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Differentiable Multi-scale Effective Field Theory Likelihoods for Beyond the Standard Model Phenomenology

Aleks Smolkovič, Peter Stangl

Abstract

Probing heavy new physics beyond the Standard Model (SM) increasingly relies on global effective field theory (EFT) likelihoods. We introduce differentiable, multi-scale EFT likelihoods that combine renormalization-group evolution, matching, observable predictions, and experimental constraints in a single differentiable framework. This enables modern gradient-based frequentist and Bayesian inference in large parameter spaces. We demonstrate these capabilities in two 374-parameter SMEFT analyses, making basis-independent, fully multi-scale global EFT analyses feasible in practice.

Differentiable Multi-scale Effective Field Theory Likelihoods for Beyond the Standard Model Phenomenology

Abstract

Probing heavy new physics beyond the Standard Model (SM) increasingly relies on global effective field theory (EFT) likelihoods. We introduce differentiable, multi-scale EFT likelihoods that combine renormalization-group evolution, matching, observable predictions, and experimental constraints in a single differentiable framework. This enables modern gradient-based frequentist and Bayesian inference in large parameter spaces. We demonstrate these capabilities in two 374-parameter SMEFT analyses, making basis-independent, fully multi-scale global EFT analyses feasible in practice.
Paper Structure (21 sections, 30 equations, 3 figures, 3 tables)

This paper contains 21 sections, 30 equations, 3 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Differentiable Multi-Scale EFT Likelihoods
  3. Applications of Differentiable EFT Likelihoods
  4. Six-dimensional $b \to s\ell\ell$ likelihood
  5. A 374-parameter SMEFT fit to Drell--Yan data
  6. Multi-scale combination with flavour observables
  7. Outlook and Implications
  8. Accompanying public tools
  9. jelli: JAX-based EFT Likelihoods
  10. Theory predictions and uncertainties.
  11. RG evolution and matching.
  12. Experimental likelihoods.
  13. rgevolve: Renormalization Group Evolution Matrices for the SMEFT and the WET
  14. Detailed results of the fits
  15. Six-dimensional $b\to s \ell \ell$ fit
  16. ...and 6 more sections

Figures (3)

  • Figure 1: One- and two-dimensional constraints on the WET Wilson coefficients of Eq. \ref{['eq:WET6D']}. The diagonal panels display the 1D marginal posteriors (blue), and Hessian-approximated (red) and profiled (orange) likelihoods. The off-diagonal panels show the HMC samples together with the 68% and 95% credible regions (blue), the corresponding Gaussian contours from the Hessian at the mode (red), and the 68% and 95% confidence regions from the profiled likelihoods (orange).
  • Figure 2: Spectrum of sample-covariance eigenvalues for the DY+$bs\bar{\nu}\nu$ setup (gray) and for the fit including the full set of low-energy flavour observables (red), expressed in terms of effective scales $\Lambda_i^{\rm eff}\equiv \lambda_i^{-1/4}$, where $\lambda_i$ denotes the corresponding covariance eigenvalue. The horizontal reference lines indicate the highest effective scales at which individual observables or classes of observables provide the dominant impact.
  • Figure S1: Normalized marginal posterior and profile likelihood for $\mathrm{Re}[C_{lq}^{(3)}]_{1111}$ from the DY + $b\to s\nu\nu$ analysis. The shaded regions show the 68% posterior credible interval and the profile likelihood 68% confidence interval, while the vertical dashed lines indicate the posterior median and the best-fit value, respectively.