Search for low-mass vector and scalar resonances decaying into a quark-antiquark pair in proton-proton collisions at $\sqrt{s}$ = 13 TeV

Using 13 TeV proton-proton collision data collected by the CMS experiment, this study searches for low-mass vector and scalar resonances decaying into quark-antiquark pairs and, finding no evidence of such signals, sets the most stringent limits to date on their couplings in the 50–250 GeV mass range.

The Gist

Imagine the Large Hadron Collider (LHC) at CERN as the world's most powerful, high-speed particle smasher. Scientists there smash two beams of protons together at nearly the speed of light, creating a chaotic explosion of tiny particles. Usually, these explosions are messy and predictable, following the rules of the "Standard Model" (the current rulebook of physics).

But what if, hidden inside that chaos, there's a secret? What if there are new, heavy particles that don't belong in the rulebook?

This paper is a report from the CMS experiment (one of the giant detectors at the LHC) saying: "We looked very hard for these secret particles, but we didn't find them. However, we now know exactly where they aren't hiding."

Here is the breakdown of their search, explained with everyday analogies:

1. The Mission: Hunting for "Ghost" Particles

The scientists were looking for resonances. Think of a resonance like a specific musical note. If you have a guitar string, it vibrates at a specific pitch. In physics, new particles would "vibrate" at a specific mass (weight).

They were looking for particles that are relatively "light" (between 50 and 300 times the mass of a proton) that decay (break apart) into a pair of quarks (the building blocks of protons and neutrons).

• The Theory: Some theories suggest there are new forces or particles (like a "Dark Matter" messenger) that might show up as these specific notes.
• The Goal: Find a "peak" in the data—a sudden spike in the number of events at a specific mass—indicating a new particle was created.

2. The Challenge: The "White Noise" of the Universe

The biggest problem is background noise.

• The Analogy: Imagine trying to hear a single person whispering a secret in the middle of a roaring stadium during a rock concert. The "roar" is the Standard Model physics (specifically, Quantum Chromodynamics or QCD), which produces billions of jets of particles every second.
• The Strategy: To hear the whisper, you need to filter out the noise. The scientists decided to only listen to the loudest, most energetic whispers. They looked for collisions where the new particle was produced alongside a massive burst of energy (called "Initial State Radiation"). This pushes the new particle to move very fast, making its debris clump together into a single, large, heavy "jet" of particles.

3. The Tool: The "ParticleNet" AI

Once they found these heavy jets, they had to figure out what was inside them.

• The Problem: Most jets are just random garbage (light quarks or gluons). They wanted to find jets made of bottom quarks (heavy, specific particles) or charm quarks.
• The Solution: They used an Artificial Intelligence algorithm called ParticleNet.
• The Analogy: Imagine a detective trying to identify a suspect in a crowd. A human might look at the face. But ParticleNet is like a super-detective that looks at the suspect's gait, the way they hold their hands, their shoe laces, and the texture of their clothes all at once. It uses a "neural network" (a brain-like computer program) to distinguish a "bottom-quark jet" from a "random junk jet" with incredible precision.

4. The Search Process

The team analyzed data from 2016–2018 (138 "inverse femtobarns" of data—imagine a library containing trillions of collision events).

1. Filter: They selected only the most energetic jets.
2. Sort: They used the AI to separate jets that might be new particles from the background noise.
3. Weigh: They measured the "invariant mass" (the weight) of these jets.
4. Look for the Spike: They plotted a graph. If a new particle existed, the graph would show a sharp mountain peak at a specific weight.

5. The Result: The "Silent" Graph

They found no mountains.
The graph was a smooth, rolling hill that matched the predictions of the Standard Model perfectly. There were no unexpected spikes.

• The Good News: This means the universe is behaving exactly as our current rulebook predicts in this mass range.
• The "Bad" News (for theorists): It means those specific theories proposing new particles in this weight range are likely wrong, or at least, those particles are much harder to find than we thought.

6. The Legacy: Setting the Boundaries

Even though they didn't find the particle, the paper is a huge success.

• The Analogy: Imagine you are looking for a lost coin in a dark field. You don't find it, but you shine a flashlight so bright that you can now say with 100% certainty: "The coin is definitely not in this 50-foot circle."
• The Impact: The scientists have set the strictest limits to date on how strongly these hypothetical particles could interact with normal matter. They have effectively told theorists: "If your new particle exists, it must be even more elusive or have different properties than you guessed."

Summary

The CMS team used a super-smart AI to sift through the loudest, most energetic collisions at the LHC, looking for a specific "whisper" of new physics. They didn't find the whisper, but they proved that the "noise" of the universe is exactly as loud and chaotic as we expected. They have successfully closed the door on many theories for new particles in the 50–250 GeV mass range, forcing scientists to look elsewhere or rethink their ideas.

Technical Summary

1. Problem and Motivation

The search addresses a critical gap in the exploration of Beyond the Standard Model (BSM) physics: low-mass dijet resonances (masses between 50 and 300 GeV).

• Theoretical Context: Many BSM theories predict new particles that couple to quark-antiquark pairs, including:
  • Extended electroweak sectors ($W'$ or $Z'$ bosons).
  • Randall–Sundrum models (Kaluza–Klein gravitons).
  • Dark matter mediators (connecting the Standard Model to a dark sector).
• Experimental Challenge: The primary background is Quantum Chromodynamics (QCD) multijet production, which has an enormous cross-section. This creates a "bandwidth bottleneck" in data acquisition, making it difficult to trigger on and analyze low-mass resonances directly. Furthermore, distinguishing a narrow resonance signal from the falling QCD background requires high-precision jet substructure analysis and flavor tagging.

