Big Dipper, Help Me Find A Way -- Dip-hunting at hadron colliders

This paper proposes a "dip-hunting" strategy using parametric neural networks to identify top-philic scalar resonances through destructive interference patterns, addressing the limitations of traditional bump-hunting methods in regions where interference invalidates the narrow-width approximation.

The Gist

Imagine you are a detective looking for a specific type of criminal in a crowded city square. Usually, you'd look for a "bump" in the crowd—a sudden, noticeable cluster of people that stands out from the normal flow. In particle physics, this is called "bump-hunting." Scientists look for a sudden spike in data that suggests a new, heavy particle has been created.

However, this paper describes a situation where the criminal is a master of disguise. Instead of creating a crowd, this new particle (a "scalar") interferes with the normal background noise in a way that actually removes people from the crowd. It creates a "dip" or a hole in the data where you expect to see something.

Here is a simple breakdown of how the authors solved this mystery:

1. The Problem: The "Ghost" in the Machine

In the world of high-energy physics (like at the Large Hadron Collider), scientists smash particles together to find new ones. Usually, if a new particle exists, it creates a "bump" on a graph. But sometimes, the new particle interacts with the background noise in a way that causes destructive interference.

Think of it like noise-canceling headphones. The background noise is the sound of the city. The new particle is a sound wave that is perfectly out of sync with the city noise. When they mix, they cancel each other out, creating a zone of silence (a "dip") instead of a loud noise.

The problem is that traditional detective tools are built to find loud noises (bumps), not silence (dips). If you only look for bumps, you will miss these "ghost" particles entirely.

2. The Solution: "Dip-Hunting"

The authors propose a new strategy called "Dip-Hunting." Instead of looking for a spike, they look for the specific shape of the silence.

To do this, they used a clever trick involving Machine Learning (AI). They treated the problem like a game of "Spot the Difference."

• The Setup: They created a massive library of computer simulations.
  • Class 0 (The Background): Simulations of what the data looks like with only normal physics (no new particles).
  • Class 1 (The Signal): Simulations of what the data looks like if a new particle is there, creating that "dip."
• The Twist: Because of the interference, some of the "Signal" simulations have "negative weights." Imagine if some of your suspect photos were printed in negative ink. This makes the math messy because probabilities can't usually be negative.
• The AI Tool: They built a special AI (a Neural Network) called the Ratio of Signed Mixtures Model (RoSMM). This AI learned to handle the "negative ink" photos. It learned to look at a specific event and say, "Based on the shape of this data, is this more likely to be normal background, or is it a 'dip' caused by a new particle?"

3. How They Tested It

The authors didn't just guess; they ran a rigorous test:

1. The Training: They taught the AI to recognize the difference between normal data and data with a "dip" for various scenarios (different masses and strengths of the new particle).
2. The Mystery: They then gave the AI a set of "mystery data" (simulated data with a hidden new particle) that the AI had never seen before.
3. The Guess: The AI scanned through thousands of possibilities to find the one that best matched the mystery data. It essentially asked, "If I assume the new particle has this mass and this strength, does it create the exact 'dip' shape I see in the data?"

4. The Results

The AI was remarkably successful.

• It could accurately identify the mass of the hidden particle (how heavy it is).
• It could identify the coupling strength (how strongly it interacts with other particles).
• Even when they changed the rules slightly (making the particle wider or changing its properties), the AI could still figure out the correct parameters, proving the method is robust.

The Big Picture

The paper claims that this "Dip-Hunting" method works as a proof-of-concept. It shows that we don't have to ignore the "silence" in our data. By using this specific type of AI, scientists can turn a confusing "hole" in the data into a clear signal of new physics.

In short: The paper says, "We built a smart AI that can find new particles not by looking for a loud explosion, but by recognizing the specific shape of the silence they leave behind." This could help physicists find new particles that were previously hiding in plain sight.

Technical Summary

1. Problem Statement

The search for Beyond the Standard Model (BSM) physics at the Large Hadron Collider (LHC) has traditionally relied on "bump-hunting": identifying local excesses in invariant mass distributions over a smooth background. However, this strategy fails in specific scenarios involving top-philic scalar resonances (scalars that couple strongly to top quarks).

• Destructive Interference: In models like the Two-Higgs-Doublet Model (2HDM), a new scalar $S$ produced via gluon fusion ($gg \to S \to t\bar{t}$) interferes destructively with the Standard Model (SM) QCD background ($gg \to t\bar{t}$).
• Failure of Narrow-Width Approximation (NWA): When interference is significant, the NWA breaks down. Instead of a resonance "bump," the signal manifests as a "dip" (a local deficiency) or a distorted line shape in the $t\bar{t}$ invariant mass ($m_{t\bar{t}}$) distribution.
• The Challenge: Traditional statistical tools struggle to interpret these dips because they are not simple excesses. Furthermore, modeling the background and interference effects accurately across the full analysis chain using detailed simulations is computationally expensive and complex. The authors pose the inverse problem: Given an observed distribution with a dip, can we determine the likelihood that it originates from a specific BSM scalar model and extract its parameters?

2. Methodology: "Dip-Hunting" via Parametric Neural Networks

The authors propose a machine learning-based framework called "Dip-Hunting" to solve the inverse problem. The core of their approach is the Ratio of Signed Mixtures Model (RoSMM) combined with parametric neural networks.

