Search for a narrow resonance with a mass between 10 and 70 GeV decaying to a pair of photons in proton-proton collisions at $\sqrt{s}$ = 13 TeV

Using 54.4 fb$^{-1}$ of 13 TeV proton-proton collision data from the CMS experiment, a search for narrow resonances decaying to diphotons in the 10–70 GeV mass range found no significant excess over the expected background, leading to the setting of upper limits on production cross sections and an interpretation within an axion-like particle framework.

The Gist

Imagine the Large Hadron Collider (LHC) at CERN as the world's most powerful "particle smashery." Scientists fire protons at each other at nearly the speed of light, hoping that when they crash, they might create something new and exotic that doesn't exist in our everyday world.

This paper is a report from the CMS experiment (one of the giant detectors at the LHC) about a specific "treasure hunt" they conducted in 2018.

The Mission: Hunting for a "Ghost" Particle

Scientists have theories suggesting there might be a new, lightweight particle hiding in the universe. They call it a "spin-zero particle" (think of it as a ghostly, invisible marble). Some theories say these particles are related to Axion-Like Particles (ALPs), which are candidates for Dark Matter—the invisible stuff that holds galaxies together.

The problem? These particles are very shy. If they exist, they might decay (fall apart) almost instantly into two beams of light (photons).

The Challenge:
For years, the LHC's "security cameras" (triggers) were set to only look for heavy, slow-moving particles. It was like having a security guard who only checks people carrying heavy suitcases, ignoring anyone with a small backpack. This meant that if a light, fast-moving particle decayed into two photons, the cameras would miss it because the photons were moving too fast and too close together.

The Breakthrough: A New "Net"

In 2018, the CMS team installed a new trigger system. Imagine they lowered the security guard's requirements. Instead of only looking for heavy suitcases, the guard now checks for any backpack, even if it's light and moving fast.

This allowed them to look at a mass range between 10 and 70 GeV (a scale of energy that was previously a "blind spot"). It's like finally being able to see the small, fast fish in the ocean that were previously swimming under the radar.

The Investigation: Sorting the Noise

When the particles smash, they create a chaotic explosion of debris. Most of the time, you just get a pile of "junk" (background noise) that looks like two photons but isn't a new particle. It's like trying to find a specific, rare coin in a massive pile of identical-looking rocks.

To solve this, the scientists used a Neural Network (AI).

• The Analogy: Imagine a master detective (the AI) who has studied millions of crime scenes. When a new scene appears, the detective looks at tiny clues: how the light is angled, how the energy is spread out, and how the particles are moving.
• The AI was trained to distinguish between the "noise" (regular particle collisions) and the "signal" (a potential new particle). It gave every event a "suspicion score." The team only kept the events with the highest scores for their final analysis.

The Results: The Quiet Room

After analyzing 54.4 inverse femtobarns of data (which is a fancy way of saying they looked at a massive amount of collision data, roughly 54 trillion proton collisions), they found... nothing.

• No Ghosts Found: They did not see any excess of events that would indicate a new particle. The data matched perfectly with what we already know about the Standard Model (our current rulebook of physics).
• The "What If" Limits: Even though they didn't find the particle, they set very strict rules. They said, "If this particle does exist, it cannot be heavier than X or lighter than Y, and it cannot interact with light more strongly than Z."

Think of it like searching a dark forest for a specific type of bird. You didn't hear the bird, but you can now confidently say, "If that bird exists, it's not in this part of the forest, and it doesn't sing this loudly."

Why This Matters

1. Closing the Door: They successfully closed a gap in our knowledge. We now know that this specific type of "lightweight ghost particle" doesn't exist in the mass range they searched.
2. The ALP Connection: They translated their results into limits for Axion-Like Particles. They essentially told theorists: "If you want your theory to be right, the 'decay constant' (a measure of how weakly these particles interact) must be very high (between 4 and 15 TeV). If it's lower, your theory is likely wrong."
3. Future Hunting: By proving they can detect these low-mass, fast-moving particles, they paved the way for future searches. They proved the "net" works, so they can cast it wider next time.

The Bottom Line

The CMS team upgraded their equipment to look for a specific, elusive type of particle that had been hiding in plain sight. They used advanced AI to filter out the noise and found no evidence of this new particle. While they didn't make a discovery, they successfully ruled out a huge chunk of possibilities, helping the rest of the physics community narrow down where to look next. It's a classic case of "finding nothing is actually finding something important."

Technical Summary

1. Problem and Motivation

The Standard Model (SM) of particle physics leaves fundamental questions unresolved, such as the nature of dark matter and the hierarchy between the electroweak and gravitational scales. Many Beyond the Standard Model (BSM) theories predict the existence of new spin-zero particles (scalars or pseudoscalars) with masses below the electroweak scale.

• Specific Target: Axion-Like Particles (ALPs), which arise from the spontaneous breaking of approximate global symmetries. Unlike the QCD axion, ALPs have independent mass and coupling parameters, potentially existing in the GeV–TeV range.
• The Gap: Previous CMS searches for diphoton resonances were limited to masses above 70 GeV due to trigger thresholds (specifically a minimum invariant mass requirement of 55 GeV inherited from Higgs searches). Similarly, dijet searches were limited to masses above 50 GeV.
• Challenge: At low masses (10–70 GeV), photon pairs from resonance decays are highly Lorentz-boosted. This leads to small angular separations, making them difficult to distinguish from background jets and challenging to reconstruct as two separate photons. Furthermore, standard triggers often fail to capture these low-mass, high-$p_T$ events efficiently.