2. Methodology

Data and Event Selection

• Dataset: Proton-proton collision data collected by the CMS experiment at $\sqrt{s} = 13$ TeV during 2016–2018, corresponding to an integrated luminosity of 138 fb$^{-1}$.
• Trigger Strategy: To bypass bandwidth limitations, the analysis targets resonances produced in association with hard Initial-State Radiation (ISR). This results in a high transverse momentum ($p_T > 500$ GeV) resonance, causing its decay products to be highly collimated.
• Reconstruction: The decay products are reconstructed as a single large-radius jet (AK8) with a two-pronged substructure.
  • Soft-Drop Mass ($m_{SD}$): Used to reduce the mass of QCD jets while preserving the mass of heavy resonances, providing a resolution of 9–14%.
  • Kinematic Cuts: Events require at least one AK8 jet with $p_T > 500$ GeV, $m_{SD} > 30$ GeV, and $|\eta| < 2.5$.

Machine Learning: PARTICLENET (PN)

A key innovation in this analysis is the use of the PARTICLENET algorithm, a graph convolutional neural network (GCN).

• Function: It distinguishes signal jets (resonance decays) from QCD background and identifies the flavor of the quark pair.
• Outputs: The network produces probabilities for four classes: QCD background, $X \to b\bar{b}$, $X \to c\bar{c}$, and $X \to q\bar{q}$ (light quarks).
• Discriminants:
  • $p_{2\text{-prong}}$: Distinguishes two-pronged resonances (any flavor) from QCD.
  • $p_{bb}$: Distinguishes $b\bar{b}$ resonances from $c\bar{c}$ and light quark resonances.

Signal Regions (SRs) and Background Estimation

Events are categorized into three regions based on PN scores:

1. QCD Control Region (CR): Events failing the $p_{2\text{-prong}}$ requirement (used to model the QCD background shape).
2. High-$p_{bb}$ SR: Targets $Z' \to b\bar{b}$ and scalar/pseudoscalar ($\phi/A \to b\bar{b}$) decays.
3. Low-$p_{bb}$ SR: Targets $Z'$ decays to light ($q\bar{q}$) and charm ($c\bar{c}$) quarks.

Background Modeling:

• QCD Multijets: Estimated directly from data using the QCD CR, with transfer functions (Bernstein polynomials) to correct for shape differences between the CR and SRs in $p_T$ and $\rho$ (a variable related to jet mass and $p_T$).
• Other Backgrounds: $W/Z$+jets, $t\bar{t}$, single top, and diboson processes are estimated using Monte Carlo (MC) simulations, corrected with data-driven scale factors derived from control regions (e.g., boosted $W$ bosons in $t\bar{t}$ events).

Statistical Analysis

• A binned maximum likelihood fit is performed on the $m_{SD}$ distributions across 203 bins (62 mass bins $\times$ 5 $p_T$ bins $\times$ 3 regions).
• Systematic uncertainties (luminosity, jet energy scale, tagging efficiency, background modeling) are included as nuisance parameters.

3. Key Contributions

1. Application of PARTICLENET: This is one of the first major low-mass resonance searches to utilize a GCN-based tagger (PARTICLENET) for both signal-background separation and flavor tagging, demonstrating superior sensitivity over traditional analytic variables (like energy correlation functions).
2. Low-Mass Reach: The analysis successfully probes the 50–300 GeV mass range, a region historically difficult to access due to trigger thresholds and overwhelming QCD backgrounds.
3. Dual Coupling Scenarios: The search simultaneously constrains two distinct BSM scenarios:
   • Spin-1 ($Z'$): Coupled equally to all quark flavors.
   • Spin-0 ($\phi/A$): Coupled preferentially to bottom quarks (motivated by Minimal Flavor Violation).

4. Results

• Observation: No significant excess of events over the Standard Model background predictions was observed.
  • The largest local deviations were $2.8\sigma$ (at $m_{Z'} = 75$ GeV and $225$ GeV) and $2.6\sigma$ (at $m_{\phi} = 70$ GeV), which are consistent with statistical fluctuations (global significances $< 2\sigma$).
• Exclusion Limits (95% Confidence Level):
  • Spin-1 ($Z'$): Limits on the universal coupling $g_q$ range from 0.03 to 0.13.
  • Spin-0 ($\phi/A$): Limits on the coupling parameters $g_{q\phi}$ and $g_{qA}$ range from 1.5 to 5.8 and 1.0 to 3.8, respectively.
• Dark Matter Interpretation: The results were recast to constrain dark photon ($\epsilon^2$) and axion-like particle (ALP) models. The analysis excludes regions of parameter space relevant for thermal relic dark matter scenarios where the mediator mass is between 50 and 300 GeV.

5. Significance

• Stringent Constraints: These results represent the most stringent limits to date on dijet resonances in the 50–250 GeV mass range, improving upon previous best limits by approximately a factor of two.
• Methodological Benchmark: The successful deployment of PARTICLENET in a high-pileup, high-rate environment validates the use of advanced deep learning techniques for future searches at the High-Luminosity LHC (HL-LHC).
• Dark Sector Probes: By setting tight constraints on light mediators, this work significantly narrows the viable parameter space for simplified dark matter models that rely on visible decays of mediators to quarks.

In summary, this paper demonstrates the CMS collaboration's capability to probe low-mass BSM physics despite the overwhelming QCD background, utilizing advanced machine learning and rigorous data-driven background estimation to set world-leading exclusion limits.