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Constraint on the Higgs boson width in the diphoton final state using signal-background interference in proton-proton collisions at $\sqrt{s}$ = 13 TeV

Using 138 fb $^{-1}$ of proton-proton collision data at $\sqrt{s}$ = 13 TeV collected by the CMS experiment, this study presents the first constraint on the Higgs boson width derived from signal-background interference in the diphoton final state, establishing a 95% confidence level upper limit of 92 MeV.

Original authors: CMS Collaboration

Published 2026-09-02

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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

In the standard model of particle physics, the universe is built from a small set of fundamental particles and the forces that govern how they interact. Among these, the Higgs boson holds a unique place. Discovered in 2012, this particle is the physical manifestation of an invisible field that permeates all of space, giving mass to other particles. While scientists have confirmed the Higgs boson exists and measured its mass to be approximately 125 gigaelectronvolts, a complete picture of its nature remains elusive. One of the most critical missing pieces is the particle's total decay width. In the language of physics, this width represents how quickly a particle decays into other forms of energy. For the Higgs boson, the standard model predicts this width to be incredibly narrow, roughly four millionths of a gigaelectronvolt. If the actual width differs from this prediction, it would signal the presence of new, undiscovered particles or forces interacting with the Higgs, potentially opening a door to physics beyond our current understanding.

The challenge lies in the fact that this predicted width is so small that it is far too narrow to be measured directly by any existing detector. The instruments used to observe these particles have a resolution that is thousands of times coarser than the width itself. Consequently, scientists have had to rely on indirect methods to constrain this value, often looking at how the Higgs behaves when it is produced in high-energy collisions but not necessarily at its exact mass. A new approach, however, has emerged from the CMS collaboration at CERN, the European Organization for Nuclear Research. By analyzing a vast amount of data from proton-proton collisions, researchers have found a way to probe the Higgs boson's width by listening to the subtle interference patterns it creates, rather than trying to measure its size directly.

The study focuses on a specific scenario where two protons smash together at nearly the speed of light, creating a Higgs boson that immediately decays into two photons, or particles of light. This process is rare, but it is not the only way to produce two photons in such a collision. Background processes can also generate pairs of photons without ever creating a Higgs boson. In the quantum world, these two pathways—the one involving the Higgs and the one that does not—can interfere with each other, much like overlapping ripples in a pond. When the Higgs boson is produced, its quantum wave interacts with the background wave of photons, creating a distinct distortion in the distribution of the photon pairs' energies. This distortion is not a simple bump in the data; it is a subtle shift in the shape of the energy spectrum that depends directly on how quickly the Higgs boson decays.

To capture this effect, the CMS team analyzed data collected between 2016 and 2018, corresponding to a massive dataset of 138 inverse femtobarns of collisions. They sifted through billions of events to find the specific signatures of two photons appearing together. The researchers then categorized these events based on the energy of the photons and the presence of other particles in the collision, creating a detailed map of how often these photon pairs appear at different energy levels. By comparing the observed data against complex computer simulations that included the effects of interference, they could determine how much the Higgs boson's width contributed to the shape of the data. If the width were larger than the standard model prediction, the interference pattern would be more pronounced, altering the number of photon pairs seen just above and below the expected mass of the Higgs.

The analysis revealed that the observed data is consistent with the standard model prediction, but it also set a strict upper limit on how large the width could possibly be. The researchers found that the Higgs boson's total decay width is less than 92 millionths of a gigaelectronvolt at a 95 percent confidence level. This means that if the width were any larger, the interference pattern would have been visible in the data, and the scientists would have seen a different distribution of photon energies. While the result is an upper limit rather than a precise measurement of the exact width, it is the most stringent constraint obtained so far from measurements of the Higgs boson when it is produced at its actual mass. The team also calculated what they expected to find based on their statistical models, estimating a limit of 138 millionths of a gigaelectronvolt, which indicates that the actual data was even more precise than anticipated.

This finding is significant because it narrows the window for potential new physics. Previous indirect measurements had allowed for a much wider range of possibilities, but this new constraint tightens the bounds significantly. The researchers confirmed that the Higgs boson behaves largely as the standard model predicts, with no evidence of hidden decay modes or unexpected interactions that would have broadened its width. The study also explored an alternative method based on the slight shift in the peak position of the Higgs mass caused by interference, but this approach yielded a much weaker limit, reinforcing the value of the primary interference shape analysis. By successfully isolating the interference signal from the background noise, the CMS collaboration has demonstrated a powerful new tool for studying the Higgs boson, one that does not rely on the particle decaying into invisible channels or being produced at energies far from its mass.

The work represents a triumph of precision and statistical power. It required the careful modeling of complex quantum mechanical effects and the ability to distinguish a tiny signal from a vast sea of background events. The researchers accounted for numerous sources of uncertainty, from the calibration of their detectors to the theoretical calculations of how particles interact. They verified that their results were robust against these variations, ensuring that the limit they set is reliable. While the study does not discover new particles, it effectively rules out a wide range of theoretical scenarios where the Higgs boson might have been significantly broader than expected. This clarity helps guide future research, telling theorists that if new physics exists, it must be subtle enough to have escaped this particular detection method.

In the end, the paper provides a clearer picture of the Higgs boson's nature. It confirms that the particle's decay rate is consistent with the standard model, placing a tight cap on any potential deviations. The ability to measure the width through interference, rather than direct observation, opens a new avenue for exploring the fundamental properties of the universe. As the Large Hadron Collider continues to operate and collect more data, these techniques will likely become even more precise, potentially revealing the faint signatures of physics that lies beyond our current understanding. For now, the Higgs boson remains a steadfast pillar of the standard model, its width constrained to be no wider than 92 millionths of a gigaelectronvolt, a testament to the precision of modern experimental physics.

