W Boson Regression Eval

---
name: w-boson-regression-eval
description: Evaluates a model's ability to reconstruct the 4-momentum and mass of a W-boson from jet constituents, testing regression accuracy and physical consistency under truth-level and detector-simulated (Delphes) conditions. It compares equivariant neural networks against traditional physics-based taggers. Use when the user wants to benchmark on W-boson 4-momentum regression dataset, or asks about evaluating this task. Reports resolution ($\sigma_{p^{T}}$, $\sigma_{m}$, $\sigma_{\Delta R}$).
metadata:
  skill_kind: dataset_eval
  source_arxiv: 2307.16506
  bibtex_key: bogatskiy2023pelican
  confidence: medium
---

# w-boson-regression-eval

> Explainable Equivariant Neural Networks for Particle Physics: PELICAN — Bogatskiy et al. (2023) (arXiv:2307.16506, 2023)

## What this evaluates

Evaluates a model's ability to reconstruct the 4-momentum and mass of a W-boson from jet constituents, testing regression accuracy and physical consistency under truth-level and detector-simulated (Delphes) conditions. It compares equivariant neural networks against traditional physics-based taggers.

## Datasets

- **W-boson 4-momentum regression dataset** — total ?; splits: test (-1)

## Metrics

- `resolution ($\sigma_{p^{T}}$, $\sigma_{m}$, $\sigma_{\Delta R}$)` **(primary)** — range: percent | centirad
  - Standard deviation of the relative error between predicted and true values for transverse momentum ($p^T$), mass ($m$), and angular separation ($\Delta R$). Expressed as percentage for $p^T$ and $m$, and centiradians for $\Delta R$.

## Input / output format

**Input**: Set of jet constituents (4-momenta) representing a hadronic jet containing a W-boson decay.

**Output**: Reconstructed 4-momentum vector of the W-boson ($p^W$) or its mass.

## Scoring recipe

```python
def compute_resolution(pred, true):
    error = np.abs(pred - true)
    resolution = np.std(error) / np.mean(true) * 100
    return resolution
```

## Common pitfalls

- Confusing truth-level inputs with detector-simulated (Delphes) inputs, which yield significantly higher resolutions.
- Mixing up 'contained' mass ($p^W_{cont}$) with true mass ($p^W_{true}$) targets, which require different model training objectives.

## Evidence (verbatim from paper)

> Table 12: PELICAN resolutions for models trained to reconstruct $p^{W}_{\mathrm{true}}$ with variable $W$ mass.

| Method | $\sigma_{p^{T}}$ (%) | $\sigma_{m}$ (%) | $\sigma_{\Delta R}$ (centirad) |

## Citation

```bibtex
@misc{bogatskiy2023pelican,
  title={Explainable Equivariant Neural Networks for Particle Physics: PELICAN},
  author={Bogatskiy et al. (2023)},
  year={2023},
  note={arXiv:2307.16506}
}
```

- arXiv: 2307.16506