[Paper Review] Higgs self coupling measurement

D. Boumediene, Gay, Pascal|ArXiv.org|Jan 6, 2008

Particle physics theoretical and experimental studies1 references3 citations

TL;DR

This paper presents a feasibility study for measuring the Higgs self-coupling ($\lambda_{\rm hhh}$) at the International Linear Collider using $e^+e^-$ collisions at $\sqrt{s} = 500~\text{GeV}$, employing neural network-based event selection and $b$-tagging to isolate the $\rm hhZ$ signal. The study finds that with optimized detector performance, the expected precision on $\lambda_{\rm hhh}$ reaches 19%, a significant improvement over the baseline 28%.

ABSTRACT

A measurement of the Higgs self coupling from e+e- collisions in the International Linear Collider is presented. The impact of the detector performance in terms of $b$-tagging and particle flow is investigated.

Motivation & Objective

• To assess the feasibility of measuring the trilinear Higgs self-coupling ($\lambda_{\rm hhh}$) via the $e^+e^- \to \rm Z\rm h\rm h$ process at the International Linear Collider.
• To evaluate the impact of detector performance—specifically $b$-tagging efficiency and particle flow resolution—on the precision of $\lambda_{\rm hhh}$ measurement.
• To optimize event selection strategies using neural networks and $b$-flavor tagging to maximize signal significance and minimize background contamination.
• To determine the optimal $b$-tagging efficiency that minimizes uncertainty in $\lambda_{\rm hhh}$, balancing signal retention and $c$-jet misidentification.

Proposed method

• Signal and background events for $\rm hhZ$, $\rm hZ$, $\rm hZZ$, $\rm ZZ$, $\rm ZZZ$, $\rm W^+W^-Z$, $\rm e^+e^-ZZ$, and $\rm e^\pm\nu ZW^\mp$ processes were simulated using Whizard and PYTHIA.
• Detector response was modeled via a parametric Monte Carlo simulation with specified energy resolutions: $\Delta E / \sqrt{E} = 10.2\%$ for ECAL and $40.5\%$ for HCAL.
• Neural networks were trained on event shape variables, di-jet mass combinations, and global $b$-flavor content to distinguish $\rm hhZ$ from backgrounds in three final states: $\rm Z \to q\bar{q}$, $\rm Z \to \ell^+\ell^-$, and $\rm Z \to \ \nu\bar{\nu}$.
• Event selection was optimized using a figure of merit $\delta = s / \sqrt{s + b}$, combining neural network output and global $b$-tagging to maximize signal-to-background ratio.
• Cross-section extraction used a two-dimensional likelihood maximization method based on the neural network output and $b$-tag distribution.
• Systematic scans were performed over particle flow resolution ($\Delta E / \sqrt{E}$ from 0% to 130%) and $b$-tagging efficiency ($\epsilon_b$ from 40% to 95%) to assess their impact on $\lambda_{\rm hhh}$ precision.

Experimental results

Research questions

• RQ1 What is the expected precision on the Higgs self-coupling ($\lambda_{\rm hhh}$) measurement using $\rm hhZ$ production at the ILC with standard detector performance?
• RQ2 How does the particle flow resolution affect the uncertainty in $\lambda_{\rm hhh}$, and what is the gain from improved particle flow algorithms?
• RQ3 What $b$-tagging efficiency ($\epsilon_b$) minimizes the uncertainty in $\lambda_{\rm hhh}$, and what is the corresponding $c$-jet misidentification rate?
• RQ4 To what extent can optimizing $b$-tagging and particle flow reduce the required luminosity for a given precision in $\lambda_{\rm hhh}$?
• RQ5 How do event selection strategies based on neural networks and $b$-content enhance signal sensitivity in the $\rm hhZ$ channel?

Key findings

• With a $b$-tagging efficiency of 90% and a particle flow resolution of $30\% / \sqrt{E}$, the expected precision on $\lambda_{\rm hhh}$ is 28%.
• The precision improves to 19% when the $b$-tagging efficiency is optimized to $\epsilon_b \approx 67\%$, corresponding to a $c$-jet misidentification rate of $\epsilon_c \approx 3\%$.
• For $\epsilon_b = 90\%$, the uncertainty on $\lambda_{\rm hhh}$ decreases from 29% (perfect particle flow) to 37% (poor resolution), indicating a 1.3-fold improvement in precision with better particle flow.
• Improving particle flow resolution enhances precision by a factor of 1.3, equivalent to reducing the required luminosity by a factor of 1.7 for the same precision.
• The optimal $b$-tagging efficiency of $67\%$ balances signal retention and $c$-jet contamination, minimizing the overall uncertainty in $\lambda_{\rm hhh}$.
• The combination of optimized neural network selection and $b$-tagging yields a signal significance of $\delta = 5.2$, with 72 signal events and 128 background events expected for $2~\text{ab}^{-1}$ luminosity.