⚛️ phenomenology

Further Reduction of the PDF Uncertainty in the High-Mass Drell-Yan Spectrum Utilizing Neutral and Charged Current Inputs

This paper updates a previously proposed strategy by incorporating charged current Drell-Yan final states alongside neutral current inputs to significantly reduce Parton Distribution Function uncertainties in high-mass Drell-Yan spectra, thereby enhancing the sensitivity of Beyond the Standard Model searches at the LHC.

Original authors: Yao Fu, Raymond Brock, Daniel Hayden, Chien-Peng Yuan

Published 2026-01-27

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CC BY 4.0

Original authors: Yao Fu, Raymond Brock, Daniel Hayden, Chien-Peng Yuan

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 Big Picture: Finding a Needle in a Haystack

Imagine the Large Hadron Collider (LHC) is a giant, high-speed car crash simulator. Scientists smash protons together to see if they can find evidence of "new physics"—particles that don't exist in our current rulebook (the Standard Model).

The problem is that these crashes produce a massive amount of "noise" (standard particles) that looks very similar to the "signal" (new particles). To find the new stuff, scientists need to know exactly how much "noise" to expect. If they guess wrong about the noise, they might think they found a new particle when they didn't, or they might miss a real one.

This paper is about reducing the guesswork regarding that noise.

The Problem: The "Recipe" is Vague

To predict the noise, scientists use something called Parton Distribution Functions (PDFs). Think of a PDF as a recipe for the inside of a proton. It tells you the probability of finding a specific ingredient (like an "up" quark or a "down" quark) at a specific speed.

The Issue: For decades, this recipe was written based on old experiments from the 1980s and 90s.
The Gap: The LHC is now smashing particles at speeds (energies) much higher than those old experiments ever reached. It's like trying to bake a cake for a giant using a recipe written for a tiny cupcake. The ingredients might behave differently at those high speeds, but the old recipe doesn't say how.
The Result: Because the recipe is vague for these high speeds, the "uncertainty" (the margin of error) in predicting the background noise is huge. This uncertainty is currently the biggest thing stopping scientists from confidently claiming they found new physics.

The Solution: A "Boutique" Recipe

The authors (Yao Fu, Raymond Brock, Daniel Hayden, and Chien-Peng Yuan) propose a clever strategy to update the recipe specifically for the high-speed crashes the LHC is doing right now.

Instead of waiting for a global team to rewrite the whole recipe from scratch, they suggest creating a "boutique" recipe. This is a specialized version of the PDF that is fine-tuned using the LHC's own data, but only from a "safe" zone where we know no new physics exists yet.

The Analogy:
Imagine you are trying to predict traffic patterns on a highway during rush hour.

Old Method: You use data from a small, quiet country road from 30 years ago. You guess the highway traffic, but your guess is very shaky because the conditions are totally different.
New Method: You set up cameras on the highway, but only in the section where traffic is flowing smoothly (no accidents, no new roads). You use that fresh, high-quality data to create a specific traffic model for the highway. Now, when you look at the section where you expect an accident (the search for new physics), your prediction is much sharper.

How They Did It: Two Types of Clues

The paper looks at two different types of particle collisions to build this better recipe:

Neutral Current (The "Z" Search): Two particles collide and produce two charged particles (like an electron and a positron).
- The Trick: The authors realized that by looking at not just the energy, but also the angle at which the particles fly out, they can separate the "up" quarks from the "down" quarks much better. It's like listening to a choir; if you know exactly where each singer is standing and how they are facing, you can hear the "up" voices much more clearly than the "down" voices.
Charged Current (The "W" Search): Two particles collide and produce a charged particle and a "ghost" (a neutrino that disappears).
- The Trick: By analyzing the "missing energy" and the angle of the visible particle, they can get a better handle on the "down" quarks, which were previously very hard to pin down.

The Results: Sharper Vision

By feeding this new, high-precision data into their "boutique" recipe, the authors found they could drastically shrink the margin of error.

Before: At very high energies (where new physics might hide), the uncertainty was around 20% to 30%. It was like looking at a blurry photo.
After: With their new strategy, the uncertainty drops to 2% to 5%. It's like switching to a high-definition camera.

They show that this works for both the "future" data (High Luminosity LHC, which will run for many years) and even the "current" data (Run 3, which is happening right now).

The Bottom Line

The paper argues that we don't need to wait for a miracle to find new physics. We just need to use the data we already have (and will soon have) to create a much more precise map of the "background noise."

By using a smart selection of data points—specifically looking at the angles and energies of particles in the "safe" zones—the authors can create a specialized tool that reduces the uncertainty by a factor of 4 to 7. This makes the search for new, heavy particles (like a new version of the Z or W boson) much more sensitive and reliable.

In short: They found a way to clean up the static on the radio so we can finally hear the new music clearly.

Technical Summary: Further Reduction of the PDF Uncertainty in the High-Mass Drell-Yan Spectrum Utilizing Neutral and Charged Current Inputs

Problem Statement
Searches for Beyond the Standard Model (BSM) physics at the Large Hadron Collider (LHC), specifically for high-mass Intermediate Vector Bosons (IVBs) such as $Z'$ and $W'$ , are increasingly limited by systematic uncertainties rather than statistical ones. Among these, uncertainties in the parametrization of Parton Distribution Functions (PDFs) have become a dominant constraint. Current global PDF fits (e.g., CT18) rely heavily on Deep Inelastic Scattering (DIS) and fixed-target data from the 1980s and 1990s. These inputs poorly constrain the quark and anti-quark momentum fractions ( $x$ ) in the high- $x$ region ( $x \gtrsim 0.2$ ) relevant for high-mass Drell-Yan (DY) processes at $\sqrt{s} = 13$ TeV and beyond. Consequently, theoretical uncertainties in the Standard Model (SM) background predictions for high-mass dilepton ( $m_{\ell\ell}$ ) and transverse mass ( $m_T$ ) spectra remain large (often exceeding 20–30% at multi-TeV scales), severely compromising the sensitivity of resonance searches and Effective Field Theory (EFT) limits.

