Finding the Truth Labels

Estimated time: 35 minutes

Overview

Questions

• Why does training a model require already knowing the right answer for each example?
• How do we identify which simulated particles came from the Higgs boson, using only ID numbers?
• How do we match a truth-level quark to an actual reconstructed jet, and why is that not automatic?
• Why does the QCD background sample not need any of this matching?
• How does all of this become the label (0, 1, or 2) attached to each training example?

Objectives

• Explain what supervised learning means and why simulated data provides a built-in answer key.
• Identify a particle’s type and parent using GenPart_pdgId and GenPart_genPartIdxMother.
• Compute the angular distance ΔR between two directions and explain why phi needs special handling.
• Explain why matching jets to truth quarks is unnecessary for the QCD background sample.
• Describe how surviving events are turned into labeled training examples.

Run this first

---

PYTHON

def delta_phi(phi1, phi2):
    dphi = phi1 - phi2
    return (dphi + np.pi) % (2*np.pi) - np.pi

def extract_features(filepath, label, is_signal=True, max_events=None):
    tree = uproot.open(filepath)["Events"]
    
    # Load required branches
    branches = FEATURE_NAMES.copy()
    if is_signal:
        branches += [
            "GenPart_pdgId", "GenPart_pt", "GenPart_eta", 
            "GenPart_phi", "GenPart_mass", "GenPart_genPartIdxMother"
        ]
    
    events = tree.arrays(branches, entry_stop=max_events)
    
    if is_signal:
        # Determine target quark based on label (0: b-quark=5, 1: c-quark=4)
        target_pdg = 5 if label == 0 else 4
        
        mother_idx = events.GenPart_genPartIdxMother
        valid = mother_idx >= 0
        mother_pdg = ak.where(valid, events.GenPart_pdgId[mother_idx], -999)
        
        is_higgs_dau = (abs(events.GenPart_pdgId) == target_pdg) & (mother_pdg == 25)
        mask = ak.num(events.GenPart_pt[is_higgs_dau]) == 2
        events = events[mask]
        is_higgs_dau = is_higgs_dau[mask]
        
        # Build 4-vectors
        jets = ak.zip({
            "pt": events.Jet_pt, "eta": events.Jet_eta,
            "phi": events.Jet_phi, "mass": events.Jet_mass
        }, with_name="Momentum4D")
        
        dau = ak.zip({
            "pt": events.GenPart_pt[is_higgs_dau], "eta": events.GenPart_eta[is_higgs_dau],
            "phi": events.GenPart_phi[is_higgs_dau], "mass": events.GenPart_mass[is_higgs_dau]
        }, with_name="Momentum4D")
        
        d1, d2 = dau[:, 0], dau[:, 1]
        
        # Match using dR < 0.4
        dr1 = np.sqrt((jets.eta - d1.eta[:, None])**2 + delta_phi(jets.phi, d1.phi[:, None])**2)
        dr2 = np.sqrt((jets.eta - d2.eta[:, None])**2 + delta_phi(jets.phi, d2.phi[:, None])**2)
        matched = (dr1 < 0.4) | (dr2 < 0.4)
        
        # Extract features for matched jets
        matched_events = events[matched]
        
        # Keep exactly 2 matched jets
        mask_2jets = ak.num(matched_events.Jet_pt) == 2
        final_events = matched_events[mask_2jets]
        
    else:
        # For QCD, require at least 2 jets and take the top 2 leading jets
        mask_2jets = ak.num(events.Jet_pt) >= 2
        events = events[mask_2jets]
        # Slice to keep only the first 2 jets
        final_events = events[:, :2]

    # Stack features into a NumPy array of shape (N_events, 2_jets, N_features)
    feature_list = []
    for feat in FEATURE_NAMES:
        # Fill missing values with 0 (e.g., puId might have NaNs depending on pt)
        arr = ak.fill_none(final_events[feat], 0)
        feature_list.append(ak.to_numpy(arr))
        
    X = np.stack(feature_list, axis=-1)
    y = np.full(X.shape[0], label)
    
    print(f"Loaded label {label}: {X.shape[0]} events")
    return X, y

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Run the block above first, then read on to see what each part does.

This defines extract_features(), which this episode builds piece by piece below - a single function that takes a file path, a label, and whether the sample is signal or background, and returns the finished (X, y) arrays. It isn’t called yet - that happens once per file in Preparing the Data.

Why we need an answer key

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To train a model with examples, we need to already know the right answer for each one - otherwise there’s nothing to learn from. This is called supervised learning: a known answer supervises (corrects) the model while it learns.

For real collision data, nobody can look at the debris and just know which quark caused which jet. But for simulated data, the simulation generated the whole event starting from “create a Higgs boson that decays to two bottom quarks,” so it also secretly records what actually happened at the truth level, before detector effects blur things. That record is stored in extra columns starting with GenPart_* (“Generator-level Particle”). We only use these truth columns to build our training labels - the model itself never sees them.

The two signal files (ttHTobb, ttHTocc): matching jets to truth

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In plain words, before any code: jets are matched to generator-level truth quarks by angular distance (ΔR), and only jets that survive that match get used to build a training label - anything that doesn’t match close enough to a truth quark is thrown away.

Truth quarks (filled dots) are matched to nearby reconstructed jets (green triangles) within a ΔR window; jets outside that window (grey triangles) are unmatched and excluded from training.

For the signal samples, we need to figure out: of all the jets in this event, which ones actually came from the Higgs boson’s b-quarks (or c-quarks)? This is a two-step process, handled inside the extract_features() function you already ran above.

