Search for dimuon resonance in the 35 to 75 GeV mass range using 140 fb$^{-1}$ of 13 TeV $pp$ collisions with the ATLAS detector

Using 140 fb$^{-1}$ of 13 TeV proton-proton collision data collected by the ATLAS detector, a model-independent search for dimuon resonances in the 35 to 75 GeV mass range employed Gaussian process regression for background modeling, found no significant excess, and established new constraints on dark-photon and dark-matter-mediator models.

The Gist

The Big Picture: Hunting for Invisible Ghosts in a Sea of Noise

Imagine you are standing in a massive, noisy stadium during a thunderstorm. The crowd is cheering, the rain is hammering down, and the wind is howling. This is the Large Hadron Collider (LHC), a giant machine that smashes protons together at nearly the speed of light. Every time two protons collide, it's like a tiny explosion that sends thousands of particles flying in all directions.

Most of the time, these collisions produce familiar particles, like muons (which are like heavy electrons). The pattern of these familiar muons is predictable; it's the "background noise" of the stadium. But physicists are looking for something rare: a new, heavy particle that decays into two muons. If such a particle exists, it would appear as a sudden, sharp spike in the data—a "ghost" appearing in the crowd that doesn't belong.

This paper is the report from the ATLAS experiment, one of the giant detectors at the LHC, describing their search for these "ghosts" in a specific mass range (between 35 and 75 GeV).

The Challenge: The "Noisy" Background

The main problem the scientists faced was that the "background noise" in this specific mass range is very tricky. Usually, when you look for a spike in data, you can draw a smooth, simple curve (like a slide) to represent the background and see if the data points jump above it.

However, in the 35–75 GeV range, the background isn't a smooth slide. It's more like a bumpy, winding mountain path with sudden dips and rises caused by the way the detectors are triggered (the "safety gates" that decide which collisions to record). Trying to fit a simple curve to this bumpy path is like trying to draw a straight line through a jagged mountain range; it doesn't work well, and you might mistake a bump in the road for a hidden treasure.

The Solution: The "Smart Rubber Sheet" (Gaussian Process Regression)

To solve this, the ATLAS team used a new, clever tool called Gaussian Process Regression (GPR).

Think of the background data as a piece of rubber.

• Old Method: Trying to force the rubber into a rigid, pre-made shape (like a parabola). If the rubber doesn't fit, you get errors.
• New Method (GPR): Imagine the rubber is smart. It knows it needs to be smooth, but it can stretch and bend to follow the actual shape of the data perfectly without being forced into a rigid shape. It learns the "bumps" and "dips" of the background noise directly from the data itself.

This allowed the scientists to model the background with incredible flexibility, separating the "noise" from any potential "signal" much better than before.

The Search: Looking for the Spike

The team analyzed 140 "inverse femtobarns" of data (a huge amount of collision data recorded between 2015 and 2018). They looked for a "bump" in the number of muon pairs at specific masses.

• The Result: They found no new particles.
• The "Almost" Moment: There was a small blip at 57.5 GeV. It looked like there might be 2.3 times more events than expected (a "2.3 sigma" effect). In the world of particle physics, this is like hearing a strange noise in the stadium that might be a ghost, but is statistically likely to just be a random cheer from the crowd. It wasn't strong enough to claim a discovery.

The Outcome: Setting the "Fences"

Even though they didn't find a new particle, the search was a success because it told them what doesn't exist.

Imagine the scientists are trying to find a specific type of bird in a forest. They didn't see the bird, but they mapped out the entire forest and said: "If this bird exists, it cannot be hiding in these specific trees, and it cannot be this heavy."

The paper sets upper limits on how often these hypothetical particles could be produced.

• They ruled out certain types of "Dark Matter mediators" (particles that might connect our world to the invisible Dark Matter universe).
• They ruled out certain types of "Dark Photons" (a hypothetical particle that could act as a bridge between normal light and dark matter).

Why This Matters

This paper is significant for two main reasons:

1. New Territory: This is the first time ATLAS has looked for these specific particles in the 35–75 GeV range. Previous searches by other experiments (like CMS and LHCb) covered different areas, so this fills a gap in the map.
2. New Tool: The use of the "Smart Rubber Sheet" (GPR) is a major innovation. It proved that machine learning techniques can handle complex, messy background data better than traditional math formulas, making future searches more sensitive.

In Summary:
The ATLAS team used a massive dataset and a new, flexible mathematical tool to scan a specific range of particle masses for signs of new physics. They didn't find the "ghosts" they were looking for, but they successfully mapped the "haunted house" so thoroughly that they can now say with high confidence that if these ghosts exist, they are much rarer or lighter/heavier than the specific scenarios they tested. They also proved that their new "smart rubber sheet" method works perfectly for future hunts.