A. Theoretical Framework

• Signal Model: A simplified model where a scalar $S$ couples to top quarks with strength $C_e$ and mass $m_S$. The Lagrangian includes a term $-C_e \frac{y_t}{\sqrt{2}} S \bar{t}t$.
• Interference: The total amplitude squared includes the signal term, the background term, and the interference term ($2 \text{Re}(M_S^* M_{\text{con.},t})$). This leads to negative event weights in Monte Carlo (MC) simulations, making the probability density a "quasi-probability."

B. The Ratio of Signed Mixtures Model (RoSMM)

Standard classifiers cannot handle negative weights directly. The RoSMM decomposes the quasi-probabilistic likelihood ratio $r(x, \vec{c}) = p_{\text{target}}(x) / p_{\text{ref}}(x)$ into four sub-densities based on the sign of the event weights ($+$ or $-$) and the class (SM or BSM):

1. $r_{++}$: Ratio of positive-weight BSM to positive-weight SM.
2. $r_{+-}$: Ratio of negative-weight BSM to positive-weight SM.
3. Coefficients: The model learns coefficients ($c_0, c_1$) that weight these ratios. Since SM events have only positive weights, the formula simplifies to a linear combination:
   $$r(x, \vec{c}) = c_1 r_{++}(x) + (1 - c_1) r_{+-}(x)$$

C. Neural Network Architecture

• Input: The network takes event observables (e.g., leading top $p_T$, pseudorapidity, $m_{t\bar{t}}$) concatenated with the BSM theory parameters ($\theta = \{C_e, m_S\}$).
• Training: The network is trained as a binary classifier to distinguish between:
  • Class 0: SM background events (re-weighted with various $\theta$ values via data augmentation).
  • Class 1: BSM signal events (generated with specific $\theta$ values).
• Architecture: A 4-layer Multi-Layer Perceptron (MLP) with ReLU activations and dropout, trained with a weighted binary cross-entropy loss to account for MC weights.

D. Inference Pipeline

1. Reference Sample: A set of SM events is selected.
2. Hypothesis Construction: A "truth" distribution (the dip) is generated from holdout data.
3. Parameter Scan: For a grid of parameters $\theta$:
   • The trained RoSMM models ($r_{++}$ and $r_{+-}$) compute a reweighting factor for each SM event.
   • The SM events are reweighted to simulate the BSM hypothesis at that specific $\theta$.
   • An $L_2$ statistic is computed between the reweighted distribution and the observed (hypothetical) data.
4. Best Fit: The parameters $\hat{\theta}$ that minimize the $L_2$ statistic are selected as the inferred values.

3. Key Contributions

1. Proof-of-Principle for Dip-Hunting: The paper demonstrates that destructive interference patterns (dips) can be successfully identified and characterized using ML, moving beyond traditional bump-hunting.
2. Parametric Likelihood Learning: The authors successfully train a neural network to learn the likelihood ratio as a continuous function of BSM parameters ($C_e, m_S$), allowing for rapid inference without re-simulating the entire detector chain for every parameter point.
3. Handling Negative Weights: The application of RoSMM effectively manages the quasi-probabilistic nature of interference-corrected MC samples, a known difficulty in high-energy physics analysis.
4. Robustness Testing: The study investigates the method's performance when model constraints (specifically the relationship between coupling and width) are relaxed, showing the method's applicability to broader classes of theories.

4. Results

The authors tested the framework using 13 TeV LHC collision simulations with $140.1 \text{ fb}^{-1}$ of integrated luminosity.

• 1D Inference (Single Parameter):

  • Coupling ($C_e$): The method accurately inferred $C_e$ values (e.g., 0.5 and 1.1) with a bias of $\approx 5\%$ at low values, attributed to the coarse-graining of the training grid.
  • Mass ($m_S$): The method accurately inferred resonance masses (e.g., 650 GeV and 870 GeV) with a bias of only $\approx 0.2\%$.
  • Performance: The Area Under the Curve (AUC) for the sub-density classifiers ranged from 0.81 to 0.95, indicating strong discrimination power.

• 2D Inference (Simultaneous $C_e$ and $m_S$):

  • The framework successfully reconstructed the 2D parameter space. The $L_2$ heat maps showed clear minima at the true parameter values.
  • The mass parameter was constrained more tightly than the coupling, consistent with the 1D results.

• Relaxing Model Constraints (Width Variation):

  • The authors tested scenarios where the resonance width $\Gamma_S$ was manually decoupled from the standard prediction (varying $\Gamma_S/m_S$ from 5% to 30%).
  • Result: The pipeline remained robust up to $\Gamma_S/m_S \approx 15\%$. Beyond this (e.g., 30%), the inference degraded due to the intrinsic degeneracy between coupling and width and the network's lack of training data in that extreme regime.
  • This demonstrates that the method can handle deviations from specific model correlations, provided the deviations remain within perturbative limits.

5. Significance and Future Outlook

• Complementary Strategy: "Dip-hunting" offers a necessary complement to bump-hunting for scenarios where interference dominates. It allows experiments to interpret data that would otherwise be discarded or misinterpreted as background fluctuations.
• Efficiency: By learning the mapping between parameters and distributions, this approach reduces the computational overhead of scanning large BSM parameter spaces, which is crucial for future high-luminosity LHC analyses.
• Model Independence: While the study used a specific simplified model, the robustness against width variations suggests the technique can be extended to more complex scenarios, including CP-odd states or mixed couplings, by adding appropriate parameters to the network input.
• Future Work: The authors plan to extend this to fully hadronized final states (including detector effects) and investigate signal-signal interference scenarios.

In conclusion, this paper establishes a viable, ML-driven methodology for extracting BSM parameters from interference-dominated signals, effectively turning the "dip" in the data into a discovery channel.