Measurement of dijet angular distributions and search for beyond the standard model physics 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 detector, this study presents the first comparison of corrected dijet angular distributions with next-to-next-to-leading order perturbative QCD predictions including electroweak corrections and sets the most stringent limits to date on various beyond-the-standard-model scenarios, including quark compositeness, extra dimensions, and anomalous gluon couplings.

The Gist

Imagine the Large Hadron Collider (LHC) at CERN as the world's most powerful smashing machine. Scientists fire two beams of protons (tiny particles that make up atoms) at each other at nearly the speed of light. When they crash, they shatter into a shower of new particles, much like smashing two complex watches together to see what gears and springs fly out.

This paper is a report from the CMS experiment, one of the giant detectors watching these crashes. They are looking at a specific type of debris: dijets. Think of a "jet" as a high-speed spray of particles shooting out from the crash site. A "dijet" is when you see two of these sprays shooting out in opposite directions.

Here is the story of what they did, why they did it, and what they found, explained simply:

1. The Goal: Looking for "New Physics"

The Standard Model is our current rulebook for how the universe works. It's a very good rulebook, but scientists know it's incomplete (it doesn't explain gravity or dark matter, for example). They are looking for "Beyond the Standard Model" (BSM) physics—new rules or new particles that don't fit the current book.

To find these new rules, the scientists didn't just count how many crashes happened. Instead, they looked at how the debris flew.

• The Analogy: Imagine throwing two tennis balls at each other. If they are just solid balls, they bounce off at predictable angles. But if one of them is actually a hollow shell hiding a spring inside, the way they bounce off might look weird.
• The Measurement: They measured the angle of the jets. Specifically, they looked at a ratio called $\chi_{dijet}$. If the jets fly straight back-to-back, the angle is small. If they fly off at a wider angle, the number is bigger.

2. The Strategy: The "Perfect" Comparison

To spot a weird angle, you need to know exactly what a "normal" angle looks like.

• The Old Way: In the past, scientists compared their data to computer simulations that were "good enough" (like a sketch).
• The New Way: For the first time, this team compared their data to a super-precise prediction (a "photorealistic 3D render"). They used a calculation called NNLO (Next-to-Next-to-Leading Order). This is like upgrading from a rough map to a satellite image with street-level detail. They even added corrections for the "weather" (electroweak effects) to make the prediction perfect.

3. The Search: Hunting for Monsters

The scientists asked: "Do the jets fly in a pattern that suggests a hidden monster?" They looked for signatures of several theoretical "monsters":

• Quark Compositeness: Are quarks (the particles inside protons) actually made of even smaller things? (Like finding out a Lego brick is made of dust).
• Extra Dimensions: Are there hidden dimensions we can't see, like a flat sheet of paper that actually has a third dimension folded up?
• Quantum Black Holes: Tiny, short-lived black holes that evaporate instantly.
• Dark Matter Mediators: Invisible messengers that carry the force of dark matter.
• Axion-like Particles: Ghostly particles that might solve why the universe behaves the way it does.

4. The Results: The Universe is Boring (But Safe)

After analyzing 138 "inverse femtobarns" of data (which is a fancy way of saying they looked at 138 trillion collisions), here is what they found:

• The Good News: The data matched the "super-precise prediction" almost perfectly. The jets flew exactly where the Standard Model said they would.
• The "Almost" News: There were tiny, tiny wiggles in the data at very high energies (masses between 2.4 and 4.8 TeV, and above 6 TeV). However, these wiggles were so small that they could just be random noise or minor imperfections in the measurement. They weren't big enough to claim a discovery.
• The Conclusion: No new monsters were found. The "rulebook" of the Standard Model is still holding up strong.

5. The Legacy: Setting the "Speed Limits"

Even though they didn't find new physics, they did something incredibly valuable: They set stricter speed limits.

Because they didn't see the monsters, they can now say: "If these monsters exist, they must be heavier than X, or their interactions must be weaker than Y."

• Quark Compositeness: If quarks are made of smaller parts, those parts must be at least 17 to 37 TeV heavy (depending on how they interact). That's heavier than we can currently create!
• Dark Matter: They ruled out dark matter mediators with masses between 4 and 6.2 TeV.
• New Forces: They set the tightest limits ever on how "strongly" certain new forces could be interacting.

