18 In-Channel Coherence of Large Hadron Collider Jets and Its Update with Event Congestion

Home ／ Appendix-Prediction and Falsification

This chapter follows the publication template for the falsification program. It uses plain language, avoids equations, and keeps the structure fixed. At first mention, we expand abbreviations for general readers: Large Hadron Collider (LHC), proton–proton (pp), pileup (multiple overlapping interactions per bunch crossing), event energy-density ρ (rho), Cambridge/Aachen (C/A), and anti-kT (a standard jet-finding algorithm). We also define key substructure tools at first mention: PileUp Per Particle Identification (PUPPI), SoftKiller (a pileup–suppression method), Soft Drop (a grooming method with parameters z_cut and β), the Lund plane (emission-history map), N-subjettiness (τ ratios), energy-correlation functions (C2, D2), and the color-flow pull angle.

I. One-Sentence Goal

Quantify whether in-channel coherence inside jets—meaning the same-direction, angle-ordered pattern of soft radiation along the color flow—exhibits a consistent, monotonic “update” as event congestion increases, where congestion is captured by pileup and local energy-flow density. The claim is supported if coherence indicators shift with congestion in the same direction across channels and algorithms, and environment-forward predictions based only on congestion proxies hit above chance under blinding. If congestion instead destroys or randomizes coherence, or if results fail to replicate across algorithms and teams, the claim is disfavored.

II. What to Measure

1. Congestion and its proxies (text tiers):
   • Global congestion: average pileup μ per bunch crossing; FastJet-style median event energy density ρ; transverse-region scalar ΣpT and charged-track multiplicity Nch.
   • Local congestion: ρ_local in an annulus around each jet (R to 2R); track–vertex association density and jet isolation in the neighborhood.
   • Binning convention: use low / medium / high congestion tiers that remain comparable across data-taking periods and triggers.
2. In-channel coherence indicators (plain-language tiers):
   • Lund-plane main ridge clarity/narrowness: graded clear / moderate / blurred; angle ordering graded enhanced / preserved / broken.
   • Groomed splitting symmetry and scale: Soft Drop z_g and R_g should shift monotonically with congestion (for example, “drifts toward moderate symmetry” vs “spreads to extreme asymmetry”).
   • Energy-correlation and substructure ratios: C2, D2, and N-subjettiness ratios (τ_21, τ_32) graded as narrows / holds / broadens.
   • Color-flow pull angle and pull magnitude: for dijets and γ/Z+jet events, test whether color-flow orientation becomes more concentrated / unchanged / more diffuse as congestion rises.
   • Soft-component co-alignment ratio: within-jet sector counts (co-aligned vs counter-aligned) graded for monotonic update.
3. Update definition (text only):
   Between low → medium → high congestion, record up / flat / down for each coherence indicator with strong / medium / weak amplitude. Combine into an overall coherence-update verdict per channel and algorithm.
4. Channel and color-flow controls:
   • Compare dijet (strong color connection) with γ+jet / Z+jet (color-neutral recoil) as color-flow baselines.
   • Use quark-enriched vs gluon-enriched subsets.
   • Contrast top-quark jets (with decay chains) with QCD jets to test generality of coherence metrics.

III. How to Do It

1. Samples and reconstruction:
   • Use multiple LHC pp periods (Run-2 / Run-3). Reconstruct jets with anti-kT (R = 0.4 / 0.6) and C/A, in parallel calorimeter / particle-flow jets and track-based jets.
   • Apply three pileup-suppression strategies—PUPPI / SoftKiller / constituent subtraction—and scan three grooming families (Soft Drop z_cut, β grids).
2. Forward prediction, blinding, and arbitration:
   • Environment team (forward): using only congestion proxies (μ, ρ, ρ_local, ΣpT in the transverse region), issue a prediction card for each channel and tier: the direction (up / flat / down) and strength (strong / medium / weak) expected for each coherence indicator when moving low → high congestion.
   • Measurement teams (independent pipelines): on a 3×3 grid (three suppression methods × three grooming families), produce text-grade distributions and trends for all indicators. Teams share only event-quality flags and tier IDs.
   • Arbitration: a third party aligns prediction cards with measured summaries, computes hit / wrong / null rates, and stratifies by channel / algorithm / data period.
3. Congestion control and baselines:
   • Zero-bias overlay: artificially overlay minimum-bias events onto the same hard scatter to create a controlled congestion ladder.
   • Transverse-region baseline: use ΣpT and Nch in the transverse region as an event-level congestion ruler, cross-calibrated with FastJet-ρ.
   • Random/shifted cones: estimate biases from non-jet soft backgrounds and remove them in text-grade fashion.
4. Color-flow and geometry stratification:
   • For back-to-back dijets and γ/Z+jet, compute pull and Lund-ridge consistency separately.
   • Recompute after stratifying by jet pT, |η|, jet radius R, and quark/gluon enrichment to test universality and transferability of in-channel coherence.

