Reusable theory representations for colliders: a demonstrator SMEFT foundation model

We develop a demonstrator foundation model for collider-scale explorations of the Standard Model Effective Field Theory (SMEFT), constructed from contrastive representations of theoretically simulated neutral-current Drell-Yan cross sections. Using a controlled sampling of the Warsaw-basis dimension-6 Wilson-coefficient space at $O(\Lambda^{-2})$, we generate a corpus of high-resolution differential distributions in $m_{\ell\ell}$ and $p_{T}$, augmented by physics-motivated Monte Carlo replicas with correlated uncertainties. A minimally parameterized encoder network is trained with a supervised contrastive loss to produce a low-dimensional latent manifold on which SMEFT-induced deformations of the Drell-Yan spectrum acquire a well-defined geometric structure. We analyze the resulting embedding and demonstrate that (i) latent directions correlate with characteristic SMEFT shape distortions, including energy-growing four-fermion contributions and electroweak vertex corrections; (ii) clusters in the embedding correspond to families of Wilson-coefficient configurations with similar phenomenological impact; and (iii) the learned representation supports downstream tasks such as classification with uncertainty quantification, anomaly detection, and nearest-neighbor retrieval. While restricted to leading-order SMEFT and simplified uncertainty modeling, this study provides the first step toward a reusable, physics-aligned foundational representation for the theory of New-Physics searches at high-energy colliders. We outline extensions towards a complete global analyses, including multi-process training corpora, higher-order corrections, and multi-objective pretraining.