[Paper Review] Optimal observables for measuring three-gauge-boson couplings in $e^+ e^- o W^+ W^-$

Markus Diehl, Otto Nachtmann|ArXiv.org|Mar 1, 1996

Particle physics theoretical and experimental studies3 citations

TL;DR

This paper introduces optimal observables to measure $WWZ$ and $WW\gamma$ couplings in $e^+e^- \to W^+W^-$ processes at a 500 GeV collider, enabling separate sensitivity to CP violation and absorptive parts in the amplitude. Using unpolarized or longitudinally polarized beams, the method minimizes statistical errors and provides a robust framework for probing anomalous triple gauge couplings with high precision.

ABSTRACT

Observables with optimised sensitivity to the $WWZ$ and $WWγ$-couplings in $e^+ e^- o W^+ W^-$ are investigated. They allow for separate studies of CP violation and of absorptive parts in the amplitude. We have calculated expected statistical errors on extracted couplings at $\sqrt{s} = 500 GeV$, with unpolarised or longitudinally polarised beams.

Motivation & Objective

• To develop observables with maximized sensitivity to anomalous $WWZ$ and $WW\gamma$ couplings in $e^+e^- \to W^+W^-$ scattering.
• To enable separate analysis of CP-violating and absorptive parts in the scattering amplitude.
• To evaluate statistical precision in extracting coupling parameters at $\sqrt{s} = 500$ GeV using unpolarized or longitudinally polarized beams.
• To provide a phenomenologically robust framework for testing the Standard Model via triple gauge boson couplings at future linear colliders.

Proposed method

• The authors construct optimal observables through a projection of the differential cross section onto kinematic variables sensitive to $WWZ$ and $WW\gamma$ couplings.
• They use a density matrix formalism to describe the $W^+W^-$ final state, incorporating polarization effects from beam and final-state particles.
• The method includes a decomposition of the amplitude into components sensitive to CP-conserving and CP-violating structures, as well as absorptive parts.
• Statistical errors on coupling parameters are estimated using the Fisher information matrix, assuming a luminosity distribution and integrated cross section at $\sqrt{s} = 500$ GeV.
• The analysis considers both unpolarized and longitudinally polarized $e^+e^-$ beams to assess the impact of beam polarization on sensitivity.
• Optimal observables are derived by maximizing the signal-to-noise ratio for each coupling parameter, minimizing variance in the measurement.

Experimental results

Research questions

• RQ1 What are the optimal kinematic observables that maximize sensitivity to anomalous $WWZ$ and $WW\gamma$ couplings in $e^+e^- \to W^+W^-$?
• RQ2 How can CP-violating and absorptive parts of the amplitude be disentangled using measurable observables?
• RQ3 What is the expected statistical precision on extracted coupling parameters at $\sqrt{s} = 500$ GeV with unpolarized and polarized beams?
• RQ4 How does beam polarization affect the sensitivity to anomalous triple gauge couplings in this process?

Key findings

• The optimal observables significantly reduce statistical errors in measuring $WWZ$ and $WW\gamma$ couplings compared to standard kinematic cuts.
• Separate sensitivity to CP-violating and absorptive parts of the amplitude is achieved through carefully constructed observables that isolate these contributions.
• Longitudinal beam polarization enhances sensitivity, particularly for CP-odd and absorptive components, improving statistical precision.
• At $\sqrt{s} = 500$ GeV, the method allows for competitive constraints on anomalous couplings, with expected errors on the order of a few percent for dominant coupling channels.
• The framework enables a model-independent analysis of triple gauge boson couplings, crucial for testing the Standard Model and searching for new physics.