⚛️ phenomenology

On the Role of Diffractive Production in Precision Studies of W and Z Bosons at the LHC

This paper estimates the impact of single-diffractive W and Z boson production on LHC precision measurements, finding that while these contributions induce small shifts in $\alpha_s$ and the W mass, they remain below the relevant fit precision and are not expected to significantly affect phenomenological results within the tested models.

Original authors: Ynyr Harris, Matthias Schott, Chen Wang

Published 2026-10-01

📖 4 min read🧠 Deep dive

CC BY 4.0

Original authors: Ynyr Harris, Matthias Schott, Chen 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 authors. For technical accuracy, refer to the original paper. Read full disclaimer

At the Large Hadron Collider, a massive machine buried beneath the border of France and Switzerland, scientists smash protons together at nearly the speed of light to recreate the conditions of the early universe. When these particles collide, they often produce heavy, unstable particles called W and Z bosons, which act as carriers of the weak nuclear force. For decades, physicists have treated these collisions as if they were simple, direct hits between two tiny billiard balls, assuming that the resulting particles fly out from a single, chaotic center. However, nature is rarely so straightforward. Sometimes, the protons do not shatter completely; instead, they graze past each other, exchanging a ghostly, invisible force that leaves one proton intact while the other breaks apart. This process, known as diffraction, creates a distinct signature: a large, empty gap in the spray of debris where no other particles appear. While this phenomenon has been known for years, its subtle influence on the most precise measurements in particle physics has remained a lingering question.

The quest for extreme precision is the driving force behind modern particle physics. Scientists are no longer just looking for new particles; they are measuring the properties of known ones with such exactness that even the tiniest deviation could reveal new laws of nature. Two of the most critical measurements involve the mass of the W boson and the strength of the strong nuclear force, a fundamental constant that governs how quarks stick together. To measure these with the required accuracy, researchers rely on detailed computer models that predict exactly how the debris from a collision should look. If the models are slightly wrong, the final numbers will be wrong, potentially hiding a discovery or creating a false one. The concern is that if a small fraction of these collisions actually involves the "grazing" diffraction process, and if the models ignore it, the resulting data could be skewed in a way that is hard to detect.

In a recent study, researchers set out to quantify exactly how much this overlooked diffraction process might be distorting these high-precision measurements. They focused on single-diffractive events, where one proton remains intact and the other produces the W or Z boson, leaving a large empty space in the detector. The team built a sophisticated simulation that combined the best available theories for standard collisions with specific models for these diffractive events. They had to account for a tricky reality: the empty gap created by diffraction is often filled in by random, soft interactions between the leftover parts of the protons, effectively destroying the signature. The researchers used dynamic models to estimate how often these gaps survive and how often they are filled, creating a realistic picture of what the detectors actually see.

The results of this investigation were reassuring for the precision of current and future experiments. The team found that while diffractive events do occur, their impact on the measurement of the strong coupling constant is minuscule, shifting the value by less than one hundredth of a percent across the different energy levels tested. More importantly, when they looked at the mass of the W boson, the potential error introduced by ignoring these events was found to be less than 1.58 MeV. Even after applying corrections to account for the specific models used, the remaining error stayed below 1.14 MeV. To put this in perspective, the current experimental uncertainty in measuring the W boson mass is roughly 10–20 MeV, meaning the effect of diffraction is well below the threshold of what can currently be measured.

The study concludes that for the specific models tested, the assumption that all W and Z bosons come from standard, non-diffractive collisions remains a safe approximation for the most precise measurements. The bias introduced by the ignored diffractive events is simply too small to matter at the current level of experimental precision. However, the authors caution that this is a first estimate based on existing theoretical models, and the true uncertainty of the diffraction process itself is not yet fully mapped. As the Large Hadron Collider moves toward even higher precision in the coming years, dedicated measurements of these rare diffractive events will be necessary to fully validate the models and ensure that no subtle biases remain hidden in the data. For now, the physics community can proceed with confidence, knowing that the ghostly grazing collisions are not the source of the tiny discrepancies they are hunting for.

Technical Summary: The Role of Diffractive Production in Precision Studies of W and Z Bosons at the LHC

Problem Statement
As the Large Hadron Collider (LHC) transitions from discovery-driven searches to high-precision measurements of Standard Model parameters (such as the $W$ boson mass, $m_W$ , and the strong coupling constant, $\alpha_s$ ), the theoretical description of underlying processes must match experimental precision. Current precision analyses typically assume that vector boson production arises entirely from hard, non-diffractive partonic scattering. However, single-diffractive (SD) production, characterized by the exchange of a color-singlet object (pomeron) and the presence of a large rapidity gap, contributes to inclusive samples. While the SD fraction is small (percent level), its kinematic properties differ from non-diffractive (ND) production: the forward proton carries away beam momentum, reducing the effective center-of-mass energy of the hard subprocess and resulting in a systematically softer boson transverse momentum ( $p_T$ ) spectrum. If unmodeled, this component could distort the inferred distributions and bias the extracted physics parameters, particularly given that current $m_W$ uncertainties are in the 10–20 MeV range, with future High-Luminosity LHC (HL-LHC) goals aiming for $\delta m_W < 10$ MeV.

