your goal is to figure out exactly what the new song sounds like without getting confused by the static.

In the world of particle physics, this "new song" is New Physics (things beyond our current understanding of the universe), and the "static" is the Parton Distribution Functions (PDFs).

The Problem: The "Static" Mimics the "Song"

Particle colliders like the Large Hadron Collider (LHC) smash protons together. Protons aren't solid balls; they are bags of smaller particles called quarks and gluons. To predict what happens when they smash, physicists need a map of how these particles are arranged inside the proton. This map is the PDF.

However, there's a tricky problem:

The Map is Fuzzy: We don't know the map perfectly, especially for the most energetic collisions (the "high-energy tails").
The Deception: If a new, heavy particle (New Physics) starts appearing in these high-energy collisions, it changes the data. But because our map (the PDF) is fuzzy, the computer fitting the data might think, "Oh, I don't need a new particle to explain this weird data. I'll just tweak the map slightly to make it fit."

The paper calls this "absorption." The New Physics signal gets "absorbed" into the map, hiding itself. If you then use this "tweaked" map to look for new physics later, you won't find it because you've already blamed it on the map!

The Two Strategies: The "Safe" vs. The "Simultaneous" Approach

The authors of this paper tested two main ways to solve this problem, using a "toy model" (a simplified simulation) and then real-world scenarios involving the Drell-Yan process (creating lepton pairs) and Top Quark production.

1. The "Conservative" Approach (The Safe Filter)

The Analogy: Imagine you are trying to find a new song, but you suspect the radio static is strongest at night. So, you decide to only listen to the radio during the day to build your map of the static. Once you have a clean map from the daytime, you use it to listen to the night-time radio to find the new song.

How it works: Physicists exclude all high-energy data (where New Physics might hide) when creating the PDF map. They only use "safe," low-energy data.
The Result: This works well! It prevents the New Physics from corrupting the map. However, because you threw away a lot of data, your map is a bit fuzzier (less precise) than it could be.
The Catch: If you are too strict and throw away too much data, your map becomes so fuzzy that you can't hear the new song clearly anyway.

2. The "Simultaneous" Approach (The Juggling Act)

The Analogy: Instead of listening to the radio in two separate shifts, you try to figure out the static and the new song at the exact same time. You tell the computer: "Here is the data. Please figure out the best map of the static AND the best description of the new song simultaneously."

How it works: The computer adjusts the PDF map and the New Physics parameters together in one giant calculation.
The Result: This is the "Golden Standard." It recovers both the correct map and the correct new physics signal. It uses all the data, so the map is very precise.
The Catch: It's computationally very heavy (like juggling 100 balls at once). If you try to add too many different types of new songs (too many theories), the computer gets overwhelmed.

The Real-World Tests

The authors tested these strategies on two specific scenarios:

The Drell-Yan Sector: A scenario where a heavy "W-prime" or "Z-prime" particle might exist.
- Outcome: Both the "Safe" (Conservative) and "Juggling" (Simultaneous) methods worked perfectly. They both found the fake signal and didn't let it hide in the map.
The Top Quark Sector: A scenario involving a "Coloron" (a heavy version of a gluon) affecting top quark production.
- Outcome: The "Safe" method worked but was a bit weak (fuzzy map). The "Juggling" method was much better, finding the signal clearly. This showed that sometimes you need the high-energy data to make a good map, so you can't just throw it away.

Practical Advice: How to Spot the Deception

Since we don't know what the new physics is in real life, how do we know if our map is being tricked? The authors suggest three "detective tricks":

The Energy Cut Test: Try building your map with different "energy cutoffs." If you cut off data at 500 GeV, then 1000 GeV, then 1500 GeV, and the map keeps changing wildly, it's a red flag. It means something weird (New Physics) is hiding in the high-energy data and messing up the map.
The "Different Radio Station" Test: Compare data from different collision energies (e.g., 9 TeV vs. 14 TeV). New Physics effects grow with energy, but the map (PDF) depends on the particle's momentum fraction. If you change the energy, the "deception" should break. If the map looks weird at one energy but normal at another, you've caught the trick.
The "Cross-Check" Test: Look at different types of collisions (e.g., Top Quarks vs. Jets). A specific New Physics model might make Top Quarks look weird but make Jets look normal (or vice versa). If your map tries to fix the Top Quark data by changing the Jet predictions, you'll see a contradiction. This inconsistency reveals the hidden New Physics.

