Machine learning techniques for jet reconstruction at LHCb and application to the search for $H \to b \bar{b}$ and $H \to c \bar{c}$ in $\sqrt{s}=13$ TeV $pp$ collisions

This paper presents machine learning techniques for jet energy calibration and flavor tagging at LHCb, which are applied to search for inclusive $H \to b\bar{b}$ and $H \to c\bar{c}$ decays in 13 TeV $pp$ collisions, resulting in observed 95% confidence level upper limits of 6.6 and 1003 times the Standard Model cross-section, respectively.

The Gist

Imagine the Large Hadron Collider (LHC) at CERN as a massive, high-speed particle smasher. When protons collide, they shatter into a chaotic spray of smaller particles. Physicists need to sort through this debris to find specific, rare events—like finding a specific type of broken glass in a pile of sand.

This paper from the LHCb experiment describes how they used artificial intelligence (machine learning) to become much better at sorting this debris, specifically to look for the Higgs boson (a famous particle) breaking apart into two specific types of "quarks" (bottom and charm).

Here is a breakdown of what they did, using simple analogies:

1. The Problem: A Noisy Crowd

When the Higgs boson decays into two quarks, those quarks fly off and turn into "jets" (sprays of particles). The challenge is that the Higgs signal is very faint, and it's buried under a mountain of background noise (ordinary particle collisions).

To find the Higgs, physicists need to do two things perfectly:

1. Measure the weight: They need to know exactly how much energy the jets have to calculate the mass of the original particle.
2. Identify the flavor: They need to know if the jets came from a "bottom" quark, a "charm" quark, or just a generic "light" quark.

2. The Solution: Two New AI Tools

The team developed two new machine learning techniques to improve their search.

Tool A: The "Smart Scale" (Jet Energy Correction)

The Old Way: Imagine trying to weigh a suitcase on a scale that is slightly off. You used a simple formula to guess the correction, but it wasn't perfect, and your measurement of the suitcase's weight was still a bit blurry.
The New Way: The team built a Regression Model (a type of AI). Instead of a simple formula, this AI looks at the "shape" of the jet, how many particles are inside it, and how they are arranged. It acts like a super-smart scale that learns from millions of examples to predict the true weight of the jet with much higher precision.
The Result: The "blur" in their measurements got sharper. They could now distinguish the Higgs signal from the background noise much more clearly.

Tool B: The "Expert Detective" (Jet Flavor Tagging)

The Old Way: To identify if a jet was a "bottom" or "charm" jet, the old method looked for a specific clue: a "secondary vertex" (a tiny spot where a particle decayed). It was like a detective looking for a single fingerprint. If the fingerprint was faint or missing, the detective couldn't make a call.
The New Way: They built a Deep Neural Network (DNN). This is like hiring a detective who doesn't just look for one fingerprint. This AI looks at everything: the tracks of every particle, the energy deposits, the decay spots, and the overall shape of the jet. It combines thousands of tiny clues to make a decision.
The Result: This "Super Detective" is much better at spotting the difference between bottom jets, charm jets, and ordinary light jets. It caught more of the real signals and ignored more of the fake ones.

3. The Big Hunt: Searching for the Higgs

With these two new tools, the team went hunting for the Higgs boson decaying into:

• Bottom quarks ($H \to b\bar{b}$)
• Charm quarks ($H \to c\bar{c}$)

They analyzed data from 2016 (1.6 fb$^{-1}$ of collisions). They didn't assume how the Higgs was made; they just looked for the decay products anywhere in the data.

The Challenge: The background noise (ordinary particle collisions) is huge. To handle this, they used a clever trick: they defined a "Control Region" (a safe zone where they knew no Higgs existed) to learn what the background noise looked like, and then used that knowledge to predict the noise in their "Signal Region" (where the Higgs might be).