Summary

Think of this paper as a high-resolution security camera footage review. The scientists watched 138 trillion security tapes of protons smashing together. They used the most advanced AI (NNLO theory) to predict exactly what the footage should look like if the universe is normal.

The footage looked almost exactly like the prediction. There were no burglars (new particles) caught on camera. But by proving that the footage is so clean, they have proven that any burglars trying to sneak in must be incredibly heavy, incredibly fast, or incredibly good at hiding. The search continues, but the "No Trespassing" signs are now much bigger and clearer.

Technical Summary

1. Problem and Motivation

The Standard Model (SM) of particle physics, while highly successful, leaves several fundamental questions unanswered, such as the nature of dark matter, the hierarchy problem, and the origin of particle masses. Many Beyond the Standard Model (BSM) theories propose new interactions or particles that would manifest in high-energy proton-proton ($pp$) collisions.

Specifically, dijet production (pairs of high-energy jets) is a sensitive probe for BSM physics because:

• Resonant signatures: New particles (e.g., $Z'$, Kaluza-Klein gravitons) could appear as resonances in the dijet invariant mass spectrum.
• Non-resonant signatures: Many BSM scenarios (e.g., quark compositeness, extra dimensions, contact interactions) modify the angular distribution of the jets rather than creating a sharp mass peak. These modifications often appear as an excess of events at small scattering angles (forward scattering) compared to SM Quantum Chromodynamics (QCD) predictions.

The primary challenge in these searches is achieving a precise theoretical prediction of the SM background. Previous measurements were compared to Next-to-Leading Order (NLO) QCD predictions. This paper aims to push the precision further by comparing data to Next-to-Next-to-Leading Order (NNLO) perturbative QCD predictions, including Next-to-Leading Order (NLO) electroweak (EW) corrections, to reduce theoretical uncertainties and enhance sensitivity to subtle BSM effects.

2. Methodology

Data and Detector

• Dataset: Proton-proton collisions at a center-of-mass energy of $\sqrt{s} = 13$ TeV, collected by the CMS detector during the 2016–2018 run.
• Integrated Luminosity: $138 \text{ fb}^{-1}$.
• Event Selection: Events are selected requiring at least two reconstructed jets. The analysis focuses on the two leading jets (highest transverse momentum, $p_T$).
  • Leading jet $p_T > 500$ GeV.
  • Sub-leading jet $p_T > 200$ GeV.
  • Dijet invariant mass ($M_{jj}$) bins ranging from 2.4 TeV up to $>7.0$ TeV.
  • Kinematic acceptance: $|y_{jet}| < 2.5$ and $|y_{boost}| < 1.11$.
• Variable of Interest: The normalized dijet angular distribution, defined by $\chi_{dijet} = \exp(|y_1 - y_2|)$, where $y_1$ and $y_2$ are the rapidities of the two leading jets.
  • SM QCD processes (dominated by $t$-channel scattering) produce a distribution that is nearly flat in $\chi_{dijet}$.
  • Many BSM processes (dominated by $s$-channel or contact interactions) predict an excess of events at low $\chi_{dijet}$ (isotropic scattering).

Analysis Strategy

The analysis employs a two-pronged approach:

1. BSM Search (Detector Level): The raw data distributions are compared directly to SM + BSM predictions. A response matrix, derived from Monte Carlo (MC) simulations (PYTHIA, MADGRAPH5 aMC@NLO), maps particle-level predictions to the detector level to account for resolution effects.
2. Precision Measurement (Particle Level): The measured distributions are "unfolded" to correct for detector effects, yielding a particle-level distribution. This allows for a direct comparison with theoretical calculations without detector smearing.