IV. Positive/Negative Controls and Removal of Artifacts

1. Positive controls (supporting a path-term contribution):
   • With pileup suppressed and grooming standardized, the Lund main ridge remains clear or clearer as congestion rises; pull angles in dijet and γ+jet become more concentrated or hold steady; z_g, R_g, D2, τ_21 show monotonic updates matching forward predictions.
   • Local congestion (ρ_local) outperforms global congestion (μ, ρ) in predicting the strength ordering of coherence updates (higher hit rate).
   • These trends persist across three suppression methods × three grooming families, multiple data periods, and independent teams.
2. Negative controls (against a path-term contribution):
   • If “coherence enhancement” survives random overlays or rotated jet axes, classify as method bias.
   • If significance appears only for calorimeter jets or one grooming choice, and is not supported by track-based jets / vertex association, classify as mismodeled pileup/associations.
   • If γ/Z+jet (color-neutral control) fails to replicate or moves oppositely to dijets, classify as color-flow artifact or underlying-event coupling.

V. Systematics and Safeguards (Three Items)

• Pileup and underlying-event modeling: over- or under-correction can fake coherence changes. Safeguard: cross-check PUPPI / SoftKiller / constituent subtraction; calibrate residuals with random cones and zero-bias overlays; report pileup dependence in stratified form.
• Trigger and selection biases: thresholds and isolation alter quark/gluon mix and coherence apertures. Safeguard: stratify by trigger menu and pT; verify consistency across triggers; use γ/Z+jet as dual baselines for color flow and triggering.
• Detector effects and out-of-time pileup: timing windows and extrapolation efficiencies impact soft-radiation reconstruction. Safeguard: use timing / vertex–track association; triangulate calorimeter vs particle-flow vs track-only jets; assign data-driven uncertainty tiers.

VI. Execution and Transparency

Pre-register congestion tiers, text-grade definitions for coherence indicators, prediction-card schema, blinding/arbitration rules, and positive/negative controls with exclusions. Maintain hold-out data slices and parameter families per channel/tier for final confirmation. Enable cross-team/algorithm replication via ATLAS/CMS open or partnered datasets and independent pipelines, exchanging four levels of outputs (objects → jets → substructure → text-grade tables). Publicly release congestion templates, prediction cards, coherence-update grade tables, pileup-suppression and grooming logs, and key intermediates. This chapter forms a closed loop with Chapters 1 (frequency-independent common terms), 15 (polarization group alignments—filament synergy), and 24/25 (high-energy coherence and engineered-vacuum chapters); cross-references are required.

VII. Pass/Fail Criteria

1. Support (passes):
   • In two or more channels (for example, dijet and γ/Z+jet) and two or more independent pipelines, coherence indicators show same-direction, monotonic updates with congestion, and environment-forward hit rates exceed chance.
   • Local congestion explains the strength ordering of updates better than global congestion.
   • Results remain robust across suppression/grooming/reconstruction algorithms, trigger variants, and zero-bias / random-cone / axis-rotation controls.
2. Refutation (fails):
   • Coherence is washed out or decorrelated by congestion, or different pipelines/algorithms yield opposite directions.
   • Forward-prediction hit rates are near chance, or significance appears only in a single algorithm or data period.
   • Color-neutral controls (γ/Z+jet) do not replicate or move oppositely, or indicators are insensitive to local vs global congestion.