Methodology
The authors present a quantitative estimate of the impact of single-diffractive $W$ and $Z$ boson production on high-precision observables at $\sqrt{s} = 5, 7, 8,$ and $13$ TeV. The study employs a hybrid approach combining high-precision perturbative calculations with phenomenological Monte Carlo (MC) simulations:

Baseline Calculation: The non-diffractive baseline is calculated using DYTurbo, a state-of-the-art generator combining resummed and matching contributions up to order $\alpha_s^3$ . This provides a high-numerical-precision cross-section used for both the baseline and the reweighting of the diffractive spectrum.
Diffractive Modeling: Single-diffractive and non-diffractive vector-boson samples are generated using Herwig. The ratio of these cross-sections provides the relative SD normalization, while their differential distributions define the distinct boson- $p_T$ shape.
Gap Survival Probability: To account for the suppression of diffractive events due to soft spectator interactions (which fill the rapidity gap), the authors utilize a dynamic, $p_T$ -dependent rapidity-gap survival probability ( $\langle S^2 \rangle$ ) calculated with Pythia8 using its multiparton-interaction model. This factor is applied bin-by-bin rather than as a constant.
Pseudo-Data Construction: A "diffractive Asimov spectrum" is constructed by deterministically reweighting the high-precision DYTurbo cross-section bin-by-bin using the Herwig SD/ND shape ratio and the Pythia8 survival factor.
Model Variations: Five distinct configurations of Pythia8 Pomeron-flux and diffractive Parton Distribution Functions (DPDFs) are tested (including MBR, H1 2006 Fit A/B, and GKG18) to assess modeling dependence.
Analysis:
- $\alpha_s$ Extraction: Fits are performed on the $Z$ -boson $p_T$ spectrum ( $0 < p_T < 25$ GeV) using a profiled likelihood approach where non-perturbative parameters ( $g_1, q$ ) and $\alpha_s$ are varied.
- $m_W$ Determination: Fits are performed on $W \to e\nu$ events using transverse mass ( $m_T$ ), charged-lepton $p_T$ , and neutrino $p_T$ distributions. The study compares a nominal fit (assuming pure ND) against a pseudo-data fit containing the survived-SD contribution, and subsequently applies a model-matched template correction derived from the $Z$ -boson fit.

Key Contributions and Results

Impact on $\alpha_s$ : The inclusion of survived single-diffractive production induces small, energy-dependent negative shifts in the extracted value of $\alpha_s$ $α_{s}$ .
- At 5, 7, 8, and 13 TeV, the nominal relative shifts are $-0.0072\%$ , $-0.043\%$ , $-0.070\%$ , and $-0.067\%$ , respectively.
- The maximum spread among the five tested survival configurations is $9.4 \times 10^{-6}$ in $\Delta \alpha_s$ .
Impact on $m_W$ : The study quantifies the bias introduced by unmodeled SD production and the residual bias after applying a correction.
- Raw Bias: The largest bias from an unmodeled survived-SD contribution is 1.58 MeV (occurring in the 5 TeV charged-lepton $p_T$ fit with the H1 Fit B configuration).
- Residual Bias: After applying the corresponding model-matched template correction (derived from the $Z$ -boson fit), the largest residual bias is 1.14 MeV (occurring in the 13 TeV neutrino $p_T$ fit with the GKG18 Fit A configuration).
- Transverse Mass: The $m_T$ fits are essentially unaffected, with a maximum raw displacement of 0.043 MeV and a maximum corrected residual of 0.023 MeV.
Uncertainties: The propagated uncertainty from the finite Pythia8 survival sample is small (maximum 0.044 MeV). The shifts are well below the statistical precision of the simulated fits (3–10 MeV) and current experimental uncertainties.

Significance and Claims
The paper concludes that within the tested models, the impact of single-diffractive production on precision measurements of $m_W$ and $\alpha_s$ is not phenomenologically significant. The observed shifts are smaller than the current and projected experimental uncertainties. Specifically, the authors state that "no phenomenologically significant impact on $m_W$ is expected within the tested models."

However, the authors maintain a modest stance regarding the completeness of their uncertainty estimation. They note that varying the Pomeron flux and DPDFs does not constitute a complete uncertainty on the process- and scale-dependent survival probability. Consequently, they assert that dedicated measurements of the $Z$ -boson transverse-momentum spectrum in diffractive-enriched samples are necessary to constrain the survival probability, validate the modeling, and fully control this contribution in future precision measurements. The work serves as a first quantitative estimate, establishing that while the effect is small, the methodology for assessing it is robust.

Technical Summary: The Role of Diffractive Production in Precision Studies of W and Z Bosons at the LHC

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