The Bottom Line

The paper concludes that simultaneous fitting (juggling the map and the new physics together) is the most powerful tool we have. It allows us to use all our data to get the most precise map while simultaneously hunting for new physics.

However, if we can't do the complex simultaneous fit, we must be careful. We should use conservative cuts (ignoring the highest energy data) to build our maps, but we must constantly check for inconsistencies using the "detective tricks" to ensure we aren't accidentally hiding the very discoveries we are looking for.

In short: Don't let the map hide the treasure. Sometimes you have to draw the map and find the treasure at the same time.

1. Problem Statement

The paper addresses a critical phenomenological challenge in high-energy physics: the degeneracy between Parton Distribution Functions (PDFs) and New Physics (NP) effects in the high-energy tails of hadron collider observables.

The Core Issue: As experimental precision increases at the High-Luminosity LHC (HL-LHC), large- $x$ PDFs (which are poorly constrained by existing data) can mimic the energy-growing signatures of Beyond-the-Standard-Model (BSM) physics.
The Risk: If PDF fitting frameworks include high-energy data that are contaminated by unaccounted NP, the PDFs may "absorb" these deviations. This leads to BSM-biased PDFs, which subsequently mask genuine NP signals in subsequent searches, resulting in false null results or incorrect constraints on Wilson coefficients.
The Dilemma: Researchers face a trade-off between:
1. Using PDFs with small uncertainties (requiring inclusion of high-energy data) but risking bias.
2. Using "conservative" PDFs (excluding high-energy data) to avoid bias, but sacrificing sensitivity due to larger uncertainties in the large- $x$ region.

2. Methodology

The authors employ a simultaneous closure-test framework to rigorously test fitting strategies. This involves generating synthetic "pseudo-data" based on a known "true" law of nature (SM + specific BSM model) and attempting to recover these parameters using different fitting methodologies.

A. Theoretical Framework

Toy Model: The study begins with an analytically tractable toy model involving two data points (low-energy for PDFs, high-energy for SMEFT) to derive the statistical behavior of separate vs. simultaneous fits.
Realistic Scenarios: Two realistic BSM scenarios are analyzed within the Standard Model Effective Field Theory (SMEFT) framework:
1. Drell-Yan (DY) Sector: A heavy $W'$ and $Z'$ boson (parameterized by $\hat{W}$ and $\hat{Y}$ ) affecting quark-antiquark luminosities.
2. Top Quark Sector: A heavy Coloron ( $G'$ ) boson (parameterized by $\hat{Z}$ ) affecting gluon-gluon luminosities and top-pair production.
Data Set: The analysis uses a synthetic dataset comprising 4,363 data points, including:
- Existing measurements from NNPDF4.0 (excluding jets to isolate top constraints).
- HL-LHC projections for high-mass DY, forward DY, and high-mass $t\bar{t}$ production.

B. Fitting Strategies Compared

The paper compares three distinct approaches:

BSM-Biased Fit: Fits PDFs to the full dataset assuming the Standard Model ( $c=0$ ). This allows PDFs to absorb NP effects.
Conservative Fit: Fits PDFs excluding all data above a specific energy cut-off ( $Q_{max}$ ) to ensure "SM safety." These PDFs are then used as fixed inputs for a separate SMEFT fit.
Simultaneous Fit: Jointly determines PDFs and SMEFT Wilson coefficients using the full dataset, allowing the parameter space to absorb correlations between PDF shifts and NP effects.