Technical Summary: Constraint on the Higgs Boson Width in the Diphoton Final State

Problem and Motivation
In the Standard Model (SM), the Higgs boson ( $H$ ) with a mass of approximately 125 GeV is predicted to have a total decay width ( $\Gamma_H$ ) of roughly 4.1 MeV. Direct experimental measurement of this width is challenging because the natural width is significantly smaller than the experimental mass resolution (on the order of 1 GeV) in the $H \to \gamma\gamma$ and $H \to ZZ \to 4\ell$ channels. Consequently, the most stringent direct limits to date are $\Gamma_H < 330$ MeV. Indirect constraints derived from off-shell production rates or unitarity arguments exist but rely on assumptions about the couplings. A deviation from the predicted width could indicate new physics, such as undetectable decay modes. However, a "flat direction" exists in the parameter space where an increase in $\Gamma_H$ due to invisible decays can be mimicked by a rescaling of all Higgs couplings, making the direct measurement of $\Gamma_H$ crucial for characterizing the boson.

Methodology
This analysis utilizes proton-proton collision data collected by the CMS experiment at $\sqrt{s} = 13$ TeV between 2016 and 2018, corresponding to an integrated luminosity of 138 fb $^{-1}$ . The study focuses on the diphoton ( $\gamma\gamma$ ) final state produced via gluon-gluon fusion (ggH).

The core methodology exploits the quantum mechanical interference between the resonant signal process ( $gg \to H \to \gamma\gamma$ ) and the non-resonant continuum background process ( $gg \to \gamma\gamma$ ).

Signal and Interference Modeling: The differential cross-sections for the signal ( $s$ ) and the interference ( $i$ ) are modeled. The signal rate is proportional to $c_{g\gamma}^2 / \Gamma_H$ , while the interference rate is proportional to $c_{g\gamma}$ . Crucially, the interference term introduces an asymmetric lineshape in the diphoton invariant mass ( $m_{\gamma\gamma}$ ) distribution, deviating from a standard Breit-Wigner shape. This asymmetry, particularly the negative contribution above the pole mass, provides sensitivity to $\Gamma_H$ .
Event Selection and Categorization: Events are selected using diphoton triggers and photon identification criteria. To maximize sensitivity, events are categorized into 11 regions: one dedicated to Vector Boson Fusion (VBF) events with two jets, and ten regions targeting gluon-gluon fusion (ggH) events. The ggH regions are defined by the diphoton transverse momentum ( $p_T$ ) and the output of a Boosted Decision Tree (BDT) trained to discriminate signal from background.
Statistical Analysis: An extended binned maximum likelihood fit is performed on the $m_{\gamma\gamma}$ spectrum across all categories. The signal model combines four components: pure ggH signal, ggH interference, VBF, and associated production (VH). The fit treats the Higgs width ( $\Gamma_H$ ) as the parameter of interest, parameterized via a transformed variable $\lambda = \sqrt{\Gamma_H/\Gamma_H^{SM}}$ . The signal strengths for ggH ( $\mu_F$ ) and VBF/VH ( $\mu_V$ ) are floated, as is the Higgs mass ( $m_H$ ).
Systematic Uncertainties: Experimental uncertainties, including photon energy scale and resolution, and theoretical uncertainties (renormalization and factorization scales, strong coupling constant), are incorporated as nuisance parameters. The background is modeled using empirical functions derived from data sidebands.

Key Contributions

First On-Shell Interference Constraint in $H \to \gamma\gamma$ : This work presents the first constraint on the Higgs boson width derived specifically from the interference between the resonant $H \to \gamma\gamma$ signal and the continuum $\gamma\gamma$ background in the on-shell region.
Novel Parameterization: The analysis utilizes a linear combination of signal and interference templates to construct a positive-definite probability density function, allowing for a robust statistical fit that disentangles the coupling modifier ( $c_{g\gamma}$ ) from the width ( $\Gamma_H$ ).
Comprehensive Categorization: By dividing the data into 11 kinematic categories, the analysis optimizes sensitivity to the interference effect, which varies with the diphoton $p_T$ .

Results
The analysis yields the following constraints on the Higgs boson total width at 95% confidence level (CL):

Observed Limit: $\Gamma_H < 92$ MeV.
Expected Limit: $\Gamma_H < 138$ MeV.

The measured value of the transformed parameter is $\lambda = -3.6^{+2.5}_{-2.4}$ , which is compatible with the SM expectation of $\lambda = 1$ within two standard deviations. The signal strengths for ggH and VBF/VH processes are consistent with SM predictions.

An alternative approach based on the interference-induced displacement of the mass peak was also studied, yielding a less stringent expected limit of $\Gamma_H < 650$ MeV, highlighting the superior sensitivity of the lineshape analysis.

Significance
This paper claims to provide the most stringent constraint on the Higgs boson width ( $\Gamma_H$ ) derived from on-shell Higgs boson measurements to date. By utilizing the interference effect in the diphoton channel, the analysis offers a direct probe of the width that is independent of the off-shell extrapolations used in previous indirect constraints. The result of $\Gamma_H < 92$ MeV significantly tightens the bounds on potential new physics contributions to the Higgs decay width within the on-shell regime.

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