Technical Summary

Technical Summary: Search for Dimuon Resonance in the 35 to 75 GeV Mass Range

Problem and Motivation
This paper presents a model-independent search for new low-mass resonances decaying into pairs of oppositely charged muons ($\mu^+\mu^-$) using proton–proton collision data at a center-of-mass energy of $\sqrt{s} = 13$ TeV. The analysis targets an invariant mass range of 35 to 75 GeV, a region previously unexplored by the ATLAS experiment in resonance searches. The motivation stems from the potential existence of physics beyond the Standard Model (BSM), particularly in the context of dark matter (DM) interactions. Theoretical frameworks suggest that DM could interact with Standard Model particles via a hidden sector mediated by new vector or axial-vector bosons, such as a $Z'$ boson or a kinetically mixed dark photon ($Z_D$). These mediators could be produced via the Drell–Yan mechanism and decay promptly into muon pairs. A significant challenge in this mass region is the accurate modeling of the dominant Standard Model background (Drell–Yan $Z/\gamma^* \to \mu\mu$), which exhibits non-trivial structures, including threshold effects from muon triggers, making traditional analytic background parameterizations difficult to apply.

Methodology
The analysis utilizes 140 fb$^{-1}$ of data collected by the ATLAS detector between 2015 and 2018. Event selection requires two muon candidates satisfying medium identification criteria, particle-flow-based isolation, and specific transverse momentum ($p_T$) and pseudorapidity ($|\eta|$) requirements to ensure trigger efficiency. The signal region is defined by a dimuon invariant mass ($m_{\mu\mu}$) between 30 and 80 GeV, with the primary search window set to 35–75 GeV to avoid edge effects.

The core methodological innovation is the application of Gaussian Process Regression (GPR) for background modeling. Unlike previous ATLAS analyses that relied on fixed analytic functions (e.g., power laws or exponentials) to describe the background shape, this study employs GPR, a non-parametric machine learning technique. The GPR assumes bin-to-bin correlations in the background spectrum follow a multivariate Gaussian distribution, governed by a Radial Basis Function (RBF) kernel. This approach allows for a flexible and robust description of the rapidly varying Drell–Yan continuum and trigger-induced structures without imposing a rigid functional form.

Signal extraction is performed using a binned simultaneous profile likelihood fit. The likelihood function incorporates the GPR-predicted background, the signal model (a Breit–Wigner distribution convolved with a double-sided Crystal Ball function to account for detector resolution), and systematic uncertainties treated as nuisance parameters. The hyper-parameters of the GPR kernel (correlation strength and length scale) are tuned using generator-smeared Monte Carlo samples to minimize bias (spurious signal) and maximize sensitivity. Systematic uncertainties include theoretical variations (QCD scales, PDFs), experimental effects (muon momentum scale, resolution, efficiencies), and the uncertainty associated with the background modeling itself.

Key Contributions

1. First ATLAS Search in the 35–75 GeV Range: This work constitutes the first resonance search by ATLAS in this specific low-mass window, extending the experiment's sensitivity to lower masses than previously accessible with standard triggers.
2. GPR for Background Modeling: The paper introduces GPR as a novel tool for modeling backgrounds in resonance searches at the LHC. It demonstrates that this technique can effectively handle complex, non-smooth background shapes where traditional analytic functions fail, thereby improving the robustness of the search.
3. Model-Independent Limits: The analysis provides model-independent upper limits on the fiducial production cross-section times branching ratio ($\sigma_{\text{fid}} \times \mathcal{B}$) for new resonances.
4. BSM Interpretation: The results are interpreted within two specific theoretical frameworks: a simplified dark matter mediator model (featuring $Z'$ bosons with vector or axial-vector couplings) and a dark photon model (featuring kinetically mixed $Z_D$).

Results
The analysis found no statistically significant excess of events over the expected Standard Model background. The largest local excess was observed at a mass of 57.5 GeV, with a local significance of 2.3$\sigma$; however, the global significance was found to be negligible.

Consequently, 95% confidence level (CL) upper limits were set on the production cross-section of narrow-width resonances decaying to muons. The observed limits range from approximately 20 fb to 110 fb across the 35–75 GeV mass range.

• $Z'$ Interpretation: Assuming a coupling of 0.1 to quarks ($g_q = 0.1$), upper limits on the coupling to leptons ($g_l$) were derived, ranging from $4 \times 10^{-4}$ to $1.4 \times 10^{-3}$.
• Dark Photon Interpretation: Upper limits on the kinetic mixing parameter squared ($\epsilon^2$) were established, ranging from $1 \times 10^{-6}$ to $9 \times 10^{-6}$.

The sensitivity in the 35–45 GeV region shows an improvement over previous CMS results obtained using a "scouting" data acquisition scheme. This improvement is attributed to the GPR's ability to model the mass shape accurately, allowing the use of standard, unprescaled muon triggers and standard offline selection criteria.

Significance and Claims
The paper claims that the use of Gaussian Process Regression provides a flexible and accurate description of the Drell–Yan continuum in a mass region characterized by trigger thresholds and complex spectral shapes. By avoiding the limitations of analytic parameterizations, the analysis achieves enhanced sensitivity to narrow resonances. The results place stringent constraints on the parameter spaces of dark-photon and dark-matter mediator models in the 35–75 GeV range, complementing existing results from CMS and LHCb. The study concludes that while no evidence for new physics was found, the methodology successfully extends the ATLAS search capabilities to lower masses with a robust statistical framework.