[Paper Review] Resurrecting $ b\overline{b}h $ with kinematic shapes

Christophe Grojean, Ayan Paul+1 more|arXiv (Cornell University)|Jan 1, 2020

Particle physics theoretical and experimental studies69 references2 citations

TL;DR

This paper proposes a kinematic shape analysis using interpretable machine learning to isolate the $ b\bar{b}h $ signal from dominant backgrounds at future hadron colliders, enabling constraints on the bottom-quark Yukawa coupling $ y_b $, including its phase. By applying Shapley values to Boosted Decision Trees, the method identifies key kinematic variables that discriminate $ y_b $-driven $ b\bar{b}h $ production from $ y_t $-driven and irreducible $ Zh $ backgrounds, achieving sensitivity to $ \kappa_b $ at 2.2% at HL-LHC and sub-1% at FCC-hh.

ABSTRACT

The associated production of a $b\bar{b}$ pair with a Higgs boson could provide an important probe to both the size and the phase of the bottom-quark Yukawa coupling, $y_b$. However, the signal is shrouded by several background processes including the irreducible $Zh, Z o b\bar{b}$ background. We show that the analysis of kinematic shapes provides us with a concrete prescription for separating the $y_b$-sensitive production modes from both the irreducible and the QCD-QED backgrounds using the $b\bar{b}\gamma\gamma$ final state. We draw a page from game theory and use Shapley values to make Boosted Decisions Trees interpretable in terms of kinematic measurables and provide physics insights into the variances in the kinematic shapes of the different channels that help us complete this feat. Adding interpretability to the machine learning algorithm opens up the black-box and allows us to cherry-pick only those kinematic variables that matter most in the analysis. We resurrect the hope of constraining the size and, possibly, the phase of $y_b$ using kinematic shape studies of $b\bar{b}h$ production with the full HL-LHC data and FCC-hh.

Motivation & Objective

• To overcome the challenge of irreducible $ Zh $ background obscuring the $ b\bar{b}h $ signal at future colliders.
• To develop an interpretable machine learning framework that identifies the most relevant kinematic variables for signal-background separation.
• To assess the feasibility of measuring the size and phase of the bottom-quark Yukawa coupling $ y_b $ using $ b\bar{b}\gamma\gamma $ final states at HL-LHC and FCC-hh.
• To provide a physics-interpretible alternative to black-box ML models in high-energy physics analyses.

Proposed method

• Applies Boosted Decision Trees (BDT) with Shapley values to quantify the contribution of each kinematic variable to signal-background discrimination.
• Uses Shapley values to interpret BDT decisions in terms of physical kinematic observables, enabling identification of the most discriminative variables.
• Simulates $ b\bar{b}h $, $ Zh $, and QCD-QED $ b\bar{b}\gamma\gamma $ processes at HL-LHC (6 ab⁻¹) and FCC-hh (30 ab⁻¹) using Monte Carlo methods.
• Performs multivariate analysis on kinematic shapes in the $ b\bar{b}\gamma\gamma $ final state to separate $ y_b^2 $- and $ y_t^2 $-driven contributions.
• Constructs a confusion matrix using a deep neural network (DNN) with 12 layers and 64 nodes per layer to validate classification performance.
• Relates effective couplings $ \kappa_g $, $ \kappa_\gamma $, and $ \tilde{\kappa}_g $ to $ \kappa_b $ and $ \tilde{\kappa}_b $ via loop-induced Higgs couplings for global EFT consistency checks.

Experimental results

Research questions

• RQ1 Can kinematic shape analysis with interpretable ML overcome the irreducible $ Zh $ background challenge in $ b\bar{b}h $ signal extraction?
• RQ2 Which kinematic variables are most critical for distinguishing $ y_b $-driven $ b\bar{b}h $ from $ y_t $-driven and $ Zh $ contributions?
• RQ3 What are the projected sensitivities on $ \kappa_b $ and its CP-violating phase at HL-LHC and FCC-hh using $ b\bar{b}\gamma\gamma $ final states?
• RQ4 How do theoretical and systematic uncertainties affect the sensitivity to $ \kappa_b $ in the $ b\bar{b}h $ channel?
• RQ5 What constraints on $ \kappa_b $ and $ \tilde{\kappa}_b $ can be derived from $ b\bar{b}h $ production, and how do they compare with EDM bounds?

Key findings

• The Shapley value analysis identifies $ m_{bb} $, $ p_{T}^{\gamma\gamma} $, $ H_T $, and $ m_{b_1h} $ as the most discriminative kinematic variables for separating $ y_b^2 $ and $ y_t^2 $ contributions.
• At HL-LHC with 6 ab⁻¹, the method achieves a sensitivity of 2.2% on $ \kappa_b $, matching the projected limit from the $ Vh \to b\bar{b} $ channel.
• At FCC-hh with 30 ab⁻¹, the sensitivity improves to below 1% on $ \kappa_b $, demonstrating the potential for high-precision $ y_b $ coupling measurements.
• The DNN confusion matrix shows a classification accuracy of ~95% for the five-channel separation (signal, $ y_b^2 $, $ y_by_t $, $ y_t^2 $, $ Zh $) at HL-LHC.
• The analysis shows that $ m_{bb} $ alone is insufficient for discrimination, but its correlation with other variables creates shape features exploitable by BDT.
• Constraints on $ \tilde{\kappa}_b $ from $ b\bar{b}h $ production are found to be competitive with those from EDM measurements, especially in the complex $ \kappa_b $-phase scenario.