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Precision luminosity measurement in proton-proton collisions at a center-of-mass energy of 13 TeV with the CMS detector at the Large Hadron Collider

The CMS collaboration reports a landmark integrated luminosity measurement for 13 TeV proton-proton collisions at the LHC with a record-breaking precision of 0.73%, achieved by calibrating multiple monitors and validating them against Z boson production rates, thereby establishing a crucial sub-percent baseline for testing the Standard Model and future High-Luminosity LHC physics.

Original authors: CMS Collaboration

Published 2026-06-26

📖 4 min read🧠 Deep dive

CC BY 4.0

Original authors: CMS Collaboration

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) at CERN as the world's most powerful particle smasher. Its job is to crash tiny particles (protons) together at nearly the speed of light to see what new things pop out. But to know if you've discovered something new, you need to know exactly how many crashes happened.

This paper is about the CMS experiment's masterful job of counting those crashes. They call this count the "integrated luminosity." Think of it like the "odometer" on a car. If you want to know how much wear and tear a car has, you look at the miles driven. In particle physics, the "miles" are the number of collisions, and the "odometer" is the luminosity.

Here is the simple breakdown of what they did and why it matters:

1. The Problem: Counting the Unseeable

You can't just put a clicker in the middle of the collision zone and count "one, two, three." The collisions happen too fast and the environment is too chaotic. Instead, the scientists use a clever trick:

They watch a specific, well-understood event (like a Z boson, which is a heavy particle that acts like a reliable "ticker tape").
They count how many of these Z bosons appear.
They use a math formula to turn that count into a total number of collisions.

But to do this accurately, they first need to calibrate their "counting machines" (detectors) against a known standard.

2. The Calibration: The "Van der Meer" Dance

To calibrate their detectors, the scientists performed a special routine called a Van der Meer (vdM) scan. Imagine two groups of people (the particle beams) walking toward each other in a hallway.

Normally, they walk right down the middle and bump into each other.
For the calibration, the scientists slowly slide the two groups apart, side-to-side and up-and-down, like two dancers slowly separating.
As they separate, the number of bumps (collisions) drops. By measuring exactly how the "bump rate" drops as they move apart, the scientists can calculate the exact size and shape of the "crowds" (the particle bunches).

This allows them to figure out the "visible cross-section"—a fancy way of saying, "How efficient is our detector at seeing these bumps?"

3. The Challenges: The "Noise" and the "Drift"

The paper details how they cleaned up the data to get a precision never seen before (0.73% uncertainty). They had to fix several "glitches":

The Ghosts and Satellites: Sometimes, the particle beams have "ghost" particles (empty spots that look like they have stuff) or "satellite" particles (stragglers hanging around the edges). The team had to subtract these false signals so they didn't inflate the count.
The Magnetic Drift: The giant magnets guiding the beams aren't perfect. Over time, the beams can drift slightly off their intended path, like a car slowly pulling to the left. The scientists had to measure this drift with micrometer precision and correct for it.
The "Fat" Beams: The paper explains that the particle bunches aren't perfectly round or uniform. Sometimes they are "squashed" or "stretched" by their own electromagnetic fields (like two magnets repelling each other). The team had to model these distortions to ensure they weren't miscounting the collisions.
Detector Aging: The detectors themselves get tired. After a year of being bombarded by radiation, they become slightly less sensitive (like a camera sensor getting dusty). The team tracked this "aging" and adjusted the numbers to keep the count accurate.

4. The Result: A New Gold Standard

By combining data from four different types of detectors (some counting particles, some measuring energy, some looking at tracks) and cross-checking them against each other, the team achieved a total precision of 0.73%.

Why is this a big deal?

Sub-Percent Precision: They crossed the "sub-percent" threshold. This means their "odometer" is accurate to within less than 1%.
The Best Ever: This is the most precise luminosity measurement ever achieved at a hadron collider (a machine that smashes protons).
The Z-Boson Check: To prove they were right, they checked their count against the rate of Z boson production. It matched perfectly, confirming their calibration was solid.

The Bottom Line

This paper doesn't discover a new particle. Instead, it refines the ruler used to measure all discoveries. By making the ruler more precise, the CMS experiment ensures that when they say, "We saw a deviation from the theory," they are absolutely sure it's a real discovery and not just a mistake in the counting. This sets a new, incredibly high standard for the future of particle physics.

Technical Summary: Precision Luminosity Measurement in Proton-Proton Collisions at 13 TeV with the CMS Detector

Problem Statement
Discovering new fundamental physics requires detecting subtle deviations between theoretical predictions and experimental data. The precision of this comparison is fundamentally limited by the knowledge of the integrated luminosity ( $L$ ), which quantifies the total number of particle interactions delivered by a collider. For the Compact Muon Solenoid (CMS) experiment at the Large Hadron Collider (LHC), luminosity uncertainty has historically been a dominant systematic error in many physics analyses. While the original design goal for systematic uncertainty was 5%, the evolution of the LHC into a precision instrument necessitated increasingly stringent accuracy. Achieving sub-percent precision is critical for fully unlocking the physics reach of the LHC, particularly as the facility moves toward the High-Luminosity LHC (HL-LHC) era, where high-pileup conditions will make precise determination even more challenging.

