[Paper Review] Studying the Higgs Potential at the e+e- Linear Collider

M. Battaglia, Eduard Boos+1 more|arXiv (Cornell University)|Nov 22, 2001

Particle physics theoretical and experimental studies4 references17 citations

TL;DR

This paper investigates the feasibility of measuring the Higgs boson triple self-coupling $g_{HHH}$ at future $e^+e^-$ linear colliders using the processes $e^+e^- \to HHZ$ and $HH\nu\bar{\nu}$, employing kinematic and spin-dependent variables to reduce background dilution. At a 3 TeV collider with 5 ab$^{-1}$ luminosity, the method achieves a 7% accuracy on $g_{HHH}$, demonstrating that linear colliders offer a unique and precise probe of the Higgs potential's shape.

ABSTRACT

The determination of the shape of the Higgs potential is needed to complete the investigation of the Higgs profile and to obtain a direct experimental proof of the mechanism of electro-weak symmetry breaking. This can be achieved, at a linear collider, by determining the Higgs triple self-coupling g_HHH in the processes e+e--> HHZ and HHnunu and, possibly, the quartic coupling. This paper summarises the results of a study of the expected accuracies on the determination of g_HHH at a TeV-class LC and at a multi-TeV LC. The statistical dilution arising from contributions not sensitive to the triple Higgs vertex, can be reduced by means of variables sensitive to the kinematics and the spin properties of the reactions.

Motivation & Objective

• To determine the shape of the Higgs potential as a direct test of electroweak symmetry breaking.
• To assess the sensitivity of $e^+e^-$ linear colliders to the Higgs triple self-coupling $g_{HHH}$.
• To reduce statistical dilution from non-triple-vertex diagrams using kinematic and spin variables.
• To compare the performance of a TeV-class LC versus a multi-TeV LC in probing $g_{HHH}$.

Proposed method

• Using CompHEP for parton-level event generation with variable $g_{HHH}$ and $M_H$, and Pythia 6 for parton showering.
• Applying detector simulation via Simdet to reconstruct $HH\nu\bar{\nu}$ final states with $b\bar{b}$ and $W^+W^-$ decays.
• Employing the $HH$ invariant mass $M_{HH}$ and the Higgs decay angle $\theta^*$ in the $HH$ rest frame to distinguish signal from background.
• Performing likelihood fits on event counts and normalized $M_{HH}$ and $|\cos\theta^*|$ distributions to extract $g_{HHH}$.
• Simulating background processes for the $HH\nu\bar{\nu}$ channel and including them in the analysis.
• Evaluating performance at $\sqrt{s}$ = 0.5, 0.8 TeV (TeV-class) and 3 TeV (multi-TeV), with luminosities of 1 ab$^{-1}$ and 5 ab$^{-1}$.

Experimental results

Research questions

• RQ1 Can the Higgs triple self-coupling $g_{HHH}$ be measured with sufficient precision at a $e^+e^-$ linear collider to test the Standard Model prediction?
• RQ2 How effective are kinematic variables like $M_{HH}$ and $|\cos\theta^*|$ in reducing dilution from non-triple-vertex diagrams?
• RQ3 What is the comparative sensitivity of the $HHZ$ and $HH\nu\bar{\nu}$ processes across different center-of-mass energies?
• RQ4 Can beam polarization further improve the accuracy of $g_{HHH}$ determination?
• RQ5 Is the quartic Higgs coupling accessible with current collider configurations?

Key findings

• At a 3 TeV $e^+e^-$ collider with 5 ab$^{-1}$ luminosity, the $HH\nu\bar{\nu}$ channel achieves a relative accuracy of $\pm 0.070$ on $g_{HHH}$ using both cross-section and $|\cos\theta^*|$ shape information.
• For $M_H = 120$ GeV, the $HH\nu\bar{\nu}$ channel at 3 TeV with 5 ab$^{-1}$ yields a $\pm 0.070$ (stat) accuracy on $g_{HHH}$, improving over the $\sigma$-only result of $\pm 0.094$.
• The $HHZ$ channel at $\sqrt{s}$ = 0.8 TeV with 1 ab$^{-1}$ achieves a $\pm 0.29$ (stat) accuracy on $g_{HHH}$, with $M_{HH}$ fitting reducing uncertainty from $\pm 0.35$.
• The $HH\nu\bar{\nu}$ process has a cross section about seven times larger than $HHZ$, making it more favorable at high energies.
• The $HH\nu\bar{\nu}$ cross section is suppressed at 10 TeV, with only about five events per year for $M_H = 120$ GeV at $\sqrt{s}$ = 10 TeV.
• The quartic Higgs coupling remains inaccessible due to extremely small cross sections and large dilution from non-signal diagrams.