Step 1 - Find the Higgs boson’s daughter quarks

Every particle in GenPart_* has: - GenPart_pdgId - an ID number identifying what the particle is, using the standard PDG ID scheme: 5 = bottom quark, 4 = charm quark (-5/-4 are their antimatter partners, hence abs(pdgId)), 25 = Higgs boson. - GenPart_genPartIdxMother - which earlier particle in the list is this particle’s “parent.”

So “find the Higgs boson’s daughter quarks” becomes: find particles whose ID is ±5 (or ±4) and whose parent’s ID is 25.

PYTHON

target_pdg = 5 if label == 0 else 4          # 5 = bottom quark, 4 = charm quark
mother_pdg = ak.where(valid, events.GenPart_pdgId[mother_idx], -999)
is_higgs_dau = (abs(events.GenPart_pdgId) == target_pdg) & (mother_pdg == 25)

A Higgs decaying to two quarks should have exactly two of these, so we throw away any event where that isn’t true:

PYTHON

mask = ak.num(events.GenPart_pt[is_higgs_dau]) == 2

ak.num(...) counts how many entries survive the filter per event (since every event can have a different number of GenPart_* entries); mask then keeps only events with exactly two daughter quarks.

Step 2 - Match those quarks to actual reconstructed jets

Knowing which truth-level quarks came from the Higgs isn’t quite enough - we need to know which reconstructed jets correspond to them. We do that with a geometric trick.

eta and phi are like latitude and longitude for a particle’s direction. We measure the “distance” between a jet and a truth quark using ΔR (“delta R”):

ΔR = sqrt( (Δeta)² + (Δphi)² )

A small ΔR means the jet and quark point in almost the same direction - good evidence the jet is the spray created by that quark. We use a threshold of ΔR < 0.4, matching the cone size CMS’s jet-clustering algorithm actually used to build the jet in the first place:

PYTHON

dr1 = np.sqrt((jets.eta - d1.eta[:, None])**2 + delta_phi(jets.phi, d1.phi[:, None])**2)
matched = (dr1 < 0.4) | (dr2 < 0.4)

matched is True for any jet within ΔR of 0.4 of either Higgs daughter quark - this is what turns “here is a truth-level quark” into “here is the jet it produced.”

Why delta_phi needs its own function

phi wraps around a circle (0 to 2π, then back to 0), like a clock face. If one jet is at phi = 0.1 and another at phi = 6.2 (near 2π), a naive subtraction says they’re almost 3.5 radians apart, when really they’re neighbors either side of the wraparound point. delta_phi fixes that by squeezing the difference back into [-π, π], so it always reports the shortest way around the circle:

PYTHON

def delta_phi(phi1, phi2):
    dphi = phi1 - phi2
    return (dphi + np.pi) % (2*np.pi) - np.pi

Keeping exactly two matched jets

Finally, we only keep events with exactly two matched jets - one per Higgs daughter quark - since MiniParT always looks at a pair:

PYTHON

mask_2jets = ak.num(matched_events.Jet_pt) == 2
final_events = matched_events[mask_2jets]

final_events now holds only clean signal events: exactly two jets, both confirmed matches to the Higgs boson’s daughter quarks.

The background file (QCD): no matching needed

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For the QCD background sample, there’s no Higgs boson to match to. So we take the simpler approach of grabbing the two highest-momentum (“leading”) jets in each event:

PYTHON

mask_2jets = ak.num(events.Jet_pt) >= 2
events = events[mask_2jets]
final_events = events[:, :2]     # keep the first 2 jets

Turning this into labels

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Every surviving event becomes one training example: 2 jets × 10 features, with one label attached:

• label = 0 → the jet pair is from Hbb
• label = 1 → the jet pair is from Hcc
• label = 2 → the jet pair is QCD background

PYTHON

X = np.stack(feature_list, axis=-1)   # shape: (n_events, 2, 10)
y = np.full(X.shape[0], label)

Quick recap

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• Truth-level (GenPart_*) columns exist only in simulation, and only get used to build labels - never fed to the model.
• We find the Higgs boson’s daughter quarks by PDG ID (5 = bottom, 4 = charm) and mother ID (25 = Higgs).
• We match those truth quarks to real jets using ΔR - a “distance on the sky” built from eta and phi.
• QCD background just uses the two leading jets, since there’s no Higgs decay to match to.
• Next: Preparing the Data - preparing this data to actually feed into a neural network.

Challenge

Question

Q: Suppose you changed the matching threshold from dr1 < 0.4 to a much stricter dr1 < 0.1 (and the same for dr2). Would you expect final_events to end up with more, fewer, or about the same number of events, and why?

Show me the solution

A: Fewer events. A stricter (smaller) ΔR threshold means a jet has to point much closer to a truth quark’s direction to count as “matched.” Some jets that would have matched at ΔR < 0.4 will now fail the ΔR < 0.1 cut, so fewer events will end up with exactly two matched jets. This is a real tradeoff: a tighter threshold gives more confidence a match is correct, at the cost of throwing away usable events.

Key Points

• Truth-level (GenPart_*) columns exist only in simulation, and only get used to build labels, never fed to the model.
• We find the Higgs boson’s daughter quarks by PDG ID (5 = bottom, 4 = charm) and mother ID (25 = Higgs).
• We match those truth quarks to real jets using ΔR, a “distance on the sky” built from eta and phi, using a 0.4 threshold that matches the jet clustering cone size.
• QCD background just uses the two leading jets, since there’s no Higgs decay to match to.