Methodology
The authors propose and implement a strategy to generate specialized, "boutique" PDF sets tailored to reduce uncertainties in specific BSM search regions. This approach utilizes the ePump framework to re-fit existing PDF ensembles (specifically CT18) by incorporating high-statistics "pseudo-data" templates derived from LHC measurements.

The core methodology involves:

Template Generation: Using the ResBos2 Monte Carlo generator (operating at N $^3$ $^{3}$ LL+NNLO accuracy) to simulate SM Drell-Yan processes.
- Neutral Current (NC): Triple-differential cross-sections ( $d^3\sigma/dm_{\ell\ell}d|y_{\ell\ell}|d\cos\theta^*$ ) are generated for the region $40 < m_{\ell\ell} < 1000$ GeV. The inclusion of the Collins-Soper angle ( $\cos\theta^*$ ) is critical, as it allows for the separation of up-type and down-type quark contributions, which exhibit distinct angular dependencies.
- Charged Current (CC): Double-differential cross-sections ( $d^2\sigma/dm_T d|y_{\ell}|$ ) are generated for $W^\pm$ production in the region $m_T < 500$ GeV. The strategy distinguishes between $W^+$ and $W^-$ final states to separately constrain $u/\bar{d}$ and $d/\bar{u}$ parton densities.
Fitting Strategy: These pseudo-data templates, assuming integrated luminosities of 600 fb $^{-1}$ (partial Run 3) and 6000 fb $^{-1}$ (High-Luminosity LHC), are fed into ePump alongside the baseline CT18 templates. This creates updated PDF sets where the high- $x$ uncertainties are constrained by the high-statistics LHC data in the low-to-intermediate mass regions, effectively extrapolating constraints to the high-mass search regions.
Validation: The resulting "boutique" PDF sets are used to recalculate background uncertainties for the high-mass search regions ( $m_{\ell\ell} > 1$ TeV and $m_T > 1$ TeV) to quantify the reduction in systematic error.

Key Contributions

Integration of Charged Current Inputs: While previous work (Phys. Rev. D99, 054004) focused on NC inputs, this paper expands the strategy to include CC Drell-Yan final states. This is significant because $W^\pm$ production provides complementary constraints on down-type quarks and anti-quarks, which are less constrained by NC data alone.
Granularity of Kinematic Variables: The paper demonstrates that moving from 1-dimensional ( $m_{\ell\ell}$ ) to 2-dimensional ( $m_{\ell\ell}, y_{\ell\ell}$ ) and finally to 3-dimensional ( $m_{\ell\ell}, y_{\ell\ell}, \cos\theta^*$ ) inputs yields progressively larger reductions in PDF uncertainty. The angular dependence is shown to be the primary driver for separating valence quark flavors at high $x$ .
Quantification of Run 3 Potential: The study calculates the impact of partial Run 3 data (600 fb $^{-1}$ ), demonstrating that significant improvements are achievable without waiting for the full HL-LHC dataset.

Results
The application of this strategy yields substantial reductions in PDF-induced systematic uncertainties for high-mass backgrounds:

Neutral Current ( $Z'$ Search): For a dilepton invariant mass $m_{\ell\ell} > 4$ TeV, the PDF uncertainty is reduced from 22.2% (CT18 baseline) to 3.5% using the combined NC+CC strategy with 6000 fb $^{-1}$ of data. Even with partial Run 3 data (600 fb $^{-1}$ ), the uncertainty drops from 22.2% to 7.7%.
Charged Current ( $W'$ Search): For transverse mass $m_T > 5$ TeV, the uncertainty is reduced from 33.0% (CT18) to 8.0% (NC+CC, 6000 fb $^{-1}$ ). With partial Run 3 data, it improves from 33.0% to 17.2%.
Flavor Separation: The results show distinct improvements for specific parton densities. The inclusion of $W^+$ data significantly tightens constraints on the $u$ and $\bar{d}$ distributions, while $W^-$ data improves constraints on $d$ and $\bar{u}$ . The $L^2$ sensitivity analysis confirms that the proposed strategy targets the specific kinematic region ( $x \sim 0.2-0.3$ , $Q \sim 3$ TeV) previously unconstrained by global fits.

Significance
The paper claims that this strategy offers a viable path to overcome the current systematic ceiling in high-mass BSM searches. By leveraging the huge statistical precision of LHC datasets (both current Run 3 and future HL-LHC) to constrain the PDFs in the relevant kinematic regime, the authors argue that the theoretical uncertainty in SM backgrounds can be reduced by factors of 3 to 7. This reduction is essential for:

Enhancing the discovery potential for resonant $Z'$ and $W'$ states.
Improving the sensitivity of non-resonant searches using Effective Field Theory (EFT) at very high masses.
Providing a framework where LHC experiments can directly contribute to the refinement of global PDF fits through the provision of multi-dimensional differential cross-section grids.

The authors conclude that the LHC experiments should provide these specific differential grids to PDF fitting groups to enable the creation of these specialized PDF sets, thereby maximizing the physics reach of the collider.