2. Methodology

Data Set and Trigger

• Data: The analysis uses proton-proton collision data collected by the CMS experiment in 2018 at a center-of-mass energy of 13 TeV.
• Integrated Luminosity: 54.4 fb$^{-1}$.
• Trigger Innovation: A crucial enabler for this search is a newly introduced diphoton trigger deployed in 2018. It features asymmetric transverse momentum ($p_T$) thresholds of 30 GeV and 18 GeV for the leading and subleading photons, respectively, with no minimum invariant mass requirement. This removed the previous 55 GeV floor, allowing access to the 10–70 GeV phase space.

Event Selection and Reconstruction

• Photon Identification: Photons are reconstructed in the Electromagnetic Calorimeter (ECAL). A "photon preselection" applies tighter offline criteria than the trigger to ensure ~100% efficiency.
• Vertexing: A Boosted Decision Tree (BDT) identifies the primary vertex of the photon pair, crucial for mass resolution.
• Multivariate Analysis (MVA): To handle the complex background and the specific topology of boosted low-mass resonances, a Neural Network (NN) classifier is employed.
  • Inputs: 10 features including photon $p_T$ scaled by invariant mass, pseudorapidities, photon ID scores, the angle between photons, primary vertex probability, and event-by-event mass resolution estimates.
  • Training: The NN is trained on simulated signal events (masses 10–70 GeV) and background events (simulated prompt diphotons and data sidebands dominated by non-prompt photons).
  • Signal Region (SR): Events are selected if the NN score exceeds a fixed threshold of 0.8, optimizing the signal-to-background ratio.

Signal and Background Modeling

• Signal Model: Simulated using MADGRAPH5_aMC@NLO (NLO QCD) with PYTHIA 8 for parton showering. The signal shape is modeled as a sum of a Double Crystal Ball and a Gaussian function to account for non-Gaussian tails and core resolution.
• Background Model: The dominant backgrounds are irreducible prompt diphoton production and reducible QCD multijet/$\gamma$+jets events where jets are misidentified as photons.
  • The background mass spectrum is complex due to "turn-on" effects from isolation criteria at low mass (12 GeV) and trigger thresholds (50 GeV).
  • Strategy: The mass range (10–70 GeV) is divided into four sub-windows (W1–W4). In each window, the background is modeled using flexible analytic functions (Bernstein polynomials, exponentials, power laws). The choice of function is treated as a discrete nuisance parameter (discrete profiling) to estimate systematic uncertainty.

Statistical Analysis

• A binned maximum-likelihood fit is performed on the diphoton invariant mass spectrum ($m_{\gamma\gamma}$).
• Systematic uncertainties (photon energy scale/resolution, trigger efficiency, luminosity, background modeling) are incorporated as nuisance parameters.
• Limits are set on the product of the production cross-section and branching fraction: $\sigma(gg \to \phi) \times \mathcal{B}(\phi \to \gamma\gamma)$.

3. Key Contributions

1. First Low-Mass Diphoton Search with New Trigger: This is the first CMS search to probe the 10–70 GeV mass range using the specific asymmetric trigger that removed the 55 GeV mass floor.
2. Advanced MVA for Boosted Topologies: The development of a specialized Neural Network classifier tailored to distinguish highly boosted diphoton signals from QCD backgrounds in a region where standard reconstruction struggles.
3. Comprehensive Background Modeling: A robust strategy using discrete profiling of background function shapes across four distinct mass windows to handle the non-trivial turn-on features of the detector response at low masses.
4. ALP Interpretation: A detailed reinterpretation of the exclusion limits within the Effective Field Theory (EFT) framework for Axion-Like Particles, constraining the decay constant $f_a$.

4. Results

• Observation: No significant excess of events above the expected background was observed across the full mass range.
• Local Significance: The largest local excess was observed at a mass hypothesis of 13.6 GeV, with a significance of 3.5 standard deviations.
• Global Significance: After accounting for the "look-elsewhere effect" (testing multiple mass hypotheses), the global significance drops to 1.9 $\pm$ 0.1 standard deviations, consistent with a background fluctuation.
• Exclusion Limits:
  • 95% Confidence Level (CL) upper limits were set on $\sigma(gg \to \phi) \times \mathcal{B}(\phi \to \gamma\gamma)$ for narrow resonances.
  • The limits are competitive with, and in some regions superior to, previous searches and comparable to ATLAS results in the overlapping mass range.
• ALP Constraints: Interpreting the results for ALPs with couplings to gluons and photons (assuming anomaly coefficients $c_1=c_2=c_3=10$), the analysis excludes decay constants $f_a$ in the range of approximately 4 to 15 TeV, depending on the ALP mass.

5. Significance

• Exploration of Uncharted Phase Space: This analysis successfully opens the "low-mass" window (10–70 GeV) for diphoton resonance searches at the LHC, a region previously inaccessible due to trigger limitations.
• Model Independence: By minimizing model-dependent assumptions and focusing on a generic spin-zero resonance, the results are applicable to a wide variety of BSM scenarios, including Two-Higgs-Doublet Models (2HDM), NMSSM, and Composite Higgs models.
• Dark Matter and Cosmology: The constraints on ALPs are relevant for dark matter candidates and cosmological models where light pseudoscalars play a role.
• Future Prospects: The methodology and trigger configuration demonstrated here pave the way for future Run 3 and High-Luminosity LHC analyses to further probe the low-mass spectrum for new physics.