4. The Results: What Did They Find?

After running the numbers, they found no evidence of the Higgs boson decaying in this specific way in their dataset. The data looked exactly like what you would expect if the Higgs wasn't there (or was too rare to see with this amount of data).

However, they set limits on how often this could be happening:

• For Bottom Quarks: They found that if the Higgs is decaying into bottom quarks, it happens at least 6.6 times less often than the Standard Model predicts. (This is a very good result; it's close to the expected limit).
• For Charm Quarks: They found that if the Higgs is decaying into charm quarks, it happens at least 1,003 times less often than predicted. (This limit is much weaker, meaning it's much harder to find the charm signal because the background noise is so loud and the charm jets are harder to spot).

5. What's Next?

The paper concludes that while they didn't find the Higgs in this specific dataset, their new AI tools are a huge success. They proved that machine learning can significantly improve how LHCb measures jets.

They predict that with more data from future runs (Run 4 and Run 5 of the LHC), these tools will be powerful enough to finally observe the Higgs decaying into bottom quarks and get much closer to observing the decay into charm quarks.

In short: They built better AI glasses to see through the particle fog. They didn't find the treasure (the Higgs signal) in this specific pile of sand, but they proved their new glasses work so well that they are confident they will find it with a bigger pile of sand in the future.

Technical Summary

Technical Summary: Machine Learning Techniques for Jet Reconstruction at LHCb and Application to $H \to b\bar{b}$ and $H \to c\bar{c}$ Searches

Problem Statement
The LHCb experiment, primarily designed for heavy-flavour physics in the forward pseudorapidity region ($2 < \eta < 5$), faces significant challenges in reconstructing and identifying jets, particularly those originating from heavy-flavour quarks ($b$ and $c$). Standard reconstruction methods suffer from degraded energy resolution due to undetected neutrinos in semileptonic decays and limited efficiency in distinguishing heavy-flavour jets from light-flavour jets (initiated by $u, d, s$ quarks or gluons). These limitations hinder the precision of inclusive Higgs boson searches ($H \to b\bar{b}$ and $H \to c\bar{c}$) in the dijet final state, where accurate dijet invariant-mass resolution and high-purity flavour tagging are critical for separating signal from the overwhelming multijet QCD background.

Methodology
The paper introduces two novel machine learning techniques to address these reconstruction and identification challenges, applied to a dataset of $pp$ collisions at $\sqrt{s} = 13$ TeV corresponding to an integrated luminosity of $1.6 \text{ fb}^{-1}$ (collected in 2016).

1. Regression-Based Jet-Energy Correction (JEC):

   • Approach: A Gradient Boosted Regressor (GBR) is employed to correct jet energies, replacing the standard multiplicative correction factor.
   • Inputs: The model utilizes a comprehensive set of 421 features, including jet kinematics ($p_T, \eta, \phi$), composition (number of constituents, charged-particle fraction), jet substructure (energy distribution in concentric rings $\Delta R$), muon information, and event-level variables (number of primary vertices).
   • Training: The regressor is trained on simulated $H \to b\bar{b}$ signal and dijet background samples to predict the truth-level jet energy. Separate models are trained for leading and subleading jets.
   • Goal: To minimize the difference between reconstructed and truth-level dijet invariant mass ($m_{reco} - m_{truth}$), thereby improving mass resolution.

2. Deep Neural Network (DNN) for Jet Flavour Tagging:

   • Approach: A Deep Neural Network, inspired by the CMS DeepJet algorithm, is developed to discriminate between $b$-jets, $c$-jets, and light jets.
   • Architecture: The network processes four categories of inputs: charged particles, neutral particles, secondary vertices, and global jet properties. It utilizes 1D convolutional layers for particle features, a Long Short-Term Memory (LSTM) layer for sequential processing of charged/neutral particles, and dense layers for final classification.
   • Inputs: Up to 20 charged particles (ordered by impact parameter) and 10 neutral particles (ordered by energy) per jet are included, alongside secondary vertex kinematics and global jet variables.
   • Output: The network outputs three probabilities ($P_b, P_c, P_q$) representing the likelihood of the jet originating from a $b$, $c$, or light quark, respectively.

