[Paper Review] Simulation-based inference in the search for CP violation in leptonic WH production

R. F. Coelho Barrue, P. Conde-Muíño+2 more|arXiv (Cornell University)|Aug 5, 2023

Particle physics theoretical and experimental studiesPhysics and Astronomy38 references3 citations

TL;DR

This paper evaluates the sensitivity of simulation-based inference using the SALLY method for detecting CP violation in leptonic Higgs-strahlung (WH) production at the LHC. It compares SALLY's performance—trained on detector-level kinematics—to traditional energy- and angular-dependent observables, showing SALLY is optimal for linear Wilson coefficient effects, while 2D combinations of $p_T^W$ and $Q_\ell\cos\delta^+$ outperform SALLY when quadratic effects dominate, improving limits by ~25% at 300 fb$^{-1}$ luminosity.

ABSTRACT

Sources of CP violation beyond the Standard Model (BSM) are required to explain the baryonic asymmetry of the Universe. In this work, we study BSM CP-violating components in the HWW interaction in WH production, parametrized by an effective dimension-6 CP-odd operator. We explore a machine learning simulation-based inference method that estimates a detector-level optimal observable - SALLY - comparing it with energy-dependent and angular observables, exploring different binnings for their distributions. We show that in regions of phase space where the interference between SM and the effective operator dominates, a SALLY observable leads to optimal limits. In regions where effects of the quadratic term of the effective operator start becoming dominant, such an observable still leads to optimal limits. This work aims to test current multivariate techniques and inform analysis strategies for LHC Run 3 and beyond.

Motivation & Objective

• To assess the sensitivity of simulation-based inference via SALLY for detecting CP violation in leptonic WH production at the LHC.
• To compare SALLY's performance against traditional 1D and 2D kinematic observables (energy- and angular-dependent) in the presence of linear and quadratic contributions from a dimension-6 CP-odd operator.
• To determine optimal analysis strategies for LHC Run 3 by disentangling linear and quadratic effects in Wilson coefficients.
• To validate the method using realistic detector effects, parton shower, and background modeling.

Proposed method

• The study uses the Standard Model Effective Field Theory (SMEFT) formalism to parametrize CP-violating contributions via a dimension-6 CP-odd operator $\tilde{O}_{HW}$, with Wilson coefficient $\tilde{c}_{HW}$.
• SALLY is trained using parton-level matrix elements, cross-sections, and their gradients w.r.t. $\tilde{c}_{HW}$, to estimate a detector-level optimal observable (score) without approximating detector or parton-shower effects.
• The method inputs detector-level kinematic variables into a neural network, with a loss function based on the joint score $t(x,z_p) = \nabla_\theta \log p(z_p|\theta)$, converging to the true optimal observable in the infinite-data limit.
• Backgrounds (e.g., $t\bar{t}$, $W$+jets) are simulated with full detector response and parton shower effects via smearing, and selection cuts are applied at generator level.
• Exclusion limits are derived using both linearized and full likelihood ratios to isolate linear and quadratic contributions from $\tilde{c}_{HW}$.
• Statistical analysis compares sensitivity across observables using 95% CL limits at $\mathcal{L} = 300\ \text{fb}^{-1}$, with binned distributions tested for energy and angular variables.

Figure 1 : Feynman diagram for WH associated production in the $\ell\nu b\bar{b}$ final state. The vertex of interest is circled in black.

Experimental results

Research questions

• RQ1 How does the SALLY method compare in sensitivity to traditional 1D and 2D kinematic observables for detecting CP violation in leptonic WH production?
• RQ2 In what phase space regions is SALLY optimal versus when a 2D combination of observables outperforms it?
• RQ3 What is the relative contribution of linear versus quadratic terms in the Wilson coefficient to the sensitivity of different observables?
• RQ4 How do different binning strategies for energy- and angular-dependent observables affect sensitivity to $\tilde{c}_{HW}$?
• RQ5 Can SALLY effectively capture the full event kinematics without approximating detector or parton-shower effects?

Key findings

• SALLY achieves ~25% better sensitivity than 2D limits using $p_T^W$ and $Q_\ell\cos\delta^+$ when linear effects dominate, confirming its optimality in this regime.
• When quadratic effects become significant, the 2D combination of $p_T^W$ and $Q_\ell\cos\delta^+$ yields the tightest limits, outperforming SALLY by approximately 25%.
• Weighting angular observables by lepton charge improves their discrimination power, enhancing sensitivity in the analysis.
• The SALLY method converges to the detector-level optimal observable in the infinite-data limit, demonstrating robustness when trained on full kinematic information.
• The analysis shows that SALLY is suboptimal when quadratic contributions dominate, due to its design being optimal only for linear signal components.
• The study's code, built with MadMiner, is publicly available on GitHub for replication and future extension to other processes or operators.

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