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A measurement of the Higgs boson mass in the diphoton decay channel in proton-proton collisions at $\sqrt{s}$ = 13 TeV

Using proton-proton collision data at 13 TeV collected by the CMS detector from 2016 to 2018, this study measures the Higgs boson mass in the diphoton decay channel to be 125.13 ± 0.15 GeV, achieving improved precision through refined calibration and new analysis techniques, and combines this result with previous measurements at 7 and 8 TeV to obtain a combined mass of 125.06 ± 0.14 GeV.

Original authors: CMS Collaboration

Published 2026-07-31

📖 6 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

The Cosmic Goldilocks Zone

Imagine the universe as a giant, intricate machine built from invisible Lego bricks. For decades, scientists have been trying to figure out exactly how these bricks stick together to form everything we see, from the smallest atoms to the biggest stars. A major part of this puzzle is a mysterious force called the "Higgs field." Think of this field like a thick, invisible snowfield covering the entire universe. Some particles, like photons (light), zip right through it without getting stuck, staying fast and massless. Others, like electrons, wade through it, getting slowed down and gaining "mass" (heaviness). Without this snowfield, particles would never clump together to form atoms, and we wouldn't be here to ask questions.

In 2012, scientists at the Large Hadron Collider (LHC) found the physical proof of this field: a particle called the Higgs boson. It's like finding a single snowflake that proves the snowfield exists. But finding it was just the beginning. Now, scientists need to measure this snowflake with extreme precision. Why? Because the exact weight of this particle is a crucial input for calculating whether the universe is stable, or if it's a house of cards that could collapse at any moment. It's a cosmic "Goldilocks" problem: if the Higgs boson is too heavy or too light, the universe might not be able to support life as we know it. So, measuring its mass isn't just about counting; it's about gathering the data needed to check the structural integrity of reality itself.

Weighing the Unweighable: A New Precision Measurement

In this new study, the CMS Collaboration, a massive team of scientists working with a giant detector called CMS at the LHC, has taken a fresh, super-sharp look at the Higgs boson. They didn't just look at old data; they analyzed a huge pile of fresh information collected between 2016 and 2018, when the LHC was smashing protons together at a record-breaking energy of 13 TeV. This corresponds to a massive amount of data, equivalent to 138 inverse femtobarns (a unit physicists use to count how many collisions happened).

The team focused on a very rare event: when a Higgs boson decays into two high-energy photons (particles of light). This happens only about 23 times out of every 10,000 Higgs bosons, making it a "needle in a haystack" situation. However, because light travels in a straight line and is easy to track, this specific decay channel acts like a high-resolution camera, allowing scientists to reconstruct the Higgs boson's mass with incredible clarity.

The Big Findings
Using these new data and some clever upgrades to their analysis, the scientists measured the mass of the Higgs boson to be 125.13 ± 0.15 GeV.

Breaking that down: The "125.13" is their best guess for the weight.
The "± 0.15" is the margin of error, meaning the true value is almost certainly between 124.98 and 125.28.
They split this error into two parts: 0.10 comes from random chance (statistical uncertainty), and 0.12 comes from the limits of their tools and methods (systematic uncertainty).

To put this in perspective, they combined this new result with their older measurements from when the LHC was running at lower energies (7 and 8 TeV). When they mashed all the data together, the combined mass came out to 125.06 ± 0.14 GeV. This is a remarkably precise number, narrowing down the possible weight of the Higgs boson more tightly than ever before.

How They Did It (The Magic Tricks)
The real story here isn't just the number, but how they got it so precise. The team had to overcome some tricky hurdles:

Calibrating the Ruler: To measure the mass, they first had to make sure their "ruler" (the detector's ability to measure energy) was perfect. They used a known particle called the Z boson, which decays into two electrons, to calibrate the electron energy scale. But photons are tricky; they interact with the detector slightly differently than electrons. To fix this, they used a special "bridge" technique involving a rare decay where a Z boson turns into two muons and a photon. This allowed them to directly compare how the detector sees electrons versus photons and correct for any differences.
Fixing the "Snow Damage": Over time, the intense radiation inside the LHC damages the crystals in the detector (like snow getting dirty), which can change how they measure energy. The team developed a new method to account for this damage specifically for photons, ensuring their measurements didn't drift over the years.
Finding the Needle: They used a smart computer program (a "boosted decision tree") to sift through millions of collisions. This program learned to spot the specific patterns that look like a Higgs boson turning into two photons, while ignoring the billions of background events that look like noise.

What They Didn't Find (and Why It Matters)
The paper doesn't claim to have discovered a new particle or a new force. Instead, it rigorously confirms that the Standard Model of physics is holding up. The measured mass is consistent with the value used in global fits of precision observables, and the signal strength is compatible with the Standard Model prediction. They also checked for a subtle effect called "interference," where the Higgs signal might get mixed up with background noise. They found this effect exists but is small, and they calculated its impact (a shift of about 27 MeV) to ensure it didn't skew their final result.

The Bottom Line
This paper is a triumph of precision engineering and statistical detective work. By refining their tools and analyzing a massive new dataset, the CMS team has tightened the noose around the Higgs boson's mass. They haven't solved the entire mystery of the universe, but they have measured one of its most critical components with such accuracy that we can now provide the precise inputs needed to test the stability of the universe. The Higgs boson weighs in at roughly 125.13 GeV, give or take a tiny fraction, and the Standard Model passes another tough test.