Methodology
This paper reports the measurement of the integrated luminosity for proton-proton ($pp$) collisions at a center-of-mass energy of $\sqrt{s} = 13$ TeV, recorded by CMS during the 2017 and 2018 data-taking periods (Run 2). The measurement relies on the van der Meer (vdM) calibration method, which determines the visible cross section ( $\sigma_{\text{vis}}$ ) by analyzing transverse beam-separation scans. The instantaneous luminosity is calculated as $L_{\text{inst}}(t) = R(t) / \sigma_{\text{vis}}$ , where $R(t)$ is the rate measured by dedicated luminometers.

The analysis employs a comprehensive suite of corrections and validation techniques to minimize systematic uncertainties:

Luminometers: The measurement utilizes four independent luminometers: the Hadron Forward (HF) calorimeter (using both occupancy, HFOC, and transverse energy sum, HFET, algorithms), the Pixel Luminosity Telescope (PLT), and Pixel Cluster Counting (PCC) in the silicon tracker. These provide redundant measurements across different pseudorapidity ranges and technologies.
vdM Calibration Corrections: The determination of $\sigma_{\text{vis}}$ $σ_{vis}$ involves rigorous corrections for several physical and instrumental effects:
- Beam-Beam Interactions: Corrections for beam-beam deflection (coherent shift) and the dynamic- $\beta$ effect (incoherent optical effect) are applied using multi-particle simulations (B*B and COMBI codes).
- Orbit Position and Drift: Systematic shifts in beam orbits due to magnet hysteresis and random drifts are corrected using Beam Position Monitor (BPM) data (both DOROS and arc BPMs). A novel approach separates linear drifts from residual non-linear drifts to improve accuracy.
- Length Scale Calibration: A two-step approach is introduced to calibrate the beam separation length scale. It combines BPM measurements with the CMS tracker coordinate system, utilizing both constant-step (cLS) and variable-step (vLS) scans to minimize uncertainties related to orbit drift and magnetic nonlinearities.
- Transverse Factorization: The assumption that bunch proton densities factorize into independent $x$ and $y$ distributions is tested and corrected using two independent methods: a Luminous Region (LR) analysis (reconstructing vertex distributions) and a 2D Rate Fit (2D-RF) method using off-axis scans.
- Bunch Intensity and Background: Corrections are applied for "ghost" and "satellite" charges (spurious protons not participating in collisions) and for background rates arising from beam-gas interactions and detector noise.
Rate Corrections for High-Luminosity Conditions: To extrapolate the vdM calibration (performed at low luminosity) to standard physics data-taking conditions (high luminosity), corrections are applied for:
- Out-of-Time (OOT) Effects: Signal spillover from preceding bunches and afterglow from detector activation.
- Nonlinearity and Efficiency: Detector response nonlinearity and efficiency degradation over time (due to radiation damage) are monitored using "emittance scans" performed during regular fills.
Cross-Validation: The stability of the luminosity measurement over time is validated against the production rate of $Z$ bosons decaying to muon pairs ( $Z \to \mu^+\mu^-$ ), a process with a well-understood cross-section that serves as an independent luminosity proxy.

Key Contributions

Sub-Percent Precision: The paper achieves a total integrated luminosity precision of 0.73% for the combined 2015–2018 Run 2 dataset. This marks the most precise luminosity measurement ever achieved at a bunched-beam hadron collider.
Refined Systematic Control: Significant improvements over previous results (e.g., Refs. [13], [23], [24]) are attributed to:
- A better understanding of beam-beam effects and their associated uncertainties.
- Improved treatment of non-factorization of proton densities in transverse coordinates.
- The introduction of a two-step length scale calibration method.
- Refined corrections for residual orbit drifts and detector-specific rate effects.
Independent Cross-Checks: The combination of four independently calibrated luminometers (HFET, HFOC, PLT, PCC) provides a rigorous cross-check, reducing the overall uncertainty through averaging.
Long-Term Stability: The consistency of the measurement across years is conclusively validated using $Z$ boson rates, confirming the stability of the calibration despite changing running conditions.

Results

2017 Data: The integrated luminosity for high-quality high-pileup physics data is measured as $42.07 \pm 0.34 \text{ fb}^{-1}$ (0.81% uncertainty). An additional $0.2113 \pm 0.0019 \text{ fb}^{-1}$ was collected at low pileup ( $\sim 3$ ).
2018 Data: The integrated luminosity for high-pileup data is $59.56 \pm 0.49 \text{ fb}^{-1}$ (0.83% uncertainty).
Combined Run 2 (2015–2018): The total integrated luminosity for high-quality high-pileup data is $140.22 \pm 1.02 \text{ fb}^{-1}$ , with a relative precision of 0.73%.
Uncertainty Breakdown: The dominant source of uncertainty for both years is residual nonlinearity in the detector response when extrapolating from vdM conditions to physics conditions. Normalization uncertainties (vdM calibration) and integration uncertainties (linearity and consistency) contribute comparably to the total error budget.

Significance
The paper claims that crossing the sub-percent precision threshold fundamentally sharpens the ability to test the Standard Model and establishes a vital baseline for the upcoming High-Luminosity LHC era. By reducing the luminosity uncertainty to 0.73%, the CMS Collaboration has set a new benchmark for bunched-beam hadron colliders. This precision is essential for constraining new physics and improving the accuracy of cross-section measurements. The authors note that while the vdM calibration has reached its sub-percent target, the extrapolation to standard physics conditions (integration) remains the leading source of uncertainty and will require further methodological improvements to meet the challenges of the HL-LHC.

1. The Problem: Counting the Unseeable

2. The Calibration: The "Van der Meer" Dance

3. The Challenges: The "Noise" and the "Drift"

4. The Result: A New Gold Standard

The Bottom Line

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