C. Diagnostic Tools

To identify biases in real-world scenarios (where the true BSM model is unknown), the authors propose:

Energy Cut-off Sensitivity: Varying $Q_{max}$ to see if PDFs and SMEFT bounds shift significantly (indicating contamination).
Center-of-Mass Energy Ratios: Comparing observables at different $\sqrt{s}$ (e.g., 9 TeV vs. 14 TeV) to break the degeneracy between Bjorken- $x$ and invariant mass $M^2$ .
Cross-Sector Consistency: Using observables from different sectors (e.g., Top vs. Dijets) that respond differently to the same BSM operator.

3. Key Contributions & Results

A. Analytic Insights (Toy Model)

BSM-Biased Fits: Produce artificially precise but shifted posteriors. The PDF uncertainty is underestimated because the fit absorbs the NP signal, leading to a systematic bias in the extracted Wilson coefficients that excludes the true theory.
Conservative Fits: Yield unbiased results but with inflated uncertainties due to the exclusion of constraining high-energy data.
Simultaneous Fits: Successfully recover both the true PDFs and the true Wilson coefficients without bias, even with a larger parameter space.

B. Drell-Yan Sector Results ( $W', Z'$ )

Absorption: In the DY sector, a BSM-biased fit completely absorbs the NP signal ( $\hat{W} \neq 0$ ) into the large- $x$ quark PDFs. The resulting SMEFT fit appears compatible with the SM, falsely excluding the true BSM model by $>5\sigma$ .
Mitigation: Both Conservative and Simultaneous fits successfully disentangle the effects.
- The Conservative fit recovers the truth but with wider error bands.
- The Simultaneous fit recovers the truth with competitive precision, demonstrating that the dataset is sufficiently constraining to handle the extra degrees of freedom.

C. Top Sector Results ( $G'$ Coloron)

Partial Absorption: In the top sector, the large- $x$ gluon absorbs the NP signal ( $\hat{Z} \neq 0$ ), but the absorption is only partial compared to the DY sector. The BSM-biased fit yields bounds that are compatible with both the SM and the true BSM model, effectively "watering down" the significance of the deviation (from $3.43\sigma$ to $1.41\sigma$ ).
Superiority of Simultaneous Fits: While the Conservative fit recovers the truth, the Simultaneous fit produces noticeably tighter bounds than the Conservative approach. This indicates that for the top sector, the constraining power of including high-mass $t\bar{t}$ data outweighs the penalty of fitting additional PDF parameters.

D. Diagnostic Recommendations

The paper validates three practical strategies to detect hidden biases:

Energy Cut-off Scan: If varying $Q_{max}$ causes the PDF luminosity or SMEFT bounds to shift systematically away from a stable value, it signals BSM contamination.
$\sqrt{s}$ Dependence: BSM-biased PDFs mimic NP at a specific $\sqrt{s}$ (e.g., 14 TeV) but fail to do so at different energies (e.g., 9 TeV), creating a visible discrepancy in ratios.
Sector Comparison: If a BSM model suppresses events in one sector (e.g., Top) but enhances them in another (e.g., Dijets), a BSM-biased PDF set will fail to describe the second sector consistently.

4. Significance and Conclusions

Robustness of Simultaneous Fits: The study concludes that simultaneous PDF-SMEFT fits are the most robust and generally preferred method. They avoid the model-dependent choice of energy cut-offs and utilize the full constraining power of the data, often yielding tighter constraints than conservative approaches (especially in the top sector).
Limitations of Conservative Fits: While conservative fits are safe, they rely on older data and extrapolations, leading to larger uncertainties. Their performance degrades if multiple sectors require exclusion.
Diagnostic Necessity: Since BSM-biased fits often maintain good $\chi^2$ values (making them hard to distinguish from valid SM fits), the proposed diagnostic tools (energy cuts, $\sqrt{s}$ ratios, cross-sector checks) are essential for experimental collaborations to validate their PDF inputs.
Future Outlook: The authors emphasize the need to integrate these strategies into global combinations (like PDF4LHC) and to apply them to real experimental data, particularly in the jet sector where BSM effects are most likely to be absorbed.

In summary, the paper provides a comprehensive roadmap for the HL-LHC era, demonstrating that while conservative strategies offer a safety net, simultaneous determination of PDFs and EFT coefficients is the superior path for maximizing sensitivity to New Physics without introducing hidden biases.