Technical Summary: A Measurement of the Higgs Boson Mass in the Diphoton Decay Channel at $\sqrt{s} = 13$ TeV

Problem and Motivation
The Higgs boson mass ( $m_H$ ) is a fundamental parameter of the Standard Model (SM) that is not predicted by the theory itself. Precision measurements of $m_H$ are critical for testing the consistency of the SM, particularly regarding the stability of the electroweak vacuum and its cosmological implications. Furthermore, $m_H$ serves as a crucial input for global fits of electroweak precision observables, where loop-level contributions involving the top quark and the Higgs boson generate radiative corrections to the $W$ boson mass. While the diphoton decay channel ( $H \to \gamma\gamma$ ) has a small branching fraction ( $\approx 0.23\%$ ), it offers excellent invariant mass resolution, making it one of the premier channels for precision mass measurements alongside the four-lepton channel ( $H \to ZZ \to 4\ell$ ). This paper presents a refined measurement of $m_H$ using the full Run 2 dataset collected by the CMS detector at a center-of-mass energy of 13 TeV, aiming to improve upon previous precision by addressing dominant systematic uncertainties, particularly those related to photon energy calibration.

Methodology
The analysis utilizes proton-proton collision data recorded between 2016 and 2018, corresponding to an integrated luminosity of 138 fb $^{-1}$ . The event selection requires two photon candidates satisfying specific kinematic thresholds ( $p_T^{\gamma,1} > m_{\gamma\gamma}/3$ and $p_T^{\gamma,2} > m_{\gamma\gamma}/4$ ) and invariant mass within the range 100–180 GeV.

Key methodological advancements over previous CMS measurements include:

Refined Energy Calibration: A three-stage calibration procedure is employed to mitigate systematic uncertainties arising from differences between electron and photon energy scales.
- Stage 1: Electron energy scales are derived using $Z \to ee$ decays.
- Stage 2: A simulation-based "uniformity" correction accounts for radiation damage in the lead tungstate (PbWO $_4$ ) crystals of the electromagnetic calorimeter (ECAL), which affects photon and electron showers differently due to their distinct longitudinal development profiles.
- Stage 3: Residual differences between photon and electron energy scales are measured directly using final-state radiation (FSR) photons from $Z \to \mu\mu\gamma$ decays. This direct measurement removes uncertainties associated with extrapolating electron calibrations to photons.
Granular Resolution Corrections: The analysis introduces transverse energy ( $E_T$ )-dependent corrections for the photon energy resolution, derived from $Z \to ee$ events, improving the modeling of the mass resolution compared to previous $E_T$ -independent approaches.
Event Categorization: Events are categorized based on the detector region (barrel vs. endcap) and a multivariate signal-to-background discriminator (BDT) trained using the XGBOOST framework. The BDT utilizes kinematic variables, photon identification scores, and event-level resolution estimates. Categories are optimized to maximize signal significance ( $S/\sqrt{B}$ ) while minimizing mass resolution.
Statistical Analysis: A simultaneous binned maximum likelihood fit is performed on the diphoton invariant mass ( $m_{\gamma\gamma}$ ) distribution across all categories. The signal model is constructed from simulated events fitted with Voigtian functions, while the background model is derived directly from data using the discrete profiling method to account for functional form uncertainties. Systematic uncertainties, including those from photon energy scale, resolution, and interference between the signal and continuum background, are implemented as nuisance parameters.

Key Contributions

Direct Photon Calibration: The primary contribution is the implementation of a calibration strategy using $Z \to \mu\mu\gamma$ events to directly measure the residual energy scale difference between photons and electrons. This significantly reduces the systematic uncertainty previously dominated by the extrapolation of electron scales to photons.
Radiation Damage Modeling: The introduction of a simulation-based correction for radiation-induced non-uniformity in the ECAL crystals, specifically addressing the differing shower profiles of photons and electrons.
Improved Resolution Modeling: The derivation of $E_T$ -dependent energy resolution corrections, acknowledging that the mean energy of photons in Higgs decays ( $\approx 60$ GeV) differs from the electrons used in calibration ( $\approx 45$ GeV).
Interference Treatment: The systematic uncertainty associated with the interference between the gluon-fusion-induced $H \to \gamma\gamma$ signal and the continuum diphoton background is explicitly estimated and included.

Results
The measurement yields a Higgs boson mass of:
$m_H = 125.13 \pm 0.15 \text{ GeV} = 125.13 \pm 0.10 \text{ (stat)} \pm 0.12 \text{ (syst)} \text{ GeV}$

The dominant systematic uncertainties arise from the statistical limitations of the $Z \to \mu\mu\gamma$ sample used for residual corrections, the muon momentum scale, and non-linearity at high $E_T$ . The total systematic uncertainty is 117 MeV, while the statistical uncertainty is 98 MeV.

When combined with the previous CMS measurement from $\sqrt{s} = 7$ and 8 TeV data (assuming no correlations between the datasets), the combined mass is:
$m_H = 125.06 \pm 0.14 \text{ GeV} = 125.06 \pm 0.09 \text{ (stat)} \pm 0.11 \text{ (syst)} \text{ GeV}$

The signal strength parameter $\mu$ is measured to be $0.95 \pm 0.06 \text{ (stat)} \pm 0.07 \text{ (syst)}$ , consistent with the Standard Model prediction of $\mu = 1$ .

Significance
The paper claims that the new analysis techniques, particularly the refined detector calibration and the use of $Z \to \mu\mu\gamma$ events for direct photon energy scale determination, have resulted in a nearly factor-of-two reduction in systematic uncertainty compared to previous CMS measurements in the diphoton channel. The result is compatible with previous CMS measurements at 7 and 8 TeV (within 1.2 standard deviations) and with ATLAS measurements. The combined result contributes to the global precision determination of the Higgs boson mass, providing a stringent test of the Standard Model's electroweak sector. The analysis demonstrates the capability of the CMS detector to achieve high-precision mass measurements through advanced calibration strategies and multivariate analysis techniques.

The Cosmic Goldilocks Zone

Weighing the Unweighable: A New Precision Measurement

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