Theoretical Predictions

• SM Background: Calculated using NNLOJET at NNLO in perturbative QCD, including NLO electroweak corrections.
• Scale Choices: Two central scale choices were tested: $\mu_F = \mu_R = M_{jj}$ and $\mu_F = \mu_R = \langle p_T \rangle$. The $M_{jj}$ choice showed better perturbative convergence.
• BSM Models Tested:
  • Quark Compositeness: Contact interactions (CI) with various chiral structures ($\Lambda_{LL}, \Lambda_{RR}, \Lambda_{VV}, \Lambda_{AA}, \Lambda_{V-A}$).
  • Extra Dimensions: Arkani-Hamed–Dimopoulos–Dvali (ADD) model with virtual graviton exchange (GRW and HLZ conventions).
  • Quantum Black Holes (QBH): Production in ADD and Randall-Sundrum (RS1) models.
  • Dark Matter (DM): Vector and axial-vector mediators coupling to quarks and DM.
  • Axion-Like Particles (ALPs): Coupling to gluons ($c_g/f_a$).
  • SMEFT: Anomalous triple-gluon coupling ($C_G/\Lambda^2$).

3. Key Contributions

1. First NNLO Comparison: This is the first time CMS has compared unfolded dijet angular distributions directly to NNLO QCD predictions (including NLO EW corrections). This represents a significant reduction in theoretical uncertainty compared to previous NLO-only analyses.
2. Extended Mass Reach: The analysis extends the search for BSM physics to dijet masses up to 8.3 TeV, significantly higher than previous angular distribution studies.
3. Comprehensive BSM Constraints: The study sets the most stringent limits to date for a wide array of BSM scenarios, including contact interactions, extra dimensions, quantum black holes, dark matter mediators, ALPs, and SMEFT operators.
4. Unfolding Procedure: The paper details a maximum likelihood unfolding method to correct detector effects, providing a robust particle-level dataset for future theoretical comparisons.

4. Results

Agreement with Standard Model

• The measured dijet angular distributions are generally in good agreement with the SM predictions.
• Small Discrepancies: A small difference in the shape of the normalized distributions is observed for $M_{jj}$ between 2.4–4.8 TeV and above 6.0 TeV.
  • The largest local deviations are found in the 3.0–3.6 TeV and 7.0–13 TeV bins, with local significances of 2.0$\sigma$ and 2.4$\sigma$, respectively.
  • However, when considering the full mass range and looking for signals that would not be localized in a single bin, the global significance is only 0.3$\sigma$. No evidence for BSM physics is found.

Exclusion Limits (95% Confidence Level)

The analysis sets the most stringent limits to date for the following scenarios:

• Quark Contact Interactions (CI):
  • Destructive interference ($\Lambda^+_{LL/RR}$): Excluded up to 17 TeV.
  • Constructive interference ($\Lambda^-_{LL/RR}$): Excluded up to 37 TeV.
• Extra Dimensions (ADD Model):
  • Virtual graviton exchange (GRW convention): Excluded up to 13.4 TeV.
  • String scale ($M_S$) in HLZ convention: Excluded up to 15.9 TeV (for $n_{ED}=3$).
• Quantum Black Holes (QBH):
  • Excluded for masses below 8.5 TeV (ADD model, $n_{ED}=6$) and 6.3 TeV (RS1 model).
• Dark Matter Mediators:
  • Vector/Axial-vector mediators with masses between 4.0 and 6.2 TeV are excluded.
• Axion-Like Particles (ALPs):
  • The coupling ratio $c_g/f_a$ is constrained to be $< 0.42 \text{ TeV}^{-1}$.
• SMEFT (Anomalous Triple-Gluon Coupling):
  • The coupling $C_G/\Lambda^2$ is constrained to be $< 0.0076 \text{ TeV}^{-2}$. This is significantly stronger than previous limits derived from multijet or top-quark production.

5. Significance

• Theoretical Precision: By utilizing NNLO QCD predictions, this analysis significantly reduces the theoretical uncertainty band, allowing for a more rigorous test of the Standard Model at the highest energy scales accessible at the LHC.
• BSM Sensitivity: The results push the energy scale of new physics exclusion to unprecedented levels (up to 37 TeV for constructive contact interactions), effectively ruling out many specific BSM parameter spaces that were previously viable.
• Model Independence: The use of normalized angular distributions minimizes dependence on Parton Distribution Functions (PDFs) and the strong coupling constant ($\alpha_s$), making the results robust against uncertainties in these fundamental inputs.
• Future Outlook: The particle-level results and the high-precision NNLO comparison provide a benchmark for future LHC runs (Run 3 and High-Luminosity LHC) and for theoretical developments in perturbative QCD. The lack of a significant BSM signal reinforces the Standard Model's resilience while narrowing the window for where new physics might hide.