3. Search Strategy and Background Estimation:

   • Signal and Control Regions: Signal Regions (SR) are defined by strict DNN probability thresholds and secondary-vertex tagging requirements. Control Regions (CR), composed of mixed-flavour jet pairs, are used to model the dominant multijet QCD background in a data-driven manner.
   • Background Modeling: A transfer function (TF), parameterized as a Bernstein polynomial, extrapolates the dijet mass shape from the CR to the SR.
   • Statistical Analysis: A binned maximum-likelihood fit is performed on the dijet invariant-mass spectrum ($45 < M_{jj} < 250 \text{ GeV}/c^2$). Systematic uncertainties (e.g., jet energy scale, tagging efficiency, background modeling) are incorporated via nuisance parameters. Upper limits are set using the $CL_s$ method.

Key Contributions

• Algorithmic Development: The paper presents the first application of a GBR-based jet energy correction and a full-substructure DNN for flavour tagging at LHCb.
• Performance Improvement:
  • The GBR correction significantly improves the dijet invariant-mass resolution compared to the standard cubic JEC method.
  • The DNN tagging algorithm demonstrates a relative efficiency improvement of $>9\%$ for $b$-jets and $>20\%$ for $c$-jets compared to the standard secondary-vertex tagging (SVT) algorithm, while maintaining a light-jet misidentification rate of $\sim 1\%$.
• Inclusive Search: Unlike previous LHCb analyses focused on vector boson associated production ($VH$), this work targets inclusive $H \to b\bar{b}$ and $H \to c\bar{c}$ decays without assumptions on the production mechanism, allowing for broader comparisons with Beyond Standard Model (BSM) theories.

Results
Using the 2016 dataset ($1.6 \text{ fb}^{-1}$), no significant excess of events attributable to Higgs boson decays was observed in either channel. The fitted signal yields were compatible with zero.

• $H \to b\bar{b}$ Search:

  • Observed 95% CL upper limit: $6.6 \times \sigma_{SM}$ (211 pb).
  • Expected 95% CL upper limit: $11.1 \times \sigma_{SM}$.
  • The observed limit is tighter than expected due to a downward statistical fluctuation in the data.

• $H \to c\bar{c}$ Search:

  • Observed 95% CL upper limit: $1003 \times \sigma_{SM}$ (1605 pb).
  • Expected 95% CL upper limit: $1834 \times \sigma_{SM}$.
  • The sensitivity is limited by a low signal-to-background ratio, reduced charm-tagging efficiency, and higher background misidentification rates.

• Systematic Uncertainties: The dominant systematic uncertainty for both searches is the jet secondary-vertex tagging efficiency (15% for $H \to b\bar{b}$, 19% for $H \to c\bar{c}$).

Significance and Future Prospects
The paper claims that these results set the most stringent limits on inclusive $H \to b\bar{b}$ and $H \to c\bar{c}$ production using the current LHCb dataset. The deployment of these machine learning techniques demonstrates their potential to enhance jet measurement precision at LHCb.

The authors provide extrapolations for future data taking (Run 3, Run 4, and Run 5). They conclude that:

• Observation of the inclusive $H \to b\bar{b}$ process is expected to be feasible by the end of Run 4 (50 $\text{fb}^{-1}$), with projected limits reaching $\sim 1.1 \times \sigma_{SM}$.
• By the end of Run 5 (300 $\text{fb}^{-1}$), the inclusive $H \to c\bar{c}$ channel is projected to constrain the charm Yukawa coupling ($y_c$) to approximately $6.7$ times the Standard Model value. This approach offers a complementary constraint to $VH$ production searches, as it is not dependent on assumptions regarding the Higgs production mechanism.