Reusable theory representations for colliders: a demonstrator SMEFT foundation model

TL;DR

This work addresses the challenge of exploring the high-dimensional SMEFT parameter space at collider scales by constructing a physics-aligned latent embedding learned from simulated neutral-current Drell–Yan spectra at linear order in $1/\Lambda^2$. A minimalist encoder trained with supervised contrastive loss derives a two-dimensional latent space in which SMEFT-induced deformations map to interpretable directions and clusters corresponding to Wilson-coefficient configurations. The embedding enables downstream tasks such as classification with uncertainty quantification, anomaly detection, and nearest-neighbor retrieval, offering a scalable, transferable representation to complement traditional global fits. While demonstrated at leading order and with simplified uncertainties for a single process, the approach provides a foundation for multi-process, higher-order analyses, and integration with global SMEFT analyses and potential agentic systems in collider phenomenology.

Abstract

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 $O(Λ^{-2})$, 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.

Figures (12)

• Figure 1: Example foundational embeddings of the differential distributions of the invariant mass and the transverse momenta in two dimensions with each SMEFT scenario labeled.
• Figure 2: An illustration of the neutral-current Drell--Yan process, $p\,p \rightarrow \mu^{+}\,\mu^{-} + X$, indicating the PDF contributions quantified by $f_{a,b}$, corresponding to the partons $\{q_a,q_b\} \in [q, \bar{q}, g]$, and the hard-scattering kernel, $\hat{\sigma}$. The orange line demonstrates a factorization of the hard scatter from the nonperturbative matrix elements containing the PDFs.
• Figure 3: Two examples of typical SMEFT contributions to the neutral-current Drell--Yan process where ( top) is an insertion of the four-fermion SMEFT operator $\mathcal{O}_{\ell q}^{(3)}$ with Wilson coefficient equal to one and the corresponding ratio with the SM, notice that the deviation from this insertion grows as a function of energy coinciding with Table \ref{['tab:processWCs']}. ( bottom) is an insertion of the bosonic operator $\mathcal{O}_{\varphi WB}$ with Wilson coefficient equal to one and its ratio with the SM, notice that the ratio peaks around the $Z$-pole and remains constant at high masses.
• Figure 4: Illustration of a fundamental physics foundation model which ingests large amounts of multi-modal inputs from experiment, theory, lattice, and BSM theories and performs a wide variety of downstream tasks such as classification, uncertainty quantification, global fits, anomaly detection, etc. The foundation model constructs a depiction of the underlying theory through neural connections.
• Figure 5: Examples of the input differential distributions for the neutral-current Drell--Yan process with $100$ "SMEFT" universes resulting in deviations from the SM predictions in ( left) the invariant mass distribution $m_{\ell \ell}$, and ( right) the transverse momentum distribution of